List of publications
Institute for Analysis and Numerics
Publications
published
- . . ‘On a Class of Nonlocal Continuity Equations on Graphs.’ European Journal of Applied Mathematics 35, № 1: 109–126. doi: 10.1017/S0956792523000128.
- . ‘Feature Engineering with Regularity Structures.’ Journal of Scientific Computing 98, № 13. doi: 10.1007/s10915-023-02401-4.
- . A priori bounds for 2-d generalised Parabolic Anderson Model arXiv. doi: 10.48550/arXiv.2402.05544.
- . . ‘The dynamical Ising-Kac model in 3D converges to Φ4/3.’ Probability Theory and Related Fields 190, № 1-2. doi: 10.1007/s00440-024-01316-x.
- . . ‘A consistent kinetic Fokker-Planck model for gas mixtures.’ Journal of Statistical Physics 191.
- . . ‘Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.’ In Large-Scale Scientific Computations, edited by , 117–125. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- . . ‘Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines.’ In Metadata and Semantic Research - 17th Research Conference, MTSR 2023, Milan, Italy, October 25–27, 2023, Revised Selected Papers, edited by , 161–168. Heidelberg: Springer. doi: 10.1007/978-3-031-65990-4_14.
- . . ‘Dynamic interplay of microtubule and actomyosin forces drive tissue extension.’ Nature Communications 15, № 1: 3198. doi: 10.1038/s41467-024-47596-8.
- . . ‘Local training and enrichment based on a residual localization strategy.’ In Proceedings of the Conference Algoritmy 2024, edited by , 76–84. Bratislava: Jednota slovenských matematikov a fyzikov.
- . . ‘Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels.’ BioRxiv 2024. doi: 10.1101/2023.12.22.572956.
- . . ‘Exact reconstruction and reconstruction from noisy data with anisotropic total variation.’ SIAM Journal on Mathematical Analysis 56, № 3: 2938–2967. doi: 10.1137/22M1508571.
- . . ‘Convergent Autoencoder Approximation of Low Bending and Low Distortion Manifold Embeddings.’ ESAIM: Mathematical Modelling and Numerical Analysis 58, № 1: 335–361. doi: 10.1051/m2an/2023088.
- . . ‘Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space.’ Applied and Computational Harmonic Analysis 70: 101631. doi: 10.1016/j.acha.2024.101631.
- . . ‘A Bayesian model for dynamic mass reconstruction from PET listmode data.’ Siam Journal on Mathematical Analysis 56, № 5: 5840–5880. doi: 10.1137/23M161923X.
- . . ‘Invariant Manifolds for the Thin Film Equation.’ Archive for Rational Mechanics and Analysis 248, № 2. doi: 10.1007/s00205-024-01968-y.
- . . ‘Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.’ In Large-Scale Scientific Computations, edited by , 108–116. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
- . . ‘Fine large-time asymptotics for the axisymmetric Navier-Stokes equations.’ Journal of Evolution Equations 24: 72. doi: 10.1007/s00028-024-01001-5.
- . . ‘Propagation of regularity for transport equations. A Littlewood-Paley approach.’ Indiana University Mathematics Journal 73, № 2: 445–473.
- . . ‘Finite-dimensional leading order dynamics for the fast diffusion equation near extinction.’ Discrete and Continuous Dynamical Systems - Series A 44, № 9: 2697–2712. doi: 10.3934/dcds.2024043.
- . . ‘On the dynamics of vortices in viscous 2D flows.’ Mathematische Annalen 388: 1937–1967. doi: 10.1007/s00208-023-02568-z.
- . . ‘Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems.’ SIAM Journal on Scientific Computing 46, № 5: A3205–A3229. doi: 10.1137/23M1613402.
- . . ‘Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems.’ Computational Science and Engineering 1, № 3: 1–30. doi: 10.1007/s44207-024-00002-z.
- . . ‘Construction of local reduced spaces for Friedrichs' systems via randomized training.’ Contributed to the Central-European Conference on Scientific Computing, ALGORITMY, Podbanské.
- . . ‘Application of an adaptive model hierarchy to parametrized optimal control problems.’ Contributed to the Algoritmy, Podbanske.
- . . ‘Brownian particle in the curl of 2-d stochastic heat equations.’ Journal of Statistical Physics 191: 16. doi: 10.1007/s10955-023-03224-1.
- . . ‘A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems.’ ESAIM: Mathematical Modelling and Numerical Analysis 58: 79–105. doi: 10.1051/m2an/2023089.
accepted / in Press (not yet published)
- . . ‘Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics.’ In Proceedings of the 18th International Conference on Metadata and Semantics Research 2024. Heidelberg: Springer.
submitted / under review
- . Stability of traveling waves for doubly nonlinear equations arXiv.org.
- . Steady ring-shaped vortex sheets arXiv.org.
- . Kernel Methods in the Deep Ritz framework: Theory and practice arXiv. doi: 10.48550/arXiv.2410.03503.
- . A Parareal algorithm without Coarse Propagator? arXiv. doi: 10.48550/arXiv.2409.02673.
- . Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems arXiv. doi: 10.48550/arXiv.2408.15900.
published
- . . ‘Magnetic skyrmions under confinement.’ Communications in Mathematical Physics 404: 1571–2023. doi: 10.1007/s00220-023-04864-w.
- . . ‘On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation.’ Journal of Elasticity 153: 455–475. doi: 10.1007/s10659-023-10011-2.
- . ‘Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets.’ Physical Review B 2023: L161405. doi: 10.1103/PhysRevB.108.L161405.
- . Phase transition for invariant measures of the focusing Schrödinger equation arXiv. doi: 10.48550/arXiv.2306.07697.
- . Martingale-driven integrals and singular SPDEs arXiv. doi: 10.48550/arXiv.2303.10245.
- . The dynamical Ising-Kac model in 3D converges to Φ43 arXiv. doi: 10.48550/arXiv.2303.10242.
- . . ‘BGK model for two-component gases near a global Maxwellian.’ SIAM Journal on Mathematical Analysis 55.
- . . ‘Hypocoercivity and reaction-diffusion limit for a non-linear generation-recombination model.’ Archive for Rational Mechanics and Analysis 247.
- . . ‘A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells.’ European Journal of Applied Mathematics 34, № 3: 554–591. doi: 10.1017/S0956792522000353.
- . ‘Model Reduction and Learning for PDE Constrained Optimization.’ Contributed to the Oberwolfach Workshop on Optimization Problems for PDEs in Weak Space-Time Form, Oberwolfach. doi: 10.4171/OWR/2023/13.
- . . ‘Randomized quasi-optimal local approximation spaces in time.’ SIAM Journal on Scientific Computing 45, № 3. doi: 10.1137/22M1481002.
- . . ‘System Order Reduction for Gas and Energy Networks.’ Contributed to the 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Aachen. doi: 10.1002/pamm.202200201.
- . . ‘A free boundary problem-in time-for the spread of Covid-19.’ Journal of Mathematical Biology 86, № 45. doi: 10.1007/s00285-023-01881-0.
- . . ‘A two level contagion process and its deterministic McKendrick limit with relevance for the Covid epidemic.’ Ensaios Matemáticos 38: 343–358. doi: 10.21711/217504322023/em3813.
- . ‘Brainstorm-DUNEuro: An integrated and user-friendly Finite Element Method for modeling electromagnetic brain activity.’ NeuroImage 267: 119851. doi: 10.1016/j.neuroimage.2022.119851.
- . ‘CutFEM forward modeling for EEG source analysis.’ Frontiers in Human Neuroscience 17: 1216758. doi: 10.3389/fnhum.2023.1216758.
- . . ‘The variational approach to the flow of Sobolev-diffeomorphisms model.’ In Scale Space and Variational Methods in Computer Vision, edited by , 551–564. Heidelberg: Springer. doi: 10.1007/978-3-031-31975-4_42.
- . . ‘Parametrizing product shape manifolds by composite networks.’ Contributed to the International Conference on Learning Representations (ICLR 2023), Kigali.
- . . ‘Convex reconstruction of moving particles with inexact motion model.’ Proceedings in Applied Mathematics and Mechanics n/a: e202300054. doi: 10.1002/pamm.202300054.
- . . ‘Asymptotics near extinction for nonlinear fast diffusion on a bounded domain.’ Archive for Rational Mechanics and Analysis 247: 16. doi: 10.1007/s00205-023-01850-3.
- . . ‘Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients.’ ESAIM: Mathematical Modelling and Numerical Analysis 57, № 4: 2131–2158. doi: 10.1051/m2an/2023035.
- . . ‘Optimal regularity of isoperimetric sets with Hölder densities.’ Calculus of Variations and Partial Differential Equations 62, № 214. doi: 10.1007/s00526-023-02542-2.
- . . ‘An overview on deep learning-based approximation methods for partial differential equations.’ Discrete and Continuous Dynamical Systems - Series B 28, № 6: 3697–3746. doi: 10.3934/dcdsb.2022238.
- . . ‘Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation.’ Journal of Mathematical Analysis and Applications 517, № 2: 126601. doi: 10.1016/j.jmaa.2022.126601.
- . . ‘Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations.’ Journal of Numerical Mathematics 31, № 2: 1–28. doi: 10.1515/jnma-2021-0111.
- . . ‘Space-time error estimates for deep neural network approximations for differential equations.’ Advances in Computational Mathematics 49, № 1: 4. doi: 10.1007/s10444-022-09970-2.
- . . ‘Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen--Cahn equations.’ Stochastics and Partial Differential Equations: Analysis and Computations 11, № 1: 211–268. doi: 10.1007/s40072-021-00226-6.
- . . ‘An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition.’ SIAM Journal on Scientific Computing 45, № 4. doi: 10.1137/21M1460016.
- . . ‘An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.’ In Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, edited by , 289–298. Heidelberg: Springer. doi: 10.1007/978-3-031-40860-1_30.
- . . ‘One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.’ Calculus of Variations and Partial Differential Equations 62, № 7: 190. doi: 10.1007/s00526-023-02525-3.
- . . ‘A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.’ SIAM Journal on Scientific Computing 45, № 3: A1039. doi: 10.1137/22M1493318.
- . . ‘A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime.’ Archive for Rational Mechanics and Analysis 247, № 3: 48. doi: 10.1007/s00205-023-01876-7.
- . ‘Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation.’ Electronic Research Archive 31, № 5: 2519–2554. doi: 10.3934/era.2023128.
- . . ‘Towards a network control theory of electroconvulsive therapy response.’ PNAS Nexus 2, № 2. doi: 10.1093/pnasnexus/pgad032.
accepted / in Press (not yet published)
- . . ‘Strong overall error analysis for the training of artificial neural networks via random initializations.’ Communications in Mathematics and Statistics 0. doi: 10.1007/s40304-022-00292-9.
- . . ‘Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality.’ Journal of Complexity 0: 101746. doi: 10.1016/j.jco.2023.101746.
- . Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems arXiv. doi: 10.48550/arXiv.2307.15590.
submitted / under review
- . DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions arXiv. doi: 10.48550/arXiv.2302.00348.
- The necessity of depth for artificial neural networks to approximate certain classes of smooth bounded functions without the curse of dimensionality arXiv.org.
- Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations arXiv.org.
- On the existence of minimizers in shallow residual ReLU neural network optimization landscapes arXiv.org.
- Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems arXiv.org.
published
- . . ‘Ergodicity of the infinite swapping algorithm at low temperature.’ Stochastic Processes and their Applications 151: 519–552. doi: 10.1016/j.spa.2022.06.015.
- . . ‘Oscillations in a Becker-Döring model with injection and depletion.’ SIAM Journal on Applied Mathematics 82, № 4: 1194–1219. doi: 10.1137/20M1398664.
- . Correction to: A Nonlocal Isoperimetric Problem with Dipolar Repulsion. doi: 10.1007/s00220-022-04426-6.
- . . ‘Optimal regularity in time and space for stochastic porous medium equations.’ Annals of Probability 50, № 6: 2288–2343. doi: 10.1214/22-AOP1583.
- . . ‘Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions.’ Probability and Mathematical Physics 3, № 2: 343–379. doi: 10.2140/pmp.2022.3.343.
- . . ‘Phase Transitions for ϕ^4_3.’ Communications in Mathematical Physics 392: 691–782. doi: 10.1007/s00220-022-04353-6.
- . . ‘A priori bounds for rough differential equations with a non-linear damping term.’ Journal of Differential Equations 318: 58–93. doi: 10.1016/j.jde.2022.02.006.
- . . ‘A review on a general multi-species BGK model: modelling, theory and numerics.’ In From Kinetik Theory to Turbulence Modeling, edited by , 217–231. Heidelberg: Springer.
- . . ‘Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit.’ Kinetic and Related Models 15.
- . . ‘Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency.’ Journal of Computational Physics 473.
- . . ‘An adaptive model hierarchy for data-augmented training of kernel models for reactive flow.’ In MATHMOD 2022 Discussion Contribution Volume, edited by , 67–68. 17th Ed. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17155.
- . „Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative).“ GAMM Rundbrief 1/2022: 40–43.
- . . ‘Optimal local approximation spaces for parabolic problems.’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 20, № 1. doi: 10.1137/20M1384294.
- . . ‘Specification and Validation of Numerical Algorithms with the Gradual Contracts Pattern.’ In Testing Software and Systems, edited by , 181–188. Basel : Springer International Publishing.
- . . ‘Next-Gen Gas Network Simulation.’ In Progress in Industrial Mathematics at ECMI 2021, edited by , 107–113. Heidelberg: Springer. doi: 10.1007/978-3-031-11818-0_15.
- . . ‘Taxis-driven persistent localization in a degenerate Keller-Segel system.’ Communications in Partial Differential Equations 47, № 12: 2341–2362. doi: 10.1080/03605302.2022.2122836.
- . . ‘Kermack and McKendrick Models on a Two-Scale Network and Connections to the Boltzmann Equations.’ In Mathematics Going Forward. Lecture Notes in Mathematics, vol 2313, edited by , 417–427. Heidelberg: Springer. doi: 10.1007/978-3-031-12244-6_29.
- . . ‘Localized Reduced Basis Additive Schwarz Methods.’ In Domain Decomposition Methods in Science and Engineering XXVI, edited by , 487–494. Basel : Springer International Publishing. doi: 10.1007/978-3-030-95025-5_52.
- . . ‘Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain.’ In MATHMOD 2022 - Discussion Contribution Volume, edited by , 57–58. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17129.
- . . „Commitment zu aktivem Daten- und -softwaremanagement in großen Forschungsverbünden: Commitment to active data and software management in large research alliances.“ Bausteine Forschungsdatenmanagement 1: 121–123. doi: 10.17192/bfdm.2022.1.8412.
- . . ‘Efficient Gas Network Simulations.’ In German Success Stories in Industrial Mathematics, edited by , 17–22. doi: 10.1007/978-3-030-81455-7_4.
- . . ‘An adaptive finite element approach for lifted branched transport problems.’ In Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization, edited by , 189–236. Berlin: De Gruyter.
- . . ‘Consistent Curvature Approximation on Riemannian Shape Spaces.’ IMA Journal of Numerical Analysis 42, № 1: 78–106.
- . . ‘Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions.’ ESAIM: Control, Optimisation and Calculus of Variations 28: 27.
- . . ‘Elastic 3D-2D Image Registration.’ Journal of Mathematical Imaging and Vision 64: 443–462.
- . . ‘Formulation of branched transport as geometry optimization.’ Journal de Mathématiques Pures et Appliquées 163: 739–779. doi: 10.1016/j.matpur.2022.05.021.
- . . ‘Duality in branched transport and urban planning.’ Applied Mathematics and Optimization 86: 45. doi: 10.1007/s00245-022-09927-3.
- . . Adaptive Reduced Basis Methods for Multiscale Problems and Large-scale PDE-constrained Optimization Dissertation thesis, WWU Münster. Münster. doi: 10.48550/arXiv.2211.09607.
- . . ‘The Scharfetter-Gummel scheme for aggregation-diffusion equations.’ IMA Journal of Numerical Analysis 42, № 3. doi: 10.1093/imanum/drab039.
- . . ‘Bounds on the rate of enhanced dissipation.’ Communications in Mathematical Physics Online first. doi: 10.1007/s00220-022-04588-3.
- . . ‘Renormalization and energy conservation for axisymmetry fluid flows.’ Mathematische Annalen 382: 1–36. doi: 10.1007/s00208-020-02050-0.
- . . ‘Optimal stability estimates and a new uniqueness result for advection-diffusion equations.’ Pure and Applied Analysis 4, № 3: 571–596. doi: 10.2140/paa.2022.4.571.
- . . ‘A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows.’ In Large-Scale Scientific Computing, edited by , 378–386. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-030-97549-4_43.
- . . ‘Model Reduction for Large Scale Systems.’ In Large-Scale Scientific Computing, edited by , 16–28. Basel : Springer International Publishing. doi: 10.1007/978-3-030-97549-4_2.
- . . ‘Uniform error estimates for artificial neural network approximations for heat equations.’ IMA Journal of Numerical Analysis 42, № 3: 1991–2054. doi: 10.1093/imanum/drab027.
- . . ‘Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities.’ Foundations of Computational Mathematics 22, № 4: 905–966. doi: 10.1007/s10208-021-09514-y.
- . . ‘Efficient approximation of high-dimensional functions with neural networks.’ IEEE Transactions on Neural Networks and Learning Systems 33, № 7: 3079–3093. doi: 10.1109/TNNLS.2021.3049719.
- . . ‘Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives.’ Discrete and Continuous Dynamical Systems - Series B 27, № 7: 3707–3724. doi: 10.3934/dcdsb.2021203.
- . ‘Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning.’ Nonlinearity 35, № 1: 278–310. doi: 10.1088/1361-6544/ac337f.
- . . ‘An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization.’ Pure and Applied Functional Analysis 7, № 5: 1561–1596.
- . . ‘On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks.’ Journal of Machine Learning 1, № 2: 141–246. doi: 10.4208/jml.220114a.
- . . ‘A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions.’ Journal of Machine Learning Research 23, № 260: 1–50.
- . . ‘A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions.’ Zeitschrift für Angewandte Mathematik und Physik 73, № 5: 188. doi: 10.1007/s00033-022-01716-w.
- . . ‘Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions.’ Journal of Nonlinear Science 32, № 5: 64. doi: 10.1007/s00332-022-09823-8.
- . . ‘A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions.’ Journal of Complexity 72: 101646. doi: 10.1016/j.jco.2022.101646.
- . . ‘Full error analysis for the training of deep neural networks.’ Infinite Dimensional Analysis, Quantum Probability and Related Topics 25, № 2: 2150020. doi: 10.1142/S021902572150020X.
- . . ‘Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms.’ SN Partial Differential Equations and Applications 3, № 4: 45. doi: 10.1007/s42985-021-00100-z.
- . ‘DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing.’ Constructive Approximation 55, № 1: 3–71. doi: 10.1007/s00365-021-09541-6.
- . . ‘Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization.’ Journal of Computational Physics 2022: 110955. doi: 10.1016/j.jcp.2022.110955.
- . . ‘Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing.’ Proceedings of the JuliaCon Conferences 1, № 1: 77. doi: 10.21105/jcon.00077.
- . . ‘On the dynamics of point vortices for the 2D Euler equation with Lp vorticity.’ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, № 2226. doi: 10.1098/rsta.2021.0046.
- . . ‘Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery.’ Advances in Computational Mathematics 2022, № 48: 73. doi: 10.1007/s10444-022-09981-z.
- . . ‘Cosh gradient systems and tilting.’ Nonlinear Analysis: Theory, Methods and Applications 2203: 113094. doi: 10.1016/j.na.2022.113094.
- . . Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition Dissertation thesis, Universität Münster. N/A: Selbstverlag / Eigenverlag.
- . . ‘Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons.’ Nonlinear Differential Equations and Applications 29, № 2: 1–42. doi: 10.1007/s00030-021-00745-0.
submitted / under review
- . Local minimizers of the interface length functional based on a concept of local paired calibrations arXiv. doi: 10.48550/arXiv.2212.11840.
- . . ‘Dynamic interplay of protrusive microtubule and contractile actomyosin forces drives tissue extension.’ eLife 2022. doi: 10.1101/2022.06.21.496930.
- . . ‘On the Performance of Machine Learning Methods for Breakthrough Curve Prediction.’ arXiv [physics.flu-dyn] 2204.11719. doi: 10.48550/arXiv.2204.11719.
- . A Super-Localized Generalized Finite Element Method arXiv 2022. doi: 10.48550/arXiv.2211.09461.
- Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing arXiv.org.
- Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions arXiv.org.
- On bounds for norms of reparameterized ReLU artificial neural network parameters: sums of fractional powers of the Lipschitz norm control the network parameter vector arXiv.org.
- Gradient descent provably escapes saddle points in the training of shallow ReLU networks arXiv.org.
- An efficient Monte Carlo scheme for Zakai equations arXiv.org.
- Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks arXiv.org.
- Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability arXiv.org.
- . . A Note on Numerical Fluxes Conserving Harten's Entropies for the Compressible Euler Equations.
- . On the existence of infinitely many realization functions of non-global local minima in the training of artificial neural networks with ReLU activation ArXiv. doi: 10.48550/arXiv.2202.11481.
- . Normalized gradient flow optimization in the training of ReLU artificial neural networks ArXiv. doi: 10.48550/arXiv.2207.06246.
published
- . . ‘Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures.’ SIAM Journal on Mathematical Analysis 53, № 4. doi: 10.1137/18M1220017.
- . . ‘Rigidity of branching microstructures in shape memory alloys.’ Archive for Rational Mechanics and Analysis 241: 1707–1783. doi: 10.1007/s00205-021-01679-8.
- . . ‘A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree ±1 harmonic maps from from R² to S².’ Archive for Rational Mechanics and Analysis 239: 219–299. doi: 10.1007/s00205-020-01575-7.
- . A priori bounds for quasi-linear SPDEs in the full sub-critical regime arXiv. doi: 10.48550/arXiv.2103.11039.
- . . ‘On multi-species BGK models with velocity dependent collision frequencies.’ In Small Collaboration: Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations (hybridmeeting), edited by , 8–10. Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. doi: 10.4171/OWR/2021/19.
- . . ‘BGK model of the multi-species Uehling Uhlenbeck equation.’ Kinetic and Related Models 14.
- . . ‘A consistent BGK model with velocity-dependent collision frequency for gas mixtures.’ Journal of Statistical Physics 184.
- . . ‘A review on BGK models for gas mixtures of mono and polyatomic molecules.’ Fluids 6.
- . . Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations Dissertation thesis, Universität Münster. N/A: Selbstverlag / Eigenverlag.
- . . ‘Signaling gradients in surface dynamics as basis for planarian regeneration.’ Journal of Mathematical Biology 83, № 6. doi: 10.1007/s00285-021-01627-w.
- . Regeneration of Tissue: Lessons Learned from Flatworms. SIAM News Blog.
- . . ‘Localized model reduction for parameterized problems.’ In Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by , 245–306. doi: 10.1515/9783110671490-006.
- . . ‘Sustainable Research Software Hand-Over.’ Journal of Open Research Software 9, № 1. doi: 10.5334/jors.307/.
- . . ‘A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations.’ ESAIM: Mathematical Modelling and Numerical Analysis 55: 2567–2608. doi: 10.1051/m2an/2021065.
- . . ‘Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms.’ In Model Reduction of Complex Dynamical Systems, edited by , 141–164. doi: 10.1007/978-3-030-72983-7_7.
- . . ‘Model Order Reduction for Gas and Energy Networks.’ Journal of Mathematics in Industry 11: 13. doi: 10.1186/s13362-021-00109-4.
- . . ‘MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.’ In Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, edited by , 233–262. doi: 10.1007/978-3-030-62732-4_11.
- . . ‘The DUNE Framework: Basic Concepts and Recent Developments.’ Computers & Mathematics with Applications 81: 75–112. doi: 10.1016/j.camwa.2020.06.007.
- . . ‘Monotonicity considerations for stabilized DG cut cell schemes for the unsteady advection equation.’ Contributed to the ENUMATH2019, Egmond aan Zee, The Netherlands.
- . . ‘Strategies for the vectorized Block Conjugate Gradients method.’ Contributed to the ENUMATH2019, Egmond aan Zee, The Netherlands.
- . . ‘DUNEuro- A software toolbox for forward modeling in bioelectromagnetism.’ PloS one 2021. doi: 10.1371/journal.pone.0252431.
- . . Hardware-Oriented Krylov Methods for High-Performance Computing Dissertation thesis, WWU Münster. N/A: Selbstverlag / Eigenverlag. doi: 10.48550/arXiv.2104.02494.
- . . ‘Learning low bending and low distortion manifold embeddings.’ In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), edited by , 4411–4419. New York City: Wiley-IEEE Press.
- . . ‘A mathematical model for cell polarization in zebrafish primordial germ cells.’ IMA Mathematical Medicine and Biology 38, № 2: 218–254.
- . . ‘Entropic regularization of continuous optimal transport problems.’ Journal of Mathematical Analysis and Applications 494, № 1: 124432.
- . . ‘Convex relaxation of discrete vector-valued optimization problems.’ SIAM Review 63, № 4: 783–821.
- . . ‘Quartic Lp-convergence of cubic Riemannian splines.’ IMA Journal of Numerical Analysis 42, № 4: 3360–3385. doi: 10.1093/imanum/drab077.
- . . ‘A note on the vanishing viscosity limit in the Yudovich class.’ Canadian Mathematical Bulletin 64, № 1: 112–122. doi: 10.4153/S0008439520000296.
- . . ‘Vortex dynamics for 2D Euler flows with unbounded vorticity.’ Revista Matematica Iberoamericana 37, № 5: 1969–1990. doi: 10.4171/rmi/1255.
- . . ‘On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity.’ Nonlinearity 34, № 5: 3112–3121. doi: 10.1088/1361-6544/abe51f.
- . . ‘A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization.’ ESAIM: Mathematical Modelling and Numerical Analysis 55: 1239–1269. doi: 10.1051/m2an/2021019.
- . . ‘A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.’ Journal of Computational Physics 2021: 110467. doi: 10.1016/j.jcp.2021.110467.
- . . ‘A conservative fully-discrete numerical method for the regularized shallow water wave equations.’ SIAM Journal on Scientific Computing 42. doi: 10.1137/20M1364606.
- . . ‘Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts.’ Journal of Scientific Computing 87. doi: 10.1007/s10915-021-01463-6.
- . . ‘A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions.’ Journal of Scientific Computing 87. doi: 10.1007/s10915-021-01454-7.
- . . ‘A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations.’ Communications in Computational Physics 29, № 4: 979–1029. doi: 10.4208/cicp.OA-2020-0119.
- . . ‘On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators.’ IMA Journal of Numerical Analysis 41, № 1: 654–682. doi: 10.1093/imanum/drz070.
- . . ‘On the robustness and performance of entropy stable discontinuous collocation methods.’ Journal of Computational Physics 426: 109891. doi: 10.1016/j.jcp.2020.109891.
- . . ‘On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations.’ Stochastics and Dynamics 21, № 8: Paper No. 2150048, 68 pp. doi: 10.1142/S0219493721500489.
- . . ‘Non-convergence of stochastic gradient descent in the training of deep neural networks.’ Journal of Complexity 64: Paper No. 101540, 10 pp.
- . . ‘Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values.’ Journal of Mathematical Analysis and Applications 495, № 1: 124558, 33. doi: 10.1016/j.jmaa.2020.124558.
- . . ‘Strong error analysis for stochastic gradient descent optimization algorithms.’ IMA Journal of Numerical Analysis 41, № 1: 455–492. doi: 10.1093/imanum/drz055.
- . . ‘Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions.’ IMA Journal of Numerical Analysis 41, № 1: 493–548. doi: 10.1093/imanum/drz063.
- . . ‘A well-posedness result for a system of cross-diffusion equations.’ Journal of Evolution Equations 21, № 2: 2471–2489. doi: 10.1007/s00028-021-00690-6.
- . . ‘A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients.’ Communications in Mathematical Sciences 19, № 5: 1167–1205. doi: 10.4310/CMS.2021.v19.n5.a1.
- . . ‘Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise.’ Nonlinear Analysis: Theory, Methods and Applications 210: Paper No. 112310. doi: 10.1016/j.na.2021.112310.
- . . ‘Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients.’ Foundations of Computational Mathematics 21, № 2: 445–536. doi: 10.1007/s10208-020-09448-x.
- . . ‘On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values.’ Journal of Mathematical Analysis and Applications 502, № 2: Paper No. 125240. doi: 10.1016/j.jmaa.2021.125240.
- . . ‘Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise.’ Applied Mathematics and Optimization 84, № suppl. 2: 1187–1217. doi: 10.1007/s00245-020-09744-6.
- . . ‘Multilevel Picard iterations for solving smooth semilinear parabolic heat equations.’ SN Partial Differential Equations and Applications 2, № 6: Paper No. 80. doi: 10.1007/s42985-021-00089-5.
- . . ‘Solving high-dimensional optimal stopping problems using deep learning.’ European Journal of Applied Mathematics 32, № 3: 470–514. doi: 10.1017/S0956792521000073.
- . . ‘On existence and uniqueness properties for solutions of stochastic fixed point equations.’ Discrete and Continuous Dynamical Systems - Series B 26, № 9: 4927–4962. doi: 10.3934/dcdsb.2020320.
- . . ‘Solving the Kolmogorov PDE by means of deep learning.’ Journal of Scientific Computing 88, № 3: Paper No. 73. doi: 10.1007/s10915-021-01590-0.
- . . ‘Deep splitting method for parabolic PDEs.’ SIAM Journal on Scientific Computing 43, № 5: A3135–A3154. doi: 10.1137/19M1297919.
- . . ‘Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.’ Communications on Applied Mathematics and Computation 2021. doi: 10.1007/s42967-021-00159-w.
- . . ‘Positivity-Preserving Adaptive Runge-Kutta Methods.’ Communications in Applied Mathematics and Computational Science 16, № 2: 155–179. doi: 10.2140/camcos.2021.16.155.
- . . ‘On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations.’ Partial Differential Equations and Applications 2, № 6: 76. doi: 10.1007/s42985-021-00126-3.
- . . ‘SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties.’ Journal of Open Source Software 6, № 64: 3454. doi: 10.21105/joss.03454.
- . . ‘Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes.’ Communications on Applied Mathematics and Computation 2021. doi: 10.1007/s42967-021-00148-z.
- . . ‘Steepening of magnetosonic waves in the inner coma of comet 67P/Churyumov-Gerasimenko.’ Annales Geophysicae 39, № 4: 721–742. doi: 10.5194/angeo-39-721-2021.
- . . ‘The Scharfetter–Gummel scheme for aggregation–diffusion equations.’ IMA Journal of Numerical Analysis 42, № 3: 2361–2402. doi: 10.1093/imanum/drab039.
- . . ‘Self-similar behavior of the exchange-driven growth model with product kernel.’ Commun. Partial. Differ. Equ. 46, № 3: 498–546. doi: 10.1080/03605302.2020.1845205.
- . . ‘Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit.’ Arch. Ration. Mech. Anal. 2021. doi: 10.1007/s00205-021-01631-w.
accepted / in Press (not yet published)
- . . ‘Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations.’ Memoirs of the American Mathematical Society 0.
submitted / under review
- . On a novel gradient flow structure for the aggregation equation arXiv. doi: 10.48550/arXiv.2112.08317.
- . . ‘Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD.’ arXiv [math.NA] 2111.00129.
- . . ‘Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases.’ arXiv 0.
- . . ‘Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions.’ arXiv 0.
- . . ‘Strong $L^p$-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations.’ arXiv 0.
- . . ‘Deep neural network approximation theory for high-dimensional functions.’ arXiv 0.
- . . ‘Full history recursive multilevel Picard approximations for ordinary differential equations with expectations.’ arXiv 0.
- . . Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws.
- . . Computing with B-series.
- . . A New Stability Approach for Positivity-Preserving Patankar-type Schemes.
published
- . . ‘Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates.’ Journal of Complexity 57: 101438. doi: 10.1016/j.jco.2019.101438.
- . . ‘The exchange-driven growth model: basic properties and longtime behavior.’ Journal of Nonlinear Science 30, № 3: 793–830. doi: 10.1007/s00332-019-09592-x.
- . . ‘Barriers of the McKean–Vlasov energy via a mountain pass theorem in the space of probability measures.’ Journal of Functional Analysis 279, № 11: 108720. doi: 10.1016/j.jfa.2020.108720.
- . . ‘Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces.’ Alea 17, № 1: 445–471. doi: 10.30757/alea.v17-18.
- . . ‘Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies.’ SIAM Journal on Mathematical Analysis 52, № 6. doi: 10.1137/20M1322182.
- . . ‘Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions.’ Physical Review B 101, № 4: 045416. doi: 10.1103/PhysRevB.101.045416.
- . . ‘Space-time localisation for the dynamic Phi-4/3 model.’ Communications on Pure and Applied Mathematics 73, № 12: 2519–2555. doi: 10.1002/cpa.21925.
- . . ‘Exponential loss of memory for the 2-dimensional Allen–Cahn equation with small noise.’ Probability Theory and Related Fields 177: 257–322. doi: 10.1007/s00440-019-00945-x.
- . . ‘Local bounds for stochastic reaction diffusion equations.’ Electronic Journal of Probability 25: 1–26. doi: 10.1214/19-EJP397.
- . . ‘Generation of Interface for Solutions of the Mass Conserved Allen--Cahn Equation.’ SIAM Journal on Mathematical Analysis 52, № 3: 2624–2654. doi: 10.1137/18M1204747.
- . . ‘Kinetic/fluid micro-macro numerical scheme for a two component gas mixture.’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 18.
- . . ‘Global minimisers for anisotropic attractive-repulsive interactions.’ European Journal of Applied Mathematics 31, № 5: 854–870. doi: 10.1017/S0956792519000299.
- . . ‘Mathematical analysis of transmission properties of electromagnetic meta-materials.’ Networks and Heterogeneous Media 15, № 1: 29–56. doi: 10.3934/nhm.2020002.
- . . ‘PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems.’ Contributed to the ALGORITMY 2020, Vysoké Tatry.
- . . ‘An environment for sustainable research software in Germany and beyond: current state, open challenges, and call for action.’ F1000Research 9, № 295. doi: 10.12688/f1000research.23224.1.
- . . ‘First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory.’ Journal of Computational Physics 416: 109547. doi: 10.1016/j.jcp.2020.109547.
- . . ‘Exa-Dune -- Flexible PDE Solvers, Numerical Methods and Applications.’ In Software for Exascale Computing - SPPEXA 2016-2019, edited by , 225–269. Basel : Springer International Publishing. doi: 10.1007/978-3-030-47956-5_9.
- . . ‘Discrete Riemannian calculus on shell space.’ In Geometric Partial Differential Equations - Part I, edited by , 621–679. Amsterdam: Elsevier. doi: 10.1016/bs.hna.2019.06.005.
- . . ‘Convex Lifting-Type Methods for Curvature Regularization.’ In Handbook of Variational Methods for Nonlinear Geometric Data, edited by , 207–233. Basel : Springer International Publishing. doi: 10.1007/978-3-030-31351-7_7.
- . . ‘Dynamic Cell Imaging in PET With Optimal Transport Regularization.’ IEEE Transactions on Medical Imaging 39, № 5: 1626–1635. doi: 10.1109/TMI.2019.2953773.
- . . ‘Phase field approximations of branched transportation problems.’ Calculus of Variations and Partial Differential Equations 59, № 1: Paper No. 37, 34. doi: 10.1007/s00526-019-1680-3.
- . . ‘Green's function for the Neumann-Poisson problem on n-dimensional balls.’ American Mathematical Monthly 127, № 8: 737–743.
- . . ‘Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets.’ BMC Bioinformatics 21, № 335.
- . . ‘Severity of current depression and remission status are associated with structural connectome alterations in major depressive disorder .’ Molecular Psychiatry 25. doi: 10.1038/s41380-019-0603-1.
- . . ‘On the Littlewood-Paley spectrum for passive scalar transport equations.’ Journal of Nonlinear Science 30, № 2: 645–656. doi: 10.1007/s00332-019-09585-w.
- . . ‘Ripples in graphene: A variational approach.’ Comm. Math. Phys. 379.
- . . ‘Crystallization in a one-dimensional periodic landscape.’ J. Stat.Phys. 179.
- . . ‘Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity.’ Arch. Ration. Mech. Anal. 237.
- . . ‘Two-well rigidity and multidimensional sharp-interface limits for Solid-Solid phase transitions.’ Calc. Var. PDE 59.
- . . ‘Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice.’ Nonlinearity 33.
- . . ‘Functionals defined on piecewise rigid functions: Integral representation and Gamma-convergence.’ Arch. Ration. Mech. Anal. 236.
- . . ‘Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes.’ In Hyperbolic Problems: Theory, Numerics, Applications, edited by , 215–222. Heidelberg: Springer.
- . . ‘Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL.’ In Proceedings of the International Workshop on OpenCL. New York, NY: ACM Press. doi: 10.1145/3388333.3403035.
- . . ‘Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators.’ In Spectral and High Order Methods for Partial Differential Equations {ICOSAHOM} 2018, edited by , 525–535. Heidelberg: Springer. doi: 10.1007/978-3-030-39647-3_42.
- . . ‘Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators.’ Communications on Applied Mathematics and Computation 2: 581–611. doi: 10.1007/s42967-019-00057-2.
- . . ‘Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.’ SIAM Journal on Scientific Computing 42, № 2: A612–A638. doi: 10.1137/19M1263480.
- . . ‘Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods.’ International Journal of Numerical Analysis and Modeling 17, № 3: 332–349.
- . . ‘Relaxation Runge-Kutta Methods for Hamiltonian Problems.’ Journal of Scientific Computing 84, № 1. doi: 10.1007/s10915-020-01277-y.
- . . ‘Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.’ Computers and Mathematics with Applications 80, № 5: 1343–1359. doi: 10.1016/j.camwa.2020.06.016.
- . . ‘General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes.’ Numerische Mathematik 146. doi: 10.1007/s00211-020-01158-4.
- . . ‘RK-Opt: A package for the design of numerical ODE solvers.’ Journal of Open Source Software 5, № 54: 2514. doi: 10.21105/joss.02514.
- . . ‘Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems.’ SIAM Journal on Numerical Analysis 58, № 6: 3382–3405. doi: 10.1137/19M1290346.
- . . ‘NodePy: A package for the analysis of numerical ODE solvers.’ Journal of Open Source Software 5, № 55: 2515. doi: 10.21105/joss.02515.
- . . ‘A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations.’ SN Partial Differential Equations and Applications 1, № 2: 10. doi: 10.1007/s42985-019-0006-9.
- . . ‘Pricing and Hedging American-Style Options with Deep Learning.’ Journal of Risk and Financial Management 13, № 7: 158. doi: 10.3390/jrfm13070158.
- . . ‘Convergence rates for the stochastic gradient descent method for non-convex objective functions.’ Journal of Machine Learning Research 21: Paper No. 136, 48.
- . . ‘Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities.’ IMA Journal of Numerical Analysis 40, № 2: 1005–1050. doi: 10.1093/imanum/drz009.
- . . ‘Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.’ SIAM Journal on Mathematics of Data Science 2, № 3: 631–657. doi: 10.1137/19M125649X.
- . ‘Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.’ Electronic Journal of Probability 25: 101. doi: 10.1214/20-EJP423.
- . . ‘Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations.’ BIT Numerical Mathematics 60, № 4: 1057–1073. doi: 10.1007/s10543-020-00807-2.
- . . ‘Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations.’ Communications in Computational Physics 28, № 5: 2109–2138. doi: 10.4208/cicp.oa-2020-0130.
- . . ‘Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions.’ Numerical Algorithms 85, № 4: 1447–1473. doi: 10.1007/s11075-019-00871-y.
- . . ‘Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations.’ Journal of Numerical Mathematics 28, № 4: 197–222. doi: 10.1515/jnma-2019-0074.
- . . ‘Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, № 2244: 630–654. doi: 10.1098/rspa.2019.0630.
- . . ‘On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients.’ Annals of Probability 48, № 1: 53–93. doi: 10.1214/19-AOP1345.
- . . ‘Numerical Upscaling of Perturbed Diffusion Problems.’ SIAM Journal on Scientific Computing 2020, № Volume 42, Issue 4: A2014–A2036. doi: 10.1137/19M1278211.
- . . ‘A Gamma-convergence result for fluid-filled fracture propagationDO - 10.1051/m2an/2020016.’ ESAIM: Mathematical Modelling and Numerical Analysis 54, № 3. doi: 10.1051/m2an/2020016.
online first
- . . ‘Model order reduction framework for problems with moving discontinuities.’ Contributed to the Proceedings of ENUMATH 2019, Egmond aan Zee.
accepted / in Press (not yet published)
- . . ‘A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction.’ Contributed to the ENUMATH 2019, Graz.
- . . ‘Parametric model order reduction using pyMOR.’ Contributed to the MODRED 2019, Graz.
- . . ‘Towards local-failure local-recovery in PDE frameworks: the case of linear solvers.’ Contributed to the HPCSE 2019, Ostrava, Czech Republic.
- . . ‘Integral representation for energies in linear elasticity with surface discontinuities.’ Adv. Calc. Var. 2020.
- . . ‘Equilibrium of immersed hyperelastic solids.’ DCDS-S 2020.
- . . ‘Numerical approximation of von Kármán viscoelastic plates.’ DCDS-S 2020.
submitted / under review
- . . ‘Stable and efficient Petrov-Galerkin methods for a kinetic Fokker-Planck equation.’ arXiv 2020.
- . . Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD.
- . . Two-well linearization for solid-solid phase transitions.
- . . Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy.
- . . Gamma-convergence for free-discontinuity problems in linear elasticity: Homogenization and relaxation.
- . . ‘Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations.’ IMA Journal of Numerical Analysis 0.
- . . ‘Overall error analysis for the training of deep neural networks via stochastic gradient descent with random initialisation.’ SIAM Journal on Numerical Analysis 0.
- . . ‘Space-time deep neural network approximations for high-dimensional partial differential equations.’ Journal of Nonlinear Science 0.
- . . Weak error analysis for stochastic gradient descent optimization algorithms. Düsseldorf: Springer VDI Verlag.
- . . ‘Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities.’ Nonlinearity 0.
- . . ‘Nonlinear Monte Carlo methods with polynomial runtime for high-dimensional iterated nested expectations.’ Advances in Computational Mathematics 0.
- . . ‘Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems.’ arXiv 0.
- . . ‘High-dimensional approximation spaces of artificial neural networks and applications to partial differential equations.’ arXiv 0.
published
- . . ‘On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations.’ Journal of Scientific Computing 79, № 3: 1534–1571. doi: 10.1007/s10915-018-00903-0.
- . . ‘Deep optimal stopping.’ Journal of Machine Learning Research 20: Paper No. 74, 25.
- . . ‘On the Alekseev-Gröbner formula in Banach spaces.’ Discrete and Continuous Dynamical Systems - Series B 24, № 8: 4475–4511. doi: 10.3934/dcdsb.2019128.
- . . ‘Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations.’ Journal of Nonlinear Science 29, № 4: 1563–1619. doi: 10.1007/s00332-018-9525-3.
- . . ‘A mild Itô formula for SPDEs.’ Transactions of the American Mathematical Society 372, № 6: 3755–3807. doi: 10.1090/tran/7165.
- . . ‘A non-local problem for the Fokker-Planck equation related to the Becker-Döring model.’ Discrete and Continuous Dynamical Systems - Series A 39, № 4: 1821–1889. doi: 10.3934/dcds.2019079.
- . . ‘Macroscopic limit of the Becker-Döring equation via gradient flows.’ ESAIM: Control, Optimisation and Calculus of Variations 25, № 22: 36. doi: 10.1051/cocv/2018011.
- . . ‘Poincaré and Log–Sobolev Inequalities for Mixtures.’ Entropy 21, № 1: 89. doi: 10.3390/e21010089.
- . . ‘Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities.’ Annals of Applied Probability 29, № 6: 3438–3488. doi: 10.1214/19-AAP1484.
- . . ‘Long-Time Behaviour and Phase Transitions for the McKean-Vlasov Equation on the Torus.’ Archive for Rational Mechanics and Analysis 235, № 1: 635–690. doi: 10.1007/s00205-019-01430-4.
- . . ‘A nonlocal isoperimetric problem with dipolar repulsion.’ Communications in Mathematical Physics 372: 1059–1115. doi: 10.1007/s00220-019-03455-y.
- . . ‘Quasi-linear SPDEs in divergence form.’ Stochastics and Partial Differential Equations: Analysis and Computations 7, № 1: 64–85. doi: 10.1007/s40072-018-0122-0.
- . . ‘Quasilinear SPDEs via Rough Paths.’ Archive for Rational Mechanics and Analysis 232, № 2: 873–950. doi: 10.1007/s00205-018-01335-8.
- . . ‘A consistent kinetic model for a two-component mixture of polyatomic molecules.’ Communications in Mathematical Sciences 17.
- . . ‘Hypocoercivity for a BGK model for gas mixtures.’ Journal of Differential Equations 267.
- . . ‘Cross-Gramian-Based Dominant Subspaces.’ Advances in Computational Mathematics 45, № 5: 2533–2553. doi: 10.1007/s10444-019-09724-7.
- . . ‘On Empirical System Gramians.’ Contributed to the 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Wien, Österrreich. doi: 10.1002/pamm.201900006.
- . . ‘Global phase diagrams of run-and-tumble dynamics: equidistribution, waves, and blowup.’ Nonlinearity 32, № 6. doi: 10.1088/1361-6544/ab046d.
- . . ‘Gamma-convergence of free-discontinuity problems.’ Ann. Inst. H. Poincaré Anal. Non Linéaire 36: 1035–1079.
- . . ‘Stochastic homogenisation of free-discontinuity problems.’ Arch. Ration. Mech. Anal. 233: 935–974.
- . . ‘Homogenization of high-contrast Mumford-Shah energies.’ SIAM J. Math. Anal. 51: 1696–1729.
- . . ‘Strong convergence for explicit space-time discrete numerical approximation methods for stochastic Burgers equations.’ Journal of Mathematical Analysis and Applications 469, № 2: 661–704. doi: 10.1016/j.jmaa.2018.09.032.
- . . ‘On arbitrarily slow convergence rates for strong numerical approximations of Cox-Ingersoll-Ross processes and squared Bessel processes.’ Finance and Stochastics 23, № 1: 139–172. doi: 10.1007/s00780-018-0375-5.
- . . ‘Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations.’ Stochastic Processes and their Applications 129, № 1: 28–69. doi: 10.1016/j.spa.2018.02.008.
- . . ‘Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients.’ Annals of Applied Probability 29, № 2: 653–716. doi: 10.1214/17-AAP1352.
- . . ‘Regularity properties for solutions of infinite dimensional Kolmogorov equations in Hilbert spaces.’ Potential Analysis 50, № 3: 347–379. doi: 10.1007/s11118-018-9685-7.
- . . ‘MULTIBAT: Unified workflow for fast electrochemical 3D simulations of lithium-ion cells combining virtual stochastic microstructures, electrochemical degradation models and model order reduction.’ Journal of Computational Science 31: 172–184. doi: 10.1016/j.jocs.2018.03.006.
- . . ‘Mass Conservative Reduced Order Modeling of a Free Boundary Osmotic Cell Swelling Problem.’ Advances in Computational Mathematics 45, № 5: 2215–2239. doi: 10.1007/s10444-019-09691-z.
- . . ‘(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods.’ SIAM Journal on Scientific Computing 41, № 1. doi: 10.1137/18M1176269.
- . . ‘A Hierarchical A-Posteriori Error Estimatorfor the Reduced Basis Method.’ Advances in Computational Mathematics 45: 2191–2214. doi: 10.1007/s10444-019-09675-z.
- . . ‘System-theoretic model order reduction with pyMOR.’ PAMM 19. doi: 10.1002/pamm.201900459.
- . . ‘Multiscale methods for perturbed diffusion problems.’ Oberwolfach Reports 16: 2099–2181. doi: 10.4171/OWR/2019/35.
- . . Optimal local approximation spaces for parabolic problems (Master's thesis).
- . . ‘A locally conservative reduced flux reconstruction for elliptic problems.’ In Special Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), edited by . New York City: John Wiley & Sons. doi: 10.1002/pamm.201900026.
- . . ‘Advances in Model Order Reduction for Large Scale or Multi-Scale Problems.’ Oberwolfach Reports 16, № 3: 2510–2512. doi: 10.4171/OWR/2019/40.
- . . An unfitted discontinuous Galerkin scheme for a phase-field approximation of pressurized fractures.
- . . ‘A framework for Wasserstein-1-type metrics.’ Journal of Convex Analysis 26, № 2: 353–396.
- . . ‘Dynamic Models of Wasserstein-1-Type Unbalanced Transport.’ ESAIM: Control, Optimisation and Calculus of Variations 25: 23.
- . . ‘Variational time discretization of Riemannian splines.’ IMA Journal of Numerical Analysis 26, № 2: 353–396. doi: 10.1093/imanum/drx077.
- . . ‘Approximation of rectifiable 1-currents and weak-{$\ast$} relaxation of the {$h$}-mass.’ Journal of Mathematical Analysis and Applications 479, № 2: 2268–2283. doi: 10.1016/j.jmaa.2019.07.059.
- . . ‘Phase field models for two-dimensional branched transportation problems.’ Calculus of Variations and Partial Differential Equations 58, № 5: Paper No. 164, 31. doi: 10.1007/s00526-019-1615-z.
- . . ‘A phase-field approximation of the perimeter under a connectedness constraint.’ SIAM Journal on Mathematical Analysis 51, № 5: 3902–3920. doi: 10.1137/18M1225197.
- . . ‘EPLIN-α and -β isoforms modulate endothelial cell dynamics through a spatio-temporally differentiated interaction with actin.’ Cell Reports 29, № 4: P1010–1026.E6.
- . . ‘Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule.’ Arch. Ration. Mech. Anal. 231.
- . . ‘Griffith energies as small strain limit of nonlinear models for nonsimple brittle materials.’ Mathematics in Engineering 2.
- . . ‘Crystallization in the hexagonal lattice for ionic dimers.’ Math. Models Methods Appl. Sci. 29.
- . . ‘A compactness result in GSBV^p and applications to Gamma-convergence for free discontinuity problems.’ Calc. Var. PDE 68.
- . . ‘Mimetic Properties of Difference Operators: Product and Chain Rules as for Functions of Bounded Variation and Entropy Stability of Second Derivatives.’ BIT Numerical Mathematics 59, № 2: 547–563. doi: 10.1007/s10543-018-0736-7.
- . . ‘Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients.’ Journal of Scientific Computing 79, № 3: 1572–1607. doi: 10.1007/s10915-018-00902-1.
- . . ‘Stability of Correction Procedure via Reconstruction With Summation-by-Parts Operators for Burgers' Equation Using a Polynomial Chaos Approach.’ ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN) 52, № 6: 2215–2245. doi: 10.1051/m2an/2018072.
- . . ‘Some Notes on Summation by Parts Time Integration Methods.’ Results in Applied Mathematics 1: 100004. doi: 10.1016/j.rinam.2019.100004.
online first
- . . ‘Three‐field mixed finite element formulations for gradient elasticity at finite strains.’ GAMM-Mitteilungen xxx. doi: 10.1002/gamm.202000002.
submitted / under review
- . . ‘First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis.’ arXiv 2019.
- . . Derivation of von Kármán plate theory in the framework of threedimensional viscoelasticity.
- . . ‘Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations.’ arXiv 0.
- . . ‘Generalised multilevel Picard approximations.’ IMA J. Numer. Anal. 0.
- . . ‘Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise.’ arXiv 0.
- . . ‘Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities.’ arXiv 0.
published
- . . ‘Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics.’ Nonlinearity 31, № 10: 4517–4566. doi: 10.1088/1361-6544/aaced5.
- . . ‘A non-local Fokker-Planck equation related to nucleation and coarsening.’ In Oberwolfach Reports Interplay Anal. Probab. Appl. Math., edited by , 311–381.: European Mathematical Society Publishing House. doi: 10.4171/OWR/2018/6.
- . . Materials Science-inspired problems in the Calculus of Variations: Rigidity of shape memory alloys and multi-phase mean curvature flow Dissertation thesis, Universität Leipzig. N/A: Selbstverlag / Eigenverlag.
- . . ‘Convergence of the Allen-Cahn equation to multi-phase mean curvature flow.’ Communications on Pure and Applied Mathematics 71, № 8: 1597–1647. doi: 10.1002/cpa.21747.
- . . ‘Maximum palinstrophy amplification in the two-dimensional Navier-Stokes equations.’ Journal of Fluid Mechanics 837: 839–857. doi: 10.1017/jfm.2017.874.
- . . ‘Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits.’ Journal of Functional Analysis 275, № 6: 1321–1367. doi: 10.1016/j.jfa.2017.12.014.
- . . ‘Spectral gap for the stochastic quantization equation on the 2-dimensional torus.’ Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 54, № 3: 1204–1249. doi: 10.1214/17-AIHP837.
- . . ‘The Schrodinger equation with spatial white noise potential.’ Electronic Journal of Probability 23: 1–16. doi: 10.1214/18-EJP143.
- . Parabolic equations with rough coefficients and singular forcing arXiv. doi: 10.48550/arXiv.1803.07884.
- . . On kinetic modelling of gas mixtures Dissertation thesis, Universität Würzburg. Würzburg University Press.
- . . ‘Kinetic ES-BGK models for a multi-component gas mixture.’ In Theory, Numerics and Applications of Hyperbolic Problems, edited by , 195–208. Heidelberg: Springer.
- . . ‘On quantifying uncertainties for the linearized BGK kinetic equation.’ In Theory, Numerics and Applications of Hyperbolic Problems, edited by , 179–193. Heidelberg: Springer.
- . . ‘Existence, Uniqueness and Positivity of solutions for BGK models for mixtures.’ Journal of Differential Equations 265.
- . . ‘A BGK model for gas mixtures of polyatomic molecules allowing for slow and fast relaxation of the temperatures.’ Journal of Statistical Physics 173.
- . . ‘On Reduced Input-Output Dynamic Mode Decomposition.’ Advances in Computational Mathematics 44, № 6: 1751–1768. doi: 10.1007/s10444-018-9592-x.
- . . ‘Gas Network Benchmark Models.’ In Applications of Differential-Algebraic Equations: Examples and Benchmarks, edited by , 171–197. doi: 10.1007/11221_2018_5.
- . . ‘emgr - The Empirical Gramian Framework.’ Algorithms 11, № 7: 91. doi: 10.3390/a11070091.
- . ‘Parametric Model Order Reduction for Gas Flow Models.’ contributed to the MoRePaS 4 - Model Reduction for Parameterized Systems, Nantes, Frankreich, . doi: 10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1.
- . ‘HAPOD - Fast, Simple and Reliable Distributed POD Computation.’ contributed to the MATHMOD 2018- 9th Vienna International Conference on Mathematical Modelling, Vienna, . doi: 10.11128/arep.55.a55283.
- . . „Mathematik Münster: Dynamik – Geometrie – Struktur.“ Mitteilungen der Deutschen Mathematiker-Vereinigung 26, № 4: 189–193. doi: 10.1515/dmvm-2018-0058.
- . . ‘Sorting phenomena in a mathematical model for two mutually attracting/repelling species.’ Siam Journal on Mathematical Analysis 50, № 3: 3210–3250. doi: 10.1137/17M1125716.
- (Eds.): . The Mathematics of Mechanobiology and Cell Signaling. Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. doi: 10.14760/OWR-2018-8.
- . . ‘Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations.’ Mathematics of Computation 87, № 311: 1353–1413. doi: 10.1090/mcom/3146.
- . . ‘Lower bounds for weak approximation errors for spatial spectral Galerkin approximations of stochastic wave equations.’ In Stochastic partial differential equations and related fields, edited by , 237–248. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-319-74929-7_13.
- . . ‘Solving high-dimensional partial differential equations using deep learning.’ Proceedings of the National Academy of Sciences of the United States of America 115, № 34: 8505–8510. doi: 10.1073/pnas.1718942115.
- . . ‘Exponential moments for numerical approximations of stochastic partial differential equations.’ Stochastics and Partial Differential Equations: Analysis and Computations 6, № 4: 565–617. doi: 10.1007/s40072-018-0116-y.
- . . ‘On the mild Itô formula in Banach spaces.’ Discrete and Continuous Dynamical Systems - Series B 23, № 6: 2217–2243. doi: 10.3934/dcdsb.2018232.
- . . ‘Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equations.’ Communications in Mathematical Sciences 16, № 6: 1489–1529. doi: 10.4310/CMS.2018.v16.n6.a2.
- . . ‘Numerical homogenization of H(curl)-problems.’ SIAM J. Numer. Anal. 56, № 3: 1570–1596. doi: 10.1137/17M1133932.
- . . ‘A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast .’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 16, № 1: 385–411. doi: 10.1137/16M1108820.
- . . Numerical multiscale methods for Maxwell's equations in heterogeneous media Dissertation thesis, Universität Münster.
- . . Randomisierte lokalisierte Modellreduktion mit Robin-Transferoperator (Masterarbeit).
- . . ‘Model reduction for parameterized systems and inverse problems.’ Oberwolfach Reports 2018, № 39: 2454–2457. doi: 10.4171/OWR/2018/39.
- . . ‘Galerkin local maximum entropy method.’ International Journal for Numerical Methods in Fluids 0. doi: 10.1002/fld.4513.
- . . ‘A high-level C++ approach to manage local errors, asynchrony and faults in an MPI application.’ Contributed to the 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing, Cambridge, Vereinigtes Königreich. doi: 10.1109/PDP2018.2018.00117.
- . . ‘Hierarchical Approximate Proper Orthogonal Decomposition.’ SIAM Journal on Scientific Computing 40, № 5: A3267–A3292.
- . . ‘Localized Model Reduction in PDE Constrained Optimization.’ In Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 , edited by , 143–163. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-90469-6_8.
- . . ‘Vector-valued multibang control of differential equations.’ SIAM Journal on Control and Optimization 56, № 3: 2295–2326.
- . . ‘Optimal micropatterns in 2D transport networks and their relation to image inpainting.’ Archive for Rational Mechanics and Analysis 228, № 1: 279–308.
- . . ‘General transport problems with branched minimizers as functionals of 1-currents with prescribed boundary.’ Calculus of Variations and Partial Differential Equations 57, № 3: Paper No. 82, 39. doi: 10.1007/s00526-018-1364-4.
- . . „Mathematik Münster: Dynamik, Geometrie, Struktur. Beispiele einer geometrischen Sichtweise.“ Mitteilungen der Deutschen Mathematiker-Vereinigung 26, № 4.
- . . ‘Optimal stability estimates for continuity equations.’ Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, № A: 1279–1296. doi: 10.1017/S0308210518000173.
- . . ‘The thin film equation close to self-similarity.’ Analysis and PDE 11, № 5: 1303–1342. doi: 10.2140/apde.2018.11.1303.
- . ‘Analysis of the implicit upwind finite volume scheme with rough coefficients.’ Numerische Mathematik 139, № 1: 155–186. doi: 10.1007/s00211-017-0935-1.
- . ‘Error analysis of a variational multiscale stabilization for convection-dominated diffusion equations in two dimensions.’ IMA Journal of Numerical Analysis 38, № 3: 1229–1253. doi: 10.1093/imanum/drx027.
- . . ‘Two low-order nonconforming finite element methods for the Stokes flow in 3D.’ IMA Journal of Numerical Analysis xxx. doi: 10.1093/imanum/dry021.
- . . ‘Graphene ground states.’ Z. Angew. Math. Phys. 69.
- . . ‘On the passage from nonlinear to linearized viscoelasticity.’ SIAM J. Math. Anal. 50.
- . . A piecewise Korn inequality in SBD and applications to embedding and density results.
- . . ‘Quasistatic crack growth in 2d-linearized elasticity.’ Ann. Inst. H. Poincaré Anal. Non Linéaire 35: 27–64. doi: 10.1016/j.anihpc.2017.03.002.
- . . ‘On a decomposition of regular domains into John domains with uniform constants.’ ESAIM Control Optim. Calc. Var. 24. doi: 10.1051/cocv/2017029.
- . . Generalised Summation-by-Parts Operators and Entropy Stability of Numerical Methods for Hyperbolic Balance Laws Dissertation thesis, TU Braunschweig. N/A: unbekannt / n.a. / unknown.
- . . ‘Artificial Viscosity for Correction Procedure via Reconstruction Using Summation-by-Parts Operators.’ In Theory, Numerics and Applications of Hyperbolic Problems II, edited by , 363–375. Basel : Springer International Publishing. doi: 10.1007/978-3-319-91548-7_28.
- . . ‘Correction Procedure via Reconstruction Using Summation-by-Parts Operators.’ In Theory, Numerics and Applications of Hyperbolic Problems II, edited by , 491–501. Basel : Springer International Publishing. doi: 10.1007/978-3-319-91548-7_37.
- . . ‘Advantages and Pitfalls of OpenCL in Computational Physics.’ In Proceedings of the International Workshop on OpenCL, 10:1. New York, NY: ACM Press. doi: 10.1145/3204919.3204929.
- . . ‘Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators.’ Applied Numerical Mathematics 128: 1–23. doi: 10.1016/j.apnum.2018.01.019.
- . . ‘Generalised Summation-by-Parts Operators and Variable Coefficients.’ Journal of Computational Physics 362: 20–48. doi: 10.1016/j.jcp.2018.02.021.
- . . ‘L_2 Stability of Explicit Runge-Kutta Schemes.’ Journal of Scientific Computing 75, № 2: 1040–1056. doi: 10.1007/s10915-017-0595-4.
- . . ‘Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations.’ Journal of Scientific Computing 76, № 1: 216–242. doi: 10.1007/s10915-017-0618-1.
accepted / in Press (not yet published)
- . . ‘Heterogeneous Multiscale Method for the Maxwell equations with high contrast.’ ESAIM Math. Model. Numer. Anal. xx.
- . . ‘On the Itô--Alekseev--Gröbner formula for stochastic differential equations.’ Ann. Inst. Henri Poincaré Probab. Stat. 0.
- . . ‘A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black--Scholes partial differential equations.’ Memoirs of the American Mathematical Society 0.
published
- . . ‘Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation.’ Nonlinear Analysis: Theory, Methods and Applications 158: 142–167. doi: 10.1016/j.na.2017.04.009.
- . . ‘An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two.’ Electronic Journal of Probability 22: 1–27. doi: 10.1214/17-EJP60.
- . . ‘Convergence of the Two-Dimensional Dynamic Ising-Kac Model to Φ24.’ Communications on Pure and Applied Mathematics 70, № 4: 717–812. doi: 10.1002/cpa.21655.
- . . ‘Gaussian Approximations for Probability Measures on Rd.’ SIAM/ASA Journal on Uncertainty Quantification 5, № 1. doi: 10.1137/16M1105384.
- . . ‘Gaussian Approximations for Transition Paths in Brownian Dynamics.’ SIAM Journal on Mathematical Analysis 49, № 4. doi: 10.1137/16M1071845.
- . . ‘GLOBAL WELL-POSEDNESS OF THE DYNAMIC Φ4 MODEL IN THE PLANE.’ Annals of Probability 45, № 4: 2398–2476. doi: 10.1214/16-AOP1116.
- . . ‘The Dynamic Phi-4/3 Model Comes Down from Infinity.’ Communications in Mathematical Physics 356, № 3: 673–753. doi: 10.1007/s00220-017-2997-4.
- . . ‘Stochastic PDEs, Regularity structures, and interacting particle systems .’ Annales de la Faculté des sciences de Toulouse: Mathématiques 6 / 26, № 4: 847–909. doi: 10.5802/afst.1555.
- . . ‘A consistent kinetic model for a two-component mixture with an application to plasma.’ Kinetic and Related Models 10.
- . . ‘Mathematics in the Life-Sciences: A personal point of view.’ Jahresbericht der deutschen Mathematiker-Vereinigung 119: 143–168. doi: 10.1365/s13291-017-0165-6.
- . . ‘A Hydrodynamic Limit for Chemotaxis in a given Heterogeneous Environment.’ Vietnam Journal of Mathematics 45, № 1-2: 127–152. doi: 10.1007/s10013-016-0209-8.
- . . ‘Wavenumber selection in coupled transport equations.’ Journal of Mathematical Biology 75, № 5: 1047–1073. doi: 10.1007/s00285-017-1107-8.
- . . ‘On the differentiability of solutions of stochastic evolution equations with respect to their initial values.’ Nonlinear Analysis: Theory, Methods and Applications 162: 128–161. doi: 10.1016/j.na.2017.03.003.
- . . ‘Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations.’ Communications in Mathematics and Statistics 5, № 4: 349–380. doi: 10.1007/s40304-017-0117-6.
- . . ‘On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, № 2207: 20170104, 16. doi: 10.1098/rspa.2017.0104.
- . . ‘Comparison of methods for parametric model order reduction of instationary problems.’ In Model Reduction and Approximation: Theory and Algorithms., edited by , 377–408. 1st Ed. Philadelphia: SIAM Publications. doi: 10.1137/1.9781611974829.ch9.
- . . ‘Book review of: A. Quarteroni et al., Reduced basis methods for partial differential equations. An introduction.’ SIAM Rev. 59, № 3: 690–692.
- (Eds.): . Model Reduction of Parametrized Systems. 1st Ed. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8.
- . . ‘Finite Volume Methods: Foundation and Analysis.’ In Encyclopedia of Computational Mechanics, edited by , –. 2nd Ed. New York City: John Wiley & Sons. doi: 10.1002/9781119176817.ecm2010.
- . . ‘Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization.’ In Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, edited by , 357–365. Basel : Springer International Publishing. doi: 10.1007/978-3-319-57394-6_38.
- . . Model Reduction and Approximation: Theory and Algorithms. Philadelphia: SIAM Publications. doi: 10.1137/1.9781611974829.
- . . ‘The DUNE-FEM-DG module.’ Archive of Numerical Software 5, № 1: 21–61. doi: 10.11588/ans.2017.1.28602.
- . . ‘Extending DUNE: The dune-xt modules.’ Archive of Numerical Software 5, № 1: 193–216. doi: 10.11588/ans.2017.1.27720.
- . ‘Heterogeneous Multiscale Method for a Helmholtz problem with high contrast.’ contributed to the Winter school on Numerical Analysis of Multiscale Problems, HIM Bonn, Germany, .
- . . ‘True Error Control for the Localized Reduced Basis Method for Parabolic Problems.’ In Model Reduction of Parametrized Systems, edited by , 169–182. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_11.
- . . ‘Localized Reduced Basis Approximation of a Nonlinear Finite Volume Battery Model with Resolved Electrode Geometry.’ In Model Reduction of Parametrized Systems, edited by , 201–212. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_13.
- . . ‘Cross-Gramian-Based Model Reduction: A Comparison.’ In Model Reduction of Parametrized Systems, edited by , 271–283. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_17.
- . . ‘Fast Low-Rank Empirical Cross Gramians.’ PAMM 17, № 1: 841–842. doi: 10.1002/pamm.201710388.
- . . Variational crimes in the Localized orthogonal decomposition method (master's thesis).
- . ‘Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth.’ Kinetic and Related Models 10, № 1: 117–140. doi: 10.3934/krm.2017005.
- . . ‘The effect of head model simplification on beamformer source localization.’ Frontiers in Neuroscience 11, № 625. doi: 10.3389/fnins.2017.00625.
- . . ‘On a cross-diffusion model for multiple species with nonlocal interaction and size exclusion.’ Nonlinear Analysis 159.
- . . ‘On the uniqueness of nonlinear diffusion coefficients in the presence of lower order terms.’ Inverse Problems 33. doi: 10.1088/1361-6420/aa8cae.
- . . ‘A Mixed Finite Element Method to Solve the EEG Forward Problem.’ IEEE Transactions on Medical Imaging 36, № 4: 930–941. doi: 10.1109/TMI.2016.2624634.
- . . ‘ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics.’ In Model Reduction of Parametrized Systems, edited by , 137–148. Basel : Springer International Publishing. doi: 10.1007/978-3-319-58786-8_9.
- . . ‘A Discontinuous Galerkin Method for the EEG Forward Problem.’ SIAM Journal on Scientific Computing 39, № 1: B138–B164. doi: 10.1137/15M1048392.
- . . ‘ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications.’ SIAM Journal on Scientific Computing 39, № 4: A1435–A1465. doi: 10.1137/15M1054213.
- . . ‘Geometric Reconstruction of Implicitly Defined Surfaces and Domains with Topological Guarantees.’ ACM Transactions on Mathematical Software 44, № 2. doi: 10.1145/3104989.
- . . ‘Numerical homogenization for indefinite H(curl)-problems.’ In Proceedings of Equadiff 2017 Conference, edited by , 137–146.
- . . ‘Endothelial Basement Membrane Laminin 511 Contributes to Endothelial Junctional Tightness and thereby Inhibits Leukocyte Transmigration.’ Cell Reports 18, № 5: 1256–1269.
- . . ‘Joint denoising and distortion correction of atomic scale scanning transmission electron microscopy images.’ Inverse Problems 33, № 9: 095002.
- . . ‘A Sinkhorn-Newton method for entropic optimal transport.’ Contributed to the Neural Information Processing Systems Conference, Long Beach, USA.
- . ‘Joint Denoising and Distortion Correction for Atomic Column Detection in Scanning Transmission Electron Microscopy Images.’ Microscopy and Microanalysis 23(S1): 164–165.
- . ‘On the Vortex Filament Conjecture for Euler Flows.’ Archive for Rational Mechanics and Analysis 224, № 1: 135–172. doi: 10.1007/s00205-016-1070-3.
- . ‘Convergence rates for upwind schemes with rough coefficients.’ SIAM Journal on Numerical Analysis 55, № 2: 812–840. doi: 10.1137/16M1084882.
- . . ‘Eulerian and Lagrangian solutions to the continuity and Euler equations with $L^1$ vorticity.’ SIAM Journal on Mathematical Analysis 49, № 5: 3973–3998. doi: 10.1137/17M1130988.
- . . ‘Optimal stability estimates for continuity equations.’ Oberwolfach Reports 14, № 1. doi: 10.4171/OWR/2017/7.
- . ‘Mixed finite element methods for linear elasticity and the Stokes equations based on the Helmholtz decomposition.’ ESAIM: Mathematical Modelling and Numerical Analysis 51, № 2: 399–425. doi: 10.1051/m2an/2016024.
- . ‘Relaxing the CFL Condition for the Wave Equation on Adaptive Meshes.’ Journal of Scientific Computing 72, № 3: 1196–1213. doi: 10.1007/s10915-017-0394-y.
- . ‘A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees.’ Computational Methods in Applied Mathematics 17, № 1: 161–185. doi: 10.1515/cmam-2016-0031.
- . . ‘Thermo-optical interactions in a dye-microcavity photon Bose-Einstein condensate.’ New Journal of Physics 19. doi: 10.1088/1367-2630/aa964c.
- . . ‘A Korn-type inequality in SBD for functions with small jump sets.’ Math. Models Methods Appl. Sci. (M3AS) 27: 2461–2484. doi: 10.1142/S021820251750049X.
- . . ‘A derivation of linearized Griffith energies from nonlinear models.’ Arch. Ration. Mech. Anal. 225: 425–467. doi: 10.1007/s00205-017-1108-1.
- . . ‘Summation-by-Parts and Correction Procedure via Reconstruction.’ In Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016, edited by , 627–637. Heidelberg: Springer. doi: 10.1007/978-3-319-65870-4_45.
- . . ‘Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods.’ GEM - International Journal on Geomathematics 8, № 1: 85–133. doi: 10.1007/s13137-016-0089-9.
- . . ‘Extended skew-symmetric form for summation-by-parts operators and varying Jacobians.’ Journal of Computational Physics 342: 13–28. doi: 10.1016/j.jcp.2017.04.044.
- . . ‘Localized Orthogonal Decomposition for two-scale Helmholtz-type problems.’ AIMS Mathematics 2, № 3: 458–478. doi: 10.3934/Math.2017.2.458.
- . . ‘Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniques.’ M2AN Math. Model. Numer. Anal. 51, № 2: 641–677. doi: 10.1051/m2an/2016031.
- . . ‘Towards Composable GPU Programming: Programming GPUs with Eager Actions and Lazy Views.’ In Proceedings of the 8th International Workshop on Programming Models and Applications for Multicores and Manycores, edited by , 58–67. New York, NY: ACM Press. doi: 10.1145/3026937.3026942.
online first
- . . ‘Variability of Stencil Computations for Porous Media.’ Concurrency and Computation: Practice and Experience Special Issue on Advanced Stencil-Code Engineering.
- . . ‘A Framework of Stencil Computations for PDE based Applications with Examples from DUNE and hypre.’ Concurrency and Computation: Practice and Experience Special Issue on Advanced Stencil-Code Engineering.
accepted / in Press (not yet published)
- . . ‘Uniqueness of solitary waves in the high-energy limit of FPU-type chains.’ Contributed to the Patterns in Dynamics, Berlin.
- . . ‘Counterexamples to regularities for the derivative processes associated to stochastic evolution equations.’ Stochastics and Partial Differential Equations: Analysis and Computations 0.
submitted / under review
- . . Randomized Local Model Order Reduction : arXiv:1706.09179, .
published
- . . ‘Gradient flow structure for McKean-Vlasov equations on discrete spaces.’ Discrete and Continuous Dynamical Systems - Series A 36, № 12: 6799–6833. doi: 10.3934/dcds.2016096.
- . . ‘On the Large Time Behavior of the Solutions of a Nonlocal Ordinary Differential Equation with Mass Conservation.’ Journal of Dynamics and Differential Equations 28, № 3-4: 707–731. doi: 10.1007/s10884-015-9465-7.
- . . ‘Sample path large deviations for Laplacian models in (1+1)-dimensions.’ Electronic Journal of Probability 21: 1–36. doi: 10.1214/16-EJP8.
- . . ‘Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.’ AIMS Mathematics 1, № 3: 261--281. doi: 10.3934/Math.2016.3.261.
- . . ‘Blowup and Global Solutions in a Chemotaxis-Growth System.’ Nonlinear Analysis: Theory, Methods and Applications 2016, № 135: 57–72. doi: 10.1016/j.na.2016.01.017.
- . ‘Stochastic homogenisation of singularly-perturbed integral functionals.’ Ann. Mat. Pura Appl. 195.
- . . ‘A simple sufficient condition for the quasiconvexity of elastic stored-energy functions in spaces which allow for cavitation.’ Calc. Var. Partial Diff. Equations 55.
- . . ‘A bridging mechanism in the homogenisation of brittle composites with soft inclusions.’ SIAM J. Math. Anal. 48.
- . . ‘Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations.’ Nonlinear Analysis: Theory, Methods and Applications 142: 152–193. doi: 10.1016/j.na.2016.03.001.
- . . ‘An exponential Wagner-Platen type scheme for SPDEs.’ SIAM Journal on Numerical Analysis 54, № 4: 2389–2426. doi: 10.1137/15M1008762.
- . . ‘On stochastic differential equations with arbitrary slow convergence rates for strong approximation.’ Communications in Mathematical Sciences 14, № 6: 1477–1500. doi: 10.4310/CMS.2016.v14.n6.a1.
- . . ‘Model Reduction for Multiscale Lithium-Ion Battery Simulation.’ In Numerical Mathematics and Advanced Applications ENUMATH 2015, edited by , 317–331. Heidelberg: Springer. doi: 10.1007/978-3-319-39929-4_31.
- . . ‘A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations.’ SIAM J. Numer. Anal. 54, № 6: 3493–3522. doi: 10.1137/15M1039225.
- . . ‘Optimal Preconditioners for Nitsche-XFEM Discretizations of Interface Problems.’ Numerische Mathematik 2016. doi: 10.1007/s00211-016-0801-6.
- . . ‘Numerical and Experimental Analysis of Local Flow Phenomena in Laminar Taylor Flow in a Square Mini-Channel.’ Physics of Fluids 28, № 1: 012109.
- . . ‘Approximation of skewed interfaces with tensor-based model reduction procedures: application to the reduced basis hierarchical model reduction approach.’ J. Comp. Phys. 321: 1185–1205. doi: 10.1016/j.jcp.2016.06.021.
- . . Model reduction for parametric multi-scale problems Dissertation thesis, Westfälische Wilhelms-Universität Münster.
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, № 5: S194–S216. doi: 10.1137/15M1026614.
- . . ‘Adaptive Localized Model Reduction.’ Oberwolfach Reports 13, № 3: 2406–2409. doi: 10.4171/OWR/2016/42.
- . . ‘A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift.’ Discrete and Continuous Dynamical Systems - Series S 9, № 5: 1393–1420. doi: 10.3934/dcdss.2016056.
- . . ‘Problem adapted hierachical model reduction for the Fokker-Planck equation.’ In ALGORITMY 2016 Proceedings of contributed papers and posters, edited by , 13–22. Bratislava: Publishing House of Slovak University of Technology.
- . . ‘Reduced Basis Methods: Success, Limitations and Future Challenges.’ In roceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016, edited by , 1–12. Bratislava: Publishing House of Slovak University of Technology.
- . ‘Spectral decompositions using one-homogeneous functionals.’ SIAM Journal on Imaging Sciences 9, № 3: 1374–1408. doi: 10.1137/15M1054687.
- . ‘Simultaneous reconstruction and segmentation for dynamic SPECT imaging.’ Inverse Problems 32, № 10. doi: 10.1088/0266-5611/32/10/104002.
- . ‘On a Boltzmann mean field model for knowledge growth.’ SIAM Journal on Applied Mathematics 76, № 5: 1799–1818. doi: 10.1137/15M1018599.
- . ‘Nonlinear Spectral Analysis via One-Homogeneous Functionals: Overview and Future Prospects.’ Journal of Mathematical Imaging and Vision 56, № 2: 300–319. doi: 10.1007/s10851-016-0665-5.
- . ‘Lane formation by side-stepping.’ SIAM Journal on Mathematical Analysis 48, № 2: 981–1005. doi: 10.1137/15M1033174.
- . ‘Flow characteristics in a crowded transport model.’ Nonlinearity 29, № 11: 3528–3550. doi: 10.1088/0951-7715/29/11/3528.
- . ‘Bregman distances in inverse problems and partial differential equations.’ In Advances in Mathematical Modeling, Optimization, and Optimal Control, edited by , 3–33. Basel : Springer International Publishing. doi: 10.1007/978-3-319-30785-5_2.
- . ‘Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem.’ NeuroImage 140, № null: 163–173. doi: 10.1016/j.neuroimage.2016.04.005.
- . . ‘An optimization approach for well-targeted transcranial direct current stimulation.’ SIAM Journal on Applied Mathematics 76, № 6: 2154–2174. doi: 10.1137/15M1026481.
- . . ‘The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem.’ IEEE Trans Biomed Eng 63, № 12: 2564–2575. doi: 10.1109/TBME.2016.2590740.
- . . ‘A phase field approach to pressurized fractures using discontinuous Galerkin methods.’ Mathematics and Computers in Simulation 137: –. doi: 10.1016/j.matcom.2016.11.001.
- . . ‘An unfitted discontinuous Galerkin scheme for conservation laws on evolving surfaces.’ In Proceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoké Tatry, Podbanské, Slovakia, March 13-18, 2016, edited by , 44–54.: Publishing House of Slovak University of Technology.
- . . ‘Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE.’ In Software for Exascale Computing - SPPEXA 2013-2015, edited by , 25–43. doi: 10.1007/978-3-319-40528-5_2.
- . . ‘Hardware-based Efficiency Advances in the EXA-DUNE Project.’ In Software for Exascale Computing - SPPEXA 2013-2015, edited by , 3–23. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-319-40528-5_1.
- . ‘Variational method for motion corrected reconstruction with MRI information in positron emission tomography.’ Contributed to the 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference, NSS/MIC 2015, usa. doi: 10.1109/NSSMIC.2015.7582045.
- . . ‘High-energy waves in superpolynomial FPU-type chains.’ Journal of Nonlinear Science 2016. doi: 10.1007/s00332-016-9331-8.
- . . ‘Instabilities and oscillations in coagulation equations with kernels of homogeneity one.’ Quarterly of Applied Mathematics 75-1. doi: 10.1090/qam/1454.
- . . ‘Differentiable piecewise-Bezier interpolation on Riemannian manifolds.’ Contributed to the European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, Bruges (Belgium).
- . . ‘Differentiable piecewise-Bezier surfaces on Riemannian manifolds.’ SIAM Journal on Imaging Sciences 9, № 4: 1788–1828.
- . . ‘On the Gamma-limit of joint segmentation and registration functionals based on phase fields.’ Interfaces and Free Boundaries 18, № 4: 441–477.
- . . ‘Protection from septic peritonitis by rapid neutrophil recruitment through omental high endothelial venules.’ Nature Communications 7: 10828.
- . . ‘Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis.’ Journal of the Mechanics and Physics of Solids 89: 194–210.
- . . ‘Optimal fine-scale structures in compliance minimization for a shear load.’ Communications in Pure and Applied Mathematics 69: 1572–1610.
- . . ‘Splines in the space of shells.’ Computer Graphics Forum 35, № 5: 111–120.
- . . ‘ Optimal energy scaling for micropatterns in transport networks.’ SIAM Journal on Mathematical Analysis 49, № 1: 311–359.
- . ‘ Equivalent formulations for the branched transport and urban planning problems.’ Journal de Mathématiques Pures et Appliquées 106: 695–724.
- . ‘A quantitative theory for the continuity equation.’ Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis 34, № 7: 1837–1850. doi: 10.1016/j.anihpc.2017.01.001.
- . ‘Global solutions to the volume-preserving mean-curvature flow.’ Calculus of Variations and Partial Differential Equations 55, № 1: 1–23. doi: 10.1007/s00526-015-0943-x.
- . ‘A natural nonconforming FEM for the Bingham flow problem is quasi-optimal.’ Numerische Mathematik 133, № 1: 37–66. doi: 10.1007/s00211-015-0738-1.
- . ‘A new discretization for mth-Laplace equations with arbitrary polynomial degrees.’ SIAM Journal on Numerical Analysis 54, № 4: 2138–2162. doi: 10.1137/15M1013651.
- . ‘Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems.’ IMA Journal of Numerical Analysis 36, № 2: 593–617. doi: 10.1093/imanum/drv019.
- . ‘L2 best approximation of the elastic stress in the Arnold-Winther FEM.’ IMA Journal of Numerical Analysis 36, № 3: 1096–1119. doi: 10.1093/imanum/drv051.
- . ‘A $C^0$ interior penalty method for elliptic optimal control problems with pointwise state constraints in three dimensions.’ In Topics in Numerical Partial Differential Equations and Scientific Computing, edited by , 1–22. doi: 10.1007/978-1-4939-6399-7.
- . . ‘The geometry of C60: A rigorous approach via Molecular Mechanics.’ SIAM J. Appl. Math. 76: 2009–2029. doi: 10.1137/16M106978X.
- . . ‘KdV waves in atomic chains with nonlocal interactions .’ Discrete and Continuous Dynamical Systems - Series A 36. doi: 10.3934/dcds.2016.36.2047.
- . . ‘Summation-by-parts operators for correction procedure via reconstruction.’ Journal of Computational Physics 311: 299–328. doi: 10.1016/j.jcp.2016.02.009.
- . . ‘Analysis of multiscale methods for time-harmonic Maxwell's equations.’ Proc. Appl. Math. Mech. 16, № 1: 559–560. doi: 10.1002/pamm.201610268.
- . ‘Optimal local approximation spaces for component-based static condensation procedures.’ SIAM J. Sci. Comput. 38, № 5: A3318––A3356. doi: 10.1137/15M1009603.
- . . ‘A note on the cross Gramian for non-symmetric systems.’ System Science and Control Engineering 4, № 1: 199–208. doi: 10.1080/21642583.2016.1215273.
- . . ‘High order unfitted finite element methods on level set domains using isoparametric mappings.’ Comp. Meth. Appl. Mech. Eng. 300, № 1: 716–733. doi: 10.1016/j.cma.2015.12.005.
online first
- . . ‘High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows.’ Comp. Meth. Appl. Mech. Eng. 2016. doi: 10.1016/j.cma.2016.04.025.
- . ‘Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy.’ Methods null, № null. doi: 10.1016/j.ymeth.2017.02.001.
- . ‘Cross-Diffusion Systems with Excluded-Volume Effects and Asymptotic Gradient Flow Structures.’ Journal of Nonlinear Science null, № null: 1–33. doi: 10.1007/s00332-016-9348-z.
- . . ‘Notes on a PDE system for biological network formation.’ Nonlinear Analysis: Theory, Methods & Applications null. doi: 10.1016/j.na.2015.12.018.
submitted / under review
- . . Efficient implementation of the Localized Orthogonal Decomposition method arXiv, .
- . . ‘Bias-Reduction in Variational Regularization.’ Journal of Mathematical Imaging and Vision Special Issue MIA 2016.
- . . ‘Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces.’ arXiv 0.
- . . L2-estimates for a high order unfitted finite element method for elliptic interface problems : arXiv eprints, .
- . . ‘Analysis of a high order unfitted finite element method for elliptic interface problems.’ arXiv preprint arXiv:1602.02970 1602.02970.
published
- . . ‘Construction of ϕ4/3 diagrams for pedestrians. In From Particle Systems to Partial Differential Equations.’ In From Particle Systems to Partial Differential Equations , edited by , 1–46. Basel : Springer International Publishing. doi: 10.1007/978-3-319-66839-0_1.
- . . ‘Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions .’ Annales de la Faculté des sciences de Toulouse: Mathématiques 6 / 24, № 1: 55–92. doi: 10.5802/afst.1442.
- . ‘Algorithms for Kullback--Leibler Approximation of Probability Measures in Infinite Dimensions.’ SIAM Journal on Scientific Computing 37, № 6. doi: 10.1137/14098171X.
- . ‘Kullback--Leibler Approximation for Probability Measures on Infinite Dimensional Spaces.’ Siam Journal on Mathematical Analysis 47, № 6: 4091–4742. doi: 10.1137/140962802.
- . . ‘A free boundary problem for cell motion.’ Differential and Integral Equations 28, № 7-8: 695–732. doi: 10.57262/die/1431347860.
- (Eds.): . Special Issue: Nonlinear Phenomena in Biology, Physics and Mechanics . New York City: John Wiley & Sons.
- . . „Mathematik und Biowissenschaften.“ In Studien- und Berufsplaner Mathematik, herausgegeben von , 124–127. Wiesbaden: Springer Fachmedien Wiesbaden. doi: 10.1007/978-3-658-04129-8.
- . . ‘Second-order edge-penalization in the Ambrosio-Tortorelli functional.’ Multiscale Model. Simul. 13, № 4: 1354–1389.
- . . ‘Gradient theory for geometrically nonlinear plasticity via the homogenization of dislocations.’ In Analysis and Computation of Microstructure in Finite Plasticity, edited by , 175–204.
- . . ‘Loss of regularity for Kolmogorov equations.’ Annals of Probability 43, № 2: 468–527. doi: 10.1214/13-AOP838.
- . . ‘A Milstein scheme for SPDEs.’ Foundations of Computational Mathematics 15, № 2: 313–362. doi: 10.1007/s10208-015-9247-y.
- . . ‘Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients.’ Memoirs of the American Mathematical Society 236, № 1112: v+99. doi: 10.1090/memo/1112.
- . . ‘Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems.’ Discrete and Continuous Dynamical Systems - Series S 8, № 1: 119–150. doi: 10.3934/dcdss.2015.8.119.
- . . ‘A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.’ Oberwolfach Reports 2/2015: 141–144. doi: 10.4171/OWR/2015/2.
- . ‘The Versatile Cross Gramian.’ contributed to the Model Reduction for Parameterized Systems (MoRePaS) III, Trieste, Italy, . doi: 10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1.
- . . ‘Model order reduction of parameterized systems (MoRePaS).’ Advances in Computational Mathematics 41, № 5: 955–960. doi: 10.1007/s10444-015-9443-y.
- . . ‘Interactive Simulations Using Localized Reduced Basis Methods.’ In IFAC-PapersOnLine, 729–730. doi: 10.1016/j.ifacol.2015.05.134.
- . . ‘Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo.’ In Proceedings of 10th International Conference on Large-Scale Scientific Computations, Sozopol 2015, edited by , 145–152. Basel : Springer International Publishing. doi: 10.1007/978-3-319-26520-9_15.
- . . ‘The Empirical Cross Gramian for Parametrized Nonlinear Systems.’ Contributed to the MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling, Vienna. doi: 10.1016/j.ifacol.2015.05.163.
- . . ‘Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment.’ SIAM J. Sci. Comput. 37, № 6: A2865–A2895. doi: 10.1137/151003660.
- . ‘Accelerating the Computation of Empirical Gramians and Related Methods.’ contributed to the 5th International Workshop on Model Reduction in Reacting Flows, Spreewald, . doi: 10.5281/zenodo.46643.
- . . ‘Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport.’ In Computational Methods for Complex Liquid-Fluid Interfaces, edited by , 353–371.
- . . ‘The Nitsche XFEM-DG Space-Time Method and its Implementation in Three Space Dimensions.’ SIAM J. Sci. Comput. 37: A245–A270. doi: 10.1137/130943534.
- . . On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems Dissertation thesis, RWTH Aachen.
- . . ‘The Localized Reduced Basis Multiscale method for two-phase flows in porous media.’ International Journal for Numerical Methods in Engineering 5, № 102: 1018–1040. doi: 10.1002/nme.4773.
- . . ‘Data-driven combined state and parameter reduction for inverse problems.’ Advances in Computational Mathematics 41, № 5: 1343–1364. doi: 10.1007/s10444-015-9420-5.
- . . ‘Adaptive Heterogeneous Multiscale Methods for immiscible two-phase flow in porous media.’ Computational Geosciences 1, № 19: 99–114. doi: 10.1007/s10596-014-9455-6.
- . . ‘A new certification framework for the port reduced static condensation reduced basis element method.’ Computer Methods in Applied Mechanics and Engineering 283: 352–383. doi: 10.1016/j.cma.2014.09.020.
- . ‘Spectral representations of one-homogeneous functionals.’ In Scale Space and Variational Methods in Computer Vision - 5th International Conference, SSVM 2015, Proceedings, 16–27. Heidelberg: Springer. doi: 10.1007/978-3-319-18461-6_2.
- . . ‘Effective equations for anisotropic glioma spread with proliferation: a multiscale approach and comparisons with previous settings.’ Mathematical Medicine and Biology 2015. doi: 10.1093/imammb/dqv030.
- . . ‘Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models.’ Physical Biology 12, № 6: 066014. doi: 10.1088/1478-3975/12/6/066014.
- . . ‘Algebraic multigrid for discontinuous Galerkin methods using local transformations.’ In Proceedings of the 22th Conference on Domain Decomposition Methods, 177–185. Heidelberg: Springer.
- . . ‘Concepts for flexible parallel Multi-Domain Simulations.’ In Proceedings of the 22th Conference on Domain Decomposition Methods.
- . . ‘Glioma Follow White Matter Tracts; a Multiscale DTI-based Model.’ Journal of Mathematical Biology 71, № 3. doi: 10.1007/s00285-014-0822-7.
- . ‘Identification of nonlinear heat conduction laws.’ Journal of Inverse and Ill-Posed Problems 23, № 5: 429–437. doi: 10.1515/jiip-2014-0030.
- . ‘Identification of chemotaxis models with volume-filling.’ SIAM Journal on Applied Mathematics 75, № 2: 275–288. doi: 10.1137/140967222.
- . ‘Second-order edge-penalization in the ambrosio-tortorelli functional.’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 13, № 4: 1354–1389. doi: 10.1137/15M1020848.
- . ‘Regularization with sparse vector fields: From image compression to TV-type reconstruction.’ In Scale Space and Variational Methods in Computer Vision - 5th International Conference, SSVM 2015, Proceedings, 191–202. Heidelberg: Springer. doi: 10.1007/978-3-319-18461-6_16.
- . ‘Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems.’ Inverse Problems 31, № 8. doi: 10.1088/0266-5611/31/8/085009.
- . ‘Locally sparse reconstruction using the l1,∞-norm.’ Inverse Problems and Imaging 9, № 4: 1093–1137. doi: 10.3934/ipi.2015.9.1093.
- . ‘Iterative solutionmethods.’ In Handbook of Mathematical Methods in Imaging: Volume 1, Second Edition, edited by , 431–470. Heidelberg: Springer. doi: 10.1007/978-1-4939-0790-8_9.
- . ‘Impact of uncertain head tissue conductivity in the optimization of transcranial direct current stimulation for an auditory target.’ Journal of Neural Engineering 12, № 4. doi: 10.1088/1741-2560/12/4/046028.
- . . „Nachwuchswissenschaftler in Deutschland - die Sicht eines Rückkehrers.“ Forschung und Lehre 2015, № 5: 365.
- . . ‘Bezier curves in the space of images.’ Contributed to the Fifth International Conference on Scale Space Methods and Variational Methods in Computer Vision, Lège Cap Ferret, France.
- . . ‘Redistancing dynamics for vector-valued multilabel segmentation with costly fidelity: grain identification in polycrystal images.’ Journal of Scientific Computing 63, № 1: 279–306.
- . . ‘A convex, lower semi-continuous approximation of Euler's elastica energy.’ SIAM Journal of Mathematical Analysis 47, № 1: 566–613.
- . . ‘Variational time discretization of geodesic calculus.’ IMA Journal of Numerical Analysis 35, № 3: 1011–1046.
- . ‘An elementary approach to linear programming duality with application to capacity constrained transport.’ Journal of Convex Analysis 22, № 3: 797–808.
- . ‘Scaling bounds on dissipation in turbulent flows.’ Journal of Fluid Mechanics 777: 591–603. doi: 10.1017/jfm.2015.384.
- . ‘The Spectrum of a Family of Fourth-Order Nonlinear Diffusions Near the Global Attractor.’ Communications in Partial Differential Equations 40, № 2: 191–218. doi: 10.1080/03605302.2014.963605.
- . ‘Dual potentials for capacity constrained optimal transport.’ Calculus of Variations and Partial Differential Equations 54, № 1: 573–584. doi: 10.1007/s00526-014-0795-9.
- . ‘Comparison results for the Stokes equations.’ Applied Numerical Mathematics 95: 118–129. doi: 10.1016/j.apnum.2013.12.005.
- . ‘Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems.’ Mathematics of Computation 84, № 293: 1061–1087. doi: 10.1090/S0025-5718-2014-02894-9.
- . ‘Medius analysis and comparison results for first-order finite element methods in linear elasticity.’ IMA Journal of Numerical Analysis 35, № 4: 1591–1621. doi: 10.1093/imanum/dru048.
- . A class of mixed finite element methods based on the Helmholtz decomposition in computational mechanics Dissertation thesis, Humboldt-Universität zu Berlin.
- . . ‘On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime.’ Netw. Heterog. Media 10: 321–342. doi: 10.3934/nhm.2015.10.321.
- . . ‘An analysis of crystal cleavage in the passage from atomistic models to continuum theory.’ Arch. Ration. Mech. Anal. 217: 263–308. doi: 10.1007/s00205-014-0833-y.
- . . ‘Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains.’ Nonlinearity 28, № 8. doi: 10.1088/0951-7715/28/8/2767.
- . . ‘A multiscale model for glioma spread including cell-fibre interactions and proliferation.’ Mathematical Biosciences and Engineering 13, № 2: 443–460. doi: 10.3934/mbe.2015011.
- . . ‘Dynamical features and spatial structures of the plasma interaction region of 67P/Churyumov-Gerasimenko and the solar wind.’ Planetary and Space Science 105: 101–116. doi: 10.1016/j.pss.2014.11.014.
- . . ‘Diffuse interface methods for inverse problems: case study for an elliptic Cauchy problem.’ Inverse Problems 31, № 12. doi: 10.1088/0266-5611/31/12/125002.
- . . Numerical methods for kinetic equations (Master's thesis).
online first
- . ‘Analysis of the Diffuse Domain Method for Second Order Elliptic Boundary Value Problems.’ Foundations of Computational Mathematics null, № null. doi: 10.1007/s10208-015-9292-6.
accepted / in Press (not yet published)
- . . The interface for functions in the dune-functions module arXiv, .
- . . ‘Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality.’ Annals of Probability 2015.
- . . ‘On Optical Flow Models for Variational Motion Estimation.’ Radon Book Series 2016.
submitted / under review
- . . ‘Phase Field Approach to Fluid Filled Fractures using Discontinuous Galerkin Methods.’ Mathematics and Computers in Simulation -.
- . . ‘A Discontinuous Galerkin Methods for the EEG Forward Problem.’ arXiv 2015.
- . Invariant manifolds for the porous medium equation.
- . . A quantitative geometric rigidity result in SBD.
- . . A Korn-Poincaré-type inequality for special functions of bounded deformation.
published
- . . ‘Color Bregman TV.’ SIAM Journal on Imaging Sciences 7, № 4: 2806. doi: 10.1137/130943388.
- . . ‘Poincaré and logarithmic Sobolev inequalities by decomposition of the energy landscape.’ Annals of Probability 42, № 5: 1809–1884. doi: 10.1214/14-AOP908.
- . . ‘Approximating Rough Stochastic PDEs.’ Communications on Pure and Applied Mathematics 67, № 5: 776–870. doi: 10.1002/cpa.21495.
- . ‘Invariant measure of the stochastic Allen-Cahn equation: the regime of small noise and large system size.’ Electronic Journal of Probability 19: 1–76. doi: 10.1214/EJP.v19-2813.
- . . ‘Combined State and Parameter Reduction.’ Contributed to the 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Erlangen. doi: 10.1002/pamm.201410393.
- . . ‘Traveling waves emerging in a diffusive moving filament system.’ In Managing complexity, reducing perplexity, Modeling biological systems, edited by , 91–99. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-319-03759-2_10.
- . . Mathematische Modellierung von Strukturbildung in zellulären Systemen. Paderborn: Ferdinand Schöningh.
- . ‘New results on Γ-limits of integral functionals.’ Ann. Inst. H. Poincaré Anal. Non Linéaire 31: 185–202.
- . ‘Geometric rigidity for incompatible fields and an application to strain-gradient plasticity.’ Indiana univ. Math. J. 63: 1365–1396.
- . . ‘Validation of Interface Capturing and Tracking Techniques with different Surface Tension Treatments against a Taylor Bubble Benchmark Problem.’ Comput. & Fluids 102: 336–352. doi: 10.1016/j.compfluid.2014.06.030.
- . . „Wenn die Probleme zahlreicher werden: Reduzierte Basis Methoden f\ür effiziente und gesicherte numerische Simulation.“ GAMM Rundbrief 2014/1: 6–13.
- . . Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects - FVCA 7, Berlin, June 2014. Basel : Springer International Publishing. doi: 10.1007/978-3-319-05684-5.
- . . Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems - FVCA 7, Berlin, June 2014. Basel : Springer International Publishing. doi: 10.1007/978-3-319-05591-6.
- . . ‘Efficient Parallel Simulation of Atherosclerotic Plaque Formation Using Higher Order Discontinuous Galerkin Schemes.’ In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, edited by , 617–625. Basel : Springer International Publishing. doi: 10.1007/978-3-319-05591-6_61.
- . . ‘A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method.’ In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, edited by , 421–429. Basel : Springer International Publishing. doi: 10.1007/978-3-319-05684-5_41.
- . . ‘A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries.’ In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, edited by , 695–702. Heidelberg: Springer. doi: 10.1007/978-3-319-05591-6_69.
- . . ‘A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.’ SIAM Journal on Scientific Computing 36, № 2: A714–A736. doi: 10.1137/130939122.
- . . ‘Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions.’ Math. Models and Methods in Appl. Sciences 24, № 5: 901–936. doi: 10.1142/S0218202513500711.
- . . ‘Model Reduction for Complex Hyperbolic Networks.’ Contributed to the 13th European Control Conference (ECC), June 24-27, 2014, Strasbourg, France. doi: 10.1109/ECC.2014.6862188.
- . . ‘Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems.’ Mathematical Problems in Engineering 2014: 1–13. doi: 10.1155/2014/843869.
- . . ‘An adaptive Multiscale Finite Element Method.’ Multiscale Mod. Simul. 12, № 3: 1078–1107. doi: 10.1137/120886856.
- . . ‘Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations.’ Applied Numerical Mathematics 85: 16–37. doi: 10.1016/j.apnum.2014.06.002.
- . . ‘A Numerically Stable A Posteriori Error Estimator for Reduced Basis Approximations of Elliptic Equations.’ In 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, edited by , 4094–4102. Barcelona: CIMNE.
- . . ‘A study of isogeometric analysis for scalar convection–diffusion equations.’ Applied Mathematics Letters 27: 43–48. doi: 10.1016/j.aml.2013.08.004.
- . . ‘New Methodology for the Forward Problem in EEG/MEG Source Analysis and in Brain Stimulation.’ Biomedical Engineering / Biomedizinische Technik 59: 657.
- . . ‘DTI-based multi-scale modelling and simulation of glioma growth.’ Oberwolfach Reports 2014.
- . . ‘EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications.’ In Euro-Par 2014: Parallel Processing Workshops, edited by , 530–541. Basel : Springer International Publishing. doi: 10.1007/978-3-319-14313-2_45.
- . . Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models , . doi: 10.1088/1478-3975/12/6/066014.
- . . ‘Boundary control of bidomainequations with state dependentswitching source functions in theionic model.’ Journal of Computational Physics 273: 227–242.
- . . ‘Scalable hybrid parallelization strategies for the DUNE grid interface.’ In Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2013, 583–590. doi: 10.1007/978-3-319-10705-9_57.
- . . ‘Heterogenous coupling for implicitly described domains.’ In Domain Decomposition Methods in Science and Engineering XXI, edited by , 809–817. Basel : Springer International Publishing. doi: 10.1007/978-3-319-05789-7_78.
- . . ‘A Case Study on a Quality Assurance Process for a Scientific Framework.’ IEEE Computing in Science and Engineering 16, № 3: 58–66.
- . ‘Stationary radiative transfer with vanishing absorption.’ Mathematical Models and Methods in Applied Sciences 24, № 5: 973–990. doi: 10.1142/S0218202513500735.
- . ‘Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem.’ Inverse Problems 30, № 3. doi: 10.1088/0266-5611/30/3/035009.
- . ‘Numerical methods for parameter identification in stationary radiative transfer.’ Computational Optimization and Applications 62, № 1: 67–83. doi: 10.1007/s10589-014-9657-9.
- . ‘Numerical identification of a nonlinear diffusion law via regularization in Hilbert scales.’ Inverse Problems 30, № 2. doi: 10.1088/0266-5611/30/2/025004.
- . ‘Diffusion asymptotics for linear transport with low regularity.’ Asymptotic Analysis 89, № null: 365–377. doi: 10.3233/ASY-141235.
- . ‘An Lp theory for stationary radiative transfer.’ Applicable Analysis 93, № 6: 1283–1296. doi: 10.1080/00036811.2013.826798.
- . ‘Stationary states and asymptotic behavior of aggregation models with nonlinear local repulsion.’ SIAM Journal on Applied Dynamical Systems 13, № 1: 397–424. doi: 10.1137/130923786.
- . ‘A framework for automated cell tracking in phase contrast microscopic videos based on normal velocities.’ Journal of Visual Communication and Image Representation 25, № 2: 396–409. doi: 10.1016/j.jvcir.2013.12.002.
- . . ‘Exploring the geometry of the space of shells.’ Computer Graphics Forum 33, № 5.
- . . ‘Optimal fine-scale structures in compliance minimization for a uniaxial load.’ Proceedings of the Royal Society A 470, № 2170: 20140432–20140448.
- . ‘Fractal regularity results on optimal irrigation patterns.’ Journal de Mathématiques Pures et Appliquées 2014, № Vol. 102, n. 5. doi: 10.1016/j.matpur.2014.02.008.
- . . ‘Conditions for choking in a poroelastic flow model.’ The IMA Journal of Applied Mathematics 79, № 2: 254–273.
- . . ‘Fast automated detection of crystal distortion and crystal defects in polycrystal images.’ SIAM Multiscale Modeling and Simulation 12, № 1: 1–24. doi: 10.1137/130916515.
- . ‘Long-time asymptotics for the porous medium equation: The spectrum of the linearized operator.’ Journal of Differential Equations 256, № 3: 1191–1223. doi: 10.1016/j.jde.2013.10.013.
- . ‘A remark on newest vertex bisection in any space dimension.’ Computational Methods in Applied Mathematics 14, № 3: 317–320. doi: 10.1515/cmam-2014-0013.
- . . ‘An atomistic-to-continuum analysis of crystal cleavage in a two-dimensional model problem.’ J. Nonlin. Sci. 24: 145–183. doi: 10.1007/s00332-013-9187-0.
- . . ‘Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control.’ Archive for Rational Mechanics and Analysis 124, № 3: 803–866. doi: 10.1007/s00205-014-0782-5.
- . . ‘Sparsity-Regularized Image Reconstruction of Decomposed K-edge Data in Spectral CT.’ Physics in Medicine and Biology 59, № 10. doi: 10.1088/0031-9155/59/10/N65.
- . . ‘A Multi-Channel Image Reconstruction Method for Grating-Based X-ray Phase-Contrast Computed Tomography.’ Contributed to the SPIE Medical Imaging 2014, San Diego, California, USA. doi: 10.1117/12.2043732.
- . . ‘Maximum a posteriori estimates in linear inverse problems with log-concave priors are proper Bayes estimators.’ Inverse Problems 30, № 11. doi: 10.1088/0266-5611/30/11/114004.
- . . ‘Total variation regularization in measurement and image space for PET reconstruction.’ Inverse Problems 30, № 10. doi: 10.1088/0266-5611/30/10/105003.
- . . ‘Registration of noisy images via maximum a-posteriori estimation.’ Lecture notes in computer science 8545 LNCS: 240. doi: 10.1007/978-3-319-08554-8_24.
- . . ‘On the asymptotic behavior of a boltzmann-type price formation model.’ Communications in Mathematical Sciences 12, № 7: 1361. doi: 10.4310/CMS.2014.v12.n7.a10.
- . . ‘Partial differential equation models in the socio-economic sciences.’ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, № 2028. doi: 10.1098/rsta.2013.0406.
- . . ‘Mean field games with nonlinear mobilities in pedestrian dynamics.’ Discrete and Continuous Dynamical Systems - Series B 19, № 5: 1333. doi: 10.3934/dcdsb.2014.19.1311.
- . . ‘Mathematical methods in biomedical imaging.’ GAMM-Mitteilungen / GAMM-Reports 37, № 2: 183. doi: 10.1002/gamm.201410008.
- . . ‘Inverse problems in geographical economics: Parameter identification in the spatial Solow model.’ Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 372, № 2028. doi: 10.1098/rsta.2013.0402.
accepted / in Press (not yet published)
- . . ‘Proximal ADMM for Multi-Channel Image Reconstruction in Spectral X-ray CT.’ IEEE Transactions on Medical Imaging -.
- . . ‘Performance of First-Order Algorithms for TV Penalized Weighted Least-Squares Denoising Problem.’ Contributed to the ICISP 2014, Cherbourg, Normandy, France.
submitted / under review
published
- . . ‘Atlas-based whole-body PET-CT segmentation using a passive contour distance.’ Lecture notes in computer science 7766 LNCS: 82–92.
- . . Rough Burgers-like equations with multiplicative noise. doi: 10.1007/s00440-011-0392-1.
- . . ‘Rough Burgers-like equations with multiplicative noise.’ Probability Theory and Related Fields 157, № 3-4: 71–126. doi: 10.1007/s00440-013-0538-4.
- . . ‘Tightness for a stochastic Allen–Cahn equation.’ Stochastics and Partial Differential Equations: Analysis and Computations 1: 175–203. doi: 10.1007/s40072-013-0004-4.
- . ‘Pattern forming instabilities driven by non-diffusive interaction.’ Networks and Heterogeneous Media 2013, № 8, no. 1: 397–432. doi: 10.3934/nhm.2013.8.397.
- . ‘Γ-convergence and H-convergence of linear elliptic operators.’ J. Math. Pures Appl. 99: 321–329.
- . . ‘Galerkin approximations for the stochastic Burgers equation.’ SIAM Journal on Numerical Analysis 51, № 1: 694–715. doi: 10.1137/110845756.
- . . ‘Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations.’ Annals of Applied Probability 23, № 5: 1913–1966. doi: 10.1214/12-AAP890.
- . . ‘Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes.’ In Advanced Finite Element Methods and Applications, edited by , 27–56. Düsseldorf: Springer VDI Verlag.
- . . ‘Analysis of a DG-XFEM Discretization for a Class of Two-Phase Mass Transport Problems.’ SIAM J. Numer. Anal. 51: 958–983. doi: 10.1137/120875260.
- . . ‘Accuracy of Two-Phase Flow Simulations.’ In Proc. Appl. Math. Mech., 595–598. Heidelberg: Springer. doi: 10.1002/pamm.201310278.
- . . ‘The localized reduced basis multi-scale method with online enrichment.’ Oberwolfach Reports 7: 406–409. doi: 10.4171/OWR/2013/07.
- . . ‘Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing.’ C. R. Acad. Sci. Paris, Ser. I 351: 901–906. doi: 10.1016/j.crma.2013.10.028.
- . . ‘Error Control Based Model Reduction for Parameter Optimization of Elliptic Homogenization Problems.’ In Proceedings of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations. doi: 10.3182/20130925-3-FR-4043.00053.
- . . ‘Homogenization of the degenerate two-phase flow equations.’ Math. Models and Methods in Appl. Sciences 23, № 12: 2323–2352. doi: 10.1142/S0218202513500334.
- . . ‘Design and Rationale of a Quality Assurance Process for a Scientific Framework.’ In Proceeding of the 2013 International workshop on Software engineering for computational science and engineering, 58–67. doi: 10.1109/SECSE.2013.6615100.
- . . ‘An Unfitted Interior Penalty Discontinuous Galerkin Method for Incompressible Navier-Stokes Two-Phase Flow.’ International Journal for Numerical Methods in Fluids 71, № 3: 269–293. doi: 10.1002/fld.3653.
- . ‘Stationary states of quadratic diffusion equations with long-range attraction.’ Communications in Mathematical Sciences 11, № 3: 709–738. doi: 10.4310/CMS.2013.v11.n3.a3.
- . ‘Rectification properties of conically shaped nanopores: Consequences of miniaturization.’ Physical Chemistry Chemical Physics 15, № 39: 16917–16926. doi: 10.1039/c3cp53105h.
- . ‘On a Boltzmann-type price formation model.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, № 2157. doi: 10.1098/rspa.2013.0126.
- . ‘Multiscale methods for polyhedral regularizations.’ SIAM Journal on Optimization 23, № 3: 1424–1456. doi: 10.1137/110858136.
- . ‘Individual based and mean-field modeling of direct aggregation.’ Physica D: Nonlinear Phenomena 260, № null: 145–158. doi: 10.1016/j.physd.2012.11.003.
- . ‘Higher-order TV methods - Enhancement via Bregman iteration.’ Journal of Scientific Computing 54, № null: 269–310. doi: 10.1007/s10915-012-9650-3.
- . ‘Convergence rates in ℓ1-regularization if the sparsity assumption fails.’ Inverse Problems 29, № 2. doi: 10.1088/0266-5611/29/2/025013.
- . ‘A hyperelastic regularization energy for image registration.’ SIAM Journal on Scientific Computing 35, № 1. doi: 10.1137/110835955.
- . ‘Structural and functional integrity of spermatozoa is compromised as a consequence of acute uropathogenic E. Coli-associated epididymitis.’ Biology of Reproduction 89, № 3. doi: 10.1095/biolreprod.113.110379.
- . ‘Identification of nonlinearities in transport-diffusion models of crowded motion.’ Inverse Problems and Imaging 7, № 4: 1157–1182. doi: 10.3934/ipi.2013.7.1157.
- . ‘EM-TV methods for inverse problems with poisson noise.’ In Level Set and PDE-based Reconstruction Methods, edited by , 71–142. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-319-01712-9-2.
- . ‘A guide to the TV zoo.’ In Level Set and PDE-based Reconstruction Methods, edited by , 1–70. N/A: unbekannt / n.a. / unknown. doi: 10.1007/978-3-319-01712-9-1.
- . . ‘A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models.’ Journal of Mathematical Imaging and Vision 47, № 3: 179–209.
- . . ‘Ground waves in atomic chains with bi-monomial double-well potential.’ Nonlinear Analysis: Theory, Methods and Applications 76: 41–51. doi: 10.1016/j.na.2012.07.013.
- . . ‘Subsonic phase transition waves in bistable lattice models with small spinodal region.’ SIAM Journal on Mathematical Analysis 45, № 5: 2625–2645. doi: 10.1137/120877878.
- . . ‘Interface dynamics in discrete forward-backward diffusion equations.’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 11, № 4: 1261–1297. doi: 10.1137/130915959.
- . ‘Variational techniques for assessing the technological signature of flat surfaces.’ Optimization and Engineering 14, № 1: 155–174. doi: 10.1007/s11081-011-9173-z.
- . . ‘Convex relaxation of a class of vertex penalizing functionals.’ Journal of Mathematical Imaging and Vision 47, № 3: 278–302. doi: 10.1007/s10851-012-0347-x.
- . . ‘Segmentation of Crystal Defects via Local Analysis of Crystal Distortion.’ In Proceedings of the 8'th International Conference on Computer Vision Theory and Applications (VISAPP'13).
- . . ‘A simple and efficient scheme for phase field crystal simulation.’ ESAIM: M2AN 47, № 5: 1413–1432. doi: 10.1051/m2an/2013074.
- . . ‘Discrete geodesic calculus in the space of viscous fluidic objects.’ SIAM Journal on Imaging Sciences 6, № 4.
- . . ‘A Phase Field based PDE Constraint Optimization Approach to Time Discrete Willmore Flow.’ International Journal of Numerical Analysis and Modeling 10, № 1: 116–138.
- . . ‘Discrete geodesic regression in shape space.’ In 9th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition.
- . ‘Crossover of the coarsening rates in demixing of binary viscous liquids.’ Communications in Mathematical Sciences 11, № 2: 441–464.
- . ‘Maximal mixing by incompressible fluid flows.’ Nonlinearity 26, № 12: 3279–3289. doi: 10.1088/0951-7715/26/12/3279.
- . ‘Laminar Boundary Layers in Convective Heat Transport.’ Communications in Mathematical Physics 324, № 3: 995–1031. doi: 10.1007/s00220-013-1826-7.
- . . ‘On the coarsening rates for attachment-limited kinetics.’ SIAM Journal on Mathematical Analysis 45, № 1: 324–344. doi: 10.1137/120865197.
- . ‘Discrete reliability for Crouzeix-Raviart FEMs.’ SIAM Journal on Numerical Analysis 51, № 5: 2935–2955. doi: 10.1137/130915856.
- . ‘Quasi-optimal adaptive pseudostress approximation of the Stokes equations.’ SIAM Journal on Numerical Analysis 51, № 3: 1715–1734. doi: 10.1137/110852346.
- . . ‘Model reduction for multiscale problems.’ Oberwolfach Reports 39: 2228–2230. doi: 10.4171/OWR/2013/39.
- . . ‘Inverse problems in imaging.’ Large Scale Inverse Problems. Computational Methods and Applications in the Earth Sciences (M. Cullen, MA Freitag, S. Kindermann, and R. Scheichl, eds.), Radon Ser. Comput. Appl. Math 13: 135–180.
- . . ‘EM-TV Methods for Inverse Problems with Poisson Noise.’ In Level Set and PDE Based Reconstruction Methods in Imaging, edited by , 71–142. doi: 10.1007/978-3-319-01712-9_2.
- . . ‘The influence of sulcus width on simulated electric fields induced by transcranial magnetic stimulation.’ Physics in Medicine and Biology 58, № 14: 4881. doi: 10.1088/0031-9155/58/14/4881.
- . . ‘Complete electrode model in EEG: relationship and differences to the point electrode model (vol 57, pg 999, 2012).’ Physics in Medicine and Biology 58, № 185: 185–185. doi: 10.1088/0031-9155/58/1/185.
- . . ‘A Unified Software Framework for Empirical Gramians.’ Journal of Mathematics 2013, № 2013: 1–6. doi: 10.1155/2013/365909.
- . . ‘On a mean field game optimal control approach modeling fast exit scenarios in human crowds.’ Contributed to the Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, Firenze. doi: 10.1109/CDC.2013.6760360.
- . . ‘An adaptive inverse scale space method for compressed sensing.’ Mathematics of Computation 82: 269–299. doi: 10.1090/S0025-5718-2012-02599-3.
online first
- . . ‘An explicit update scheme for inverse parameter and interface estimation of piecewise constant coefficients in linear elliptic PDEs.’ SIAM Journal on Scientific Computing 35.
published
- . . ‘The iteratively regularized Gauss-Newton method with convex constraints and applications in 4Pi microscopy.’ Inverse Problems 28, № 1. doi: 10.1088/0266-5611/28/1/015012.
- . . ‘A variational approach for sharpening high dimensional images.’ SIAM Journal on Imaging Sciences 5, № 1: 150–178. doi: 10.1137/100810356.
- . . ‘Sparse recovery in myocardial blood flow quantification via PET.’ Contributed to the IEEE NSS/MIC, San Diego.
- . . ‘Reconstruction of short time PET scans using Bregman iterations.’ Contributed to the IEEE NSS/MIC, San Diego.
- . . ‘Nonlinear Poisson-Nernst-Planck equations for ion flux through confined geometries.’ Nonlinearity 25, № 4: 961–990. doi: 10.1088/0951-7715/25/4/961.
- . . ‘Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors .’ Inverse Problems 28, № 12: 125012. doi: 10.1088/0266-5611/28/12/125012.
- . . ‘Triviality of the 2D stochastic Allen-Cahn equation.’ Electronic Journal of Probability 17, № 39: 1–14. doi: 10.1214/EJP.v17-1731.
- . . ‘Simultaneous Blowup and Mass Separation During Collapse in an Interacting System of Chemotactic Species.’ Differential and Integral Equations 25, № 3-4: 251–288. doi: 10.57262/die/1356012736.
- Asymptotic Analysis of a Chemotaxis System with Non-Diffusive Memory MiS Preprint Repository.
- . ‘Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy.’ SIAM Journal on Mathematical Analysis 44, № 4: 2372–2400. doi: 10.1137/110824851.
- . . ‘Asymptotic analysis of nonsymmetric linear operators via Γ-convergence.’ SIAM Journal on Mathematical Analysis 44, № 3: 1617–1635. doi: 10.1137/110834330.
- . . ‘Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise.’ Journal of Differential Equations 252, № 1: 114–136. doi: 10.1016/j.jde.2011.08.050.
- . . ‘Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem.’ SIAM J. Sci. Comput. 34: 2740–2759. doi: 10.1137/110855235.
- . . ‘Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwells Equations.’ In Numerical and Symbolic Scientific Computing: Progress and Prospects, edited by , 105–122. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-7091-0794-2_6.
- . . ‘Extension of centered hydrodynamical schemes to unstructured deforming conical meshes: the case of circles.’ In CEMRACS'11: Multiscale Coupling of Complex Models in Scientific Computing, 135–162. Les Ulis: EDP Sciences. doi: 10.1051/proc/201238008.
- . . ‘Error control based model reduction for multiscale problems.’ In Proceedings of Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, edited by , 1–10.
- . . ‘Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management.’ In Progress in Industrial Mathematics at ECMI 2010, 561–567. Heidelberg: Springer. doi: 10.1007/978-3-642-25100-9_65.
- . . ‘A reduced basis method for parameter optimization of multiscale problems.’ In Submitted to Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012.
- . . On Finitely Summable K-Homology Dissertation thesis, Universität Münster.
- . . ‘The Localized Reduced Basis Multiscale Method.’ Contributed to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske.
- . . ‘System Testing for a Scientific Framework Using a Regression Test Environment.’ Computing in Science and Engeneering 14, № 2: 38–45. doi: 10.1109/MCSE.2011.115.
- . . ‘DUNE-UDG: A Cut-Cell Framework for Unfitted Discontinuous Galerkin Methods.’ In Advances in DUNE, edited by , 89–100. Heidelberg: Springer. doi: 10.1007/978-3-642-28589-9_7.
- . ‘Sparse recovery in myocardial blood flow quantification via PET.’ Contributed to the 2011 IEEE Nuclear Science Symposium and Medical Imaging Conference, NSS/MIC 2011, Valencia, esp. doi: 10.1109/NSSMIC.2011.6153707.
- . ‘Regularized regression and density estimation based on optimal transport.’ Applied Mathematics Research eXpress 2012, № 2: 209–253. doi: 10.1093/amrx/abs007.
- . ‘Reconstruction of short time PET scans using Bregman iterations.’ Contributed to the 2011 IEEE Nuclear Science Symposium and Medical Imaging Conference, NSS/MIC 2011, Valencia, esp. doi: 10.1109/NSSMIC.2011.6153884.
- . ‘Pipeline for motion correction in dual gated PET.’ Contributed to the 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record, NSS/MIC 2012, Anaheim, CA, usa. doi: 10.1109/NSSMIC.2012.6551681.
- . ‘Mass-preserving motion correction of PET: Displacement field vs. spline transformation.’ Contributed to the 2011 IEEE Nuclear Science Symposium and Medical Imaging Conference, NSS/MIC 2011, Valencia, esp. doi: 10.1109/NSSMIC.2011.6152559.
- . ‘Mass-preserving motion correction of dual gated cardiac PET.’ Contributed to the 2011 IEEE Nuclear Science Symposium and Medical Imaging Conference, NSS/MIC 2011, Valencia, esp. doi: 10.1109/NSSMIC.2011.6153658.
- . ‘Impact of physical noise modeling on image segmentation in echocardiography.’ Contributed to the 3rd Eurographics Workshop on VisualComputing in Biology and Medicine, EG VCBM 2012, Norrkoping, swe. doi: 10.2312/VCBM/VCBM12/033-040.
- . ‘Atlas-based segmentation using passive contours.’ Contributed to the 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record, NSS/MIC 2012, Anaheim, CA, usa. doi: 10.1109/NSSMIC.2012.6551688.
- . ‘A simplified pipeline for motion correction in dual gated cardiac PET.’ Contributed to the Workshops Bildverarbeitung fur die Medizin: Algorithmen - Systeme - Anwendungen, BVM 2012 - Workshop on Image Processing for Medicine: Algorithms - Systems - Applications, BVM 2012, Berlin, deu. doi: 10.1007/978-3-642-28502-8-11.
- . . ‘Comparison of boundary element and finite element approaches to the EEG forward problem.’ Biomedical Engineering / Biomedizinische Technik 57 Suppl 1.
- . . ‘Comparison of direct and reciprocal forward modeling approaches in EEG source analysis.’ Biomedical Engineering / Biomedizinische Technik 57 1: –. doi: 10.1515/bmt-2012-4069.
- . . ‘Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: depth localization and source separation for focal primary currents.’ NeuroImage 61, № 4: 1364–1382. doi: 10.1016/j.neuroimage.2012.04.017.
- . . ‘Diffeomorphic susceptibility artifact correction of diffusion-weighted magnetic resonance images.’ Physics in Medicine and Biology 57, № 18: 5715–5731.
- . . ‘Motion Correction in Dual Gated Cardiac PET Using Mass-Preserving Image Registration.’ IEEE Transactions on Medical Imaging 31, № 3: 698–712.
- . . ‘Motion correction in dual gated cardiac PET using mass preserving image registration.’ IEEE Transactions on Medical Imaging 31, № 3: 171–174. doi: 10.1109/TMI.2011.2175402.
- . . ‘A variational approach for sharpening high-dimensional images.’ SIAM Journal on Imaging Sciences 5, № 1: 150–178. doi: 10.1137/100810356.
- . . ‘The iteratively regularized Gauss-Newton method with convex constraints and applications in 4pi-microscopy.’ Inverse Problems 28. doi: 10.1088/0266-5611/28/1/015012.
- . . ‘On selection criteria for problems with moving inhomogeneities.’ Continuum Mechanics and Thermodynamics 24, № 1: 21–36. doi: 10.1007/s00161-011-0206-9.
- . . ‘Oscillatory waves in discrete scalar conservation laws.’ Mathematical Models and Methods in Applied Sciences 22, № 1: 1150002, 21. doi: 10.1142/S021820251200585X.
- . . ‘Self-similar solutions to a kinetic model for grain growth.’ Journal of Nonlinear Science 22, № 3: 399–427. doi: 10.1007/s00332-011-9122-1.
- . . ‘Kramers and non-Kramers phase transitions in many-particle systems with dynamical constraint.’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 10, № 3: 818–852. doi: 10.1137/110851882.
- . . ‘Simulation of cerebral infusion tests using a poroelastic model.’ International Journal of Numerical Analysis and Modeling Series B 3, № 1: 52–64.
- . . ‘Optimization methods on Riemannian manifolds and their application to shape space.’ SIAM Journal on Optimization 22, № 2: 596–627. doi: 10.1137/11082885X.
- . . ‘A Phase-Field Model for Compliance Shape Optimization in Nonlinear Elasticity.’ ESAIM: Control, Optimisation and Calculus of Variations 18, № 1: 229–258. doi: 10.1051/cocv/2010045.
- . . ‘Time-Discrete Geodesics in the Space of Shells.’ Computer Graphics Forum 31, № 5: 1755–1764. doi: 10.1111/j.1467-8659.2012.03180.x.
- . . ‘Comparison results of finite element methods for the Poisson model problem.’ SIAM J. Numer. Anal. 50, № 6: 2803–2823. doi: 10.1137/110845707.
- . . ‘Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients.’ Annals of Applied Probability 22, № 4: 1611–1641.
- . ‘Sensitivity of EEG leads to volume conductor properties.’ Biomedical Engineering / Biomedizinische Technik 57 Suppl 1: 793. doi: 10.1515/bmt-2012-4065.
- . ‘Sensitivity of EEG leads to volume conductor properties.’ Biomedical Engineering / Biomedizinische Technik 57, № SI-1-Track-O: 793. doi: 10.1515/bmt-2012-4065.
- . . ‘Reduced Basis Model Reduction of Parametrized Two-Phase Flow in Porous Media.’ In 7th Vienna International Conference on Mathematical Modelling, 722–727. doi: 10.3182/20120215-3-AT-3016.00128.
- . . ‘Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation.’ SIAM Journal on Scientific Computing 34: A937–A969. doi: 10.1137/10081157X.
- . . ‘Influences of skull segmentation inaccuracies on EEG source analysis.’ NeuroImage 62, № 1: 418. doi: 10.1016/j.neuroimage.2012.05.006.
- . ‘Hierarchical Bayesian inference for the EEG inverse problem using realistic FE head models: Depth localization and source separation for focal primary currents.’ NeuroImage 61, № 4: 1364–1382. doi: 10.1016/j.neuroimage.2012.04.017.
- . ‘Complete electrode model in EEG: relationship and differences to the point electrode model.’ Physics in Medicine and Biology 57, № 4: 999–1017. doi: 10.1088/0031-9155/57/4/999.
online first
- . . ‘A multiscale approach to cell migration in tissue networks.’ Mathematical Models and Methods in the Applied Sciences 22, № 3.
accepted / in Press (not yet published)
- . . ‘A simplified pipeline for motion correction in dual gated cardiac PET.’ Contributed to the Bildverarbeitung für die Medizin, Berlin.
published
- . . ‘Hierarchical bayesian models for eeg inversion: Depth localization and source separation for focal sources in realistic FE head models.’
- . . ‘Inverse problems in ion channel modelling.’ Inverse Problems 27, № 8. doi: 10.1088/0266-5611/27/8/083001.
- . . „Angewandte Analysis.“ In Facettenreiche Mathematik: Einblicke in die moderne mathematische Forschung für alle, die mehr von Mathematik verstehen wollen, herausgegeben von , 327–346. Wiesbaden: Vieweg Verlag. doi: 10.1007/978-3-8348-8173-1_17.
- . . ‘Origins of Theoretical Biology.’ European Communications in Mathematical and Theoretical Biology 2011, № 14: 94–103.
- . ‘Asymptotic analysis of a second-order singular perturbation model for phase transitions.’ Calculus of Variations and Partial Differential Equations 41, № 1-2: 127–150. doi: 10.1007/s00526-010-0356-9.
- . . ‘Higher order pathwise numerical approximations of SPDEs with additive noise.’ SIAM Journal on Numerical Analysis 49, № 2: 642–667. doi: 10.1137/080740714.
- . . ‘Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, № 2130: 1563–1576. doi: 10.1098/rspa.2010.0348.
- . . ‘Efficient simulation of nonlinear parabolic SPDEs with additive noise.’ Annals of Applied Probability 21, № 3: 908–950. doi: 10.1214/10-AAP711.
- . . Taylor approximations for stochastic partial differential equations. N/A: Selbstverlag / Eigenverlag. doi: 10.1137/1.9781611972016.
- . . ‘Convergence of the stochastic Euler scheme for locally Lipschitz coefficients.’ Foundations of Computational Mathematics 11, № 6: 657–706. doi: 10.1007/s10208-011-9101-9.
- . . ‘A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems.’ In Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011) held in Paris, France, 6-8 June 2011, edited by , 343–354. Barcelona: CIMNE.
- . . ‘Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition.’ Mathematical and Computer Modelling of Dynamical Systems 17, № 2: 145–161. doi: 10.1080/13873954.2010.514703.
- . . ‘Inflow-Implicit/Outflow-Explicit scheme for solving advection equations.’ In Finite Volumes for Complex Applications VI - Problems & Perspectives, edited by , 683–691. Heidelberg: Springer. doi: 10.1007/978-3-642-20671-9_72.
- . . ‘Nitsche-XFEM for a Transport Problem in Two- Phase Incompressible Flows.’ In Proc. Appl. Math. Mech., 613–614. New York City: John Wiley & Sons. doi: 10.1002/pamm.201110296.
- . ‘Hierarchical bayesian models for EEG inversion: Depth localization and source separation for focal sources in realistic FE head models.’ Biomedical Engineering / Biomedizinische Technik 56: 1–4. doi: 10.1515/BMT.2011.817.
- . . ‘Supporting the Testing of Scientific Frameworks with Software Product Line Engineering: A Proposed Approach.’ In Proceeding of the 4th international workshop on Software engineering for computational science and engineering, 10–18. doi: 10.1145/1985782.1985785.
- . . ‘An Unfitted Discontinuous Galerkin Method for Pore-Scale Simulations of Solute Transport.’ Mathematics and Computers in Simulation 81, № 10: 2051–2061. doi: 10.1016/j.matcom.2010.12.024.
- . . ‘A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space.’ Mathematical and Computer Modelling of Dynamical Systems 2011, № 17 (4): 423–442. doi: 10.1080/13873954.2011.547674.
- . . ‘A Note on Homogenization of Advection-Diffusion Problems with Large Expected Drift.’ Zeitschrift für Analysis und ihre Anwendungen 2011, № 30(3): 319–339. doi: 10.4171/ZAA/1437.
- . Sparse Model-Based Reconstruction in Dynamic Positron Emission Tomography.
- . . ‘In situ visualization of damaged DNA in human sperm by Raman microspectroscopy.’ Human Reproduction 26, № 7: 1641–1649.
- . . ‘Continuous limit of a crowd motion and herding model: Analysis and numerical simulations.’ Kinetic and Related Methods 4: 1025–1047.
- . . ‘Population dynamics in a spatial Solow model with a convex-concave production function.’ In Mathematical and Statistical Methods for Actuarial Sciences and Finance, edited by . Heidelberg: Springer.
- . . ‘Action minimising fronts in general FPU-type chains.’ Journal of Nonlinear Science 21, № 1: 33–55. doi: 10.1007/s00332-010-9075-9.
- . . ‘On a model for mass aggregation with maximal size.’ Kinetic and Related Models 4, № 2: 427–439. doi: 10.3934/krm.2011.4.427.
- . . ‘Hysteresis and phase transition in many-particle storage systems.’ Continuum Mechanics and Thermodynamics 23, № 3: 211–231. doi: 10.1007/s00161-010-0178-1.
- . . ‘Kramers' formula for chemical reactions in the context of Wasserstein gradient flows.’ Communications in Mathematical Sciences 9, № 2: 623–635. doi: 10.4310/CMS.2011.v9.n2.a15.
- . . ‘Homoclinic standing waves in focusing DNLS equations.’ Discrete and Continuous Dynamical Systems - Series A 31, № 3: 737–752. doi: 10.3934/dcds.2011.31.737.
- . . ‘Filament breaches during air-gap spinning.’ Chemical Fibers International 61: 38–39.
- . ‘On the Hölder regularity of the landscape function.’ Interfaces and Free Boundaries 13, № 2: 191–222. doi: 10.4171/IFB/254.
- . . ‘Robust optimisation with normal vectors on critical manifolds of transient stability loss.’ Journal of Nonlinear Science 21: 57–92. doi: 10.1007/s00332-010-9076-8.
- . . ‘Stability-preserving optimization in presence of fast disturbances.’ IEEE Transactions on Automatic Control 56, № 11: 2683–2687. doi: 10.1109/TAC.2011.2160029.
- . . ‘A Continuum Mechanical Approach to Geodesics in Shape Space.’ International Journal of Computer Vision 93, № 3: 293–318. doi: 10.1007/s11263-010-0416-9.
- . . ‘An elasticity-based covariance analysis of shapes.’ International Journal of Computer Vision 92, № 3: 281–295. doi: 10.1007/s11263-010-0358-2.
- . . ‘Variational methods in shape analysis.’ In Handbook of Mathematical Methods in Imaging, edited by , 1363–1401. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-0-387-92920-0_31.
- . . ‘A level set based shape optimization method for an elliptic obstacle problem.’21: 619–649.
- . ‘Rayleigh-Bénard convection: Improved bounds on the Nusselt number.’ Journal of Mathematical Physics 52, № 8. doi: 10.1063/1.3623417.
- . . ‘On the coarsening rates in demixing binary viscous liquids.’ Oberwolfach Reports 8, № 4. doi: 10.4171/OWR/2011/55.
- . . Scaling laws in two models for thermodynamically driven fluid flows Dissertation thesis, Universität Leipzig. Leipzig.
- . . (Nonlocal) Total Variation in Medical Imaging Dissertation thesis, WWU Münster.
- . . ‘Primal and Dual Bregman Methods with Application to Optical Nanoscopy.’ International Journal of Computer Vision 92, № 2: 211–229. doi: 10.1007/s11263-010-0339-5.
- . . ‘Error estimates for general fidelities.’ El. Trans. Numer. Anal. 38: 44–68.
- . . ‘On some models for cancer cell migration through tissue.’ Mathematical Biosciences and Engineering 8: 575–589.
- . . ‘Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations.’ In Finite Volumes for Complex Applications VI - Problems & Perspectives, edited by , 369–377. Heidelberg: Springer. doi: 10.1007/978-3-642-20671-9_39.
- . . ‘Reconstruction of short time PET scans using Bregman iterations.’ Contributed to the IEEE NSS/MIC 2011, Valencia, Spain. doi: 10.1109/NSSMIC.2011.6153884.
- . ‘Hierarchical Bayesian Models for EEG Inversion: Depth Localization and Source Separation for Focal Sources in Realistic FE Head Models.’ Contributed to the Annual meeting of the DGBMT, Freiburg.
- . . ‘Mathematical modeling with stochastic processes and stochastic differential equations.’ European Communications in Mathematical and Theoretical Biology 14: 106–117.
- . . ‘Detection of Sperm DNA damage by Raman microspectroscopy.’ doi: 10.1016/j.fertnstert.2011.07.900.
- . . ‘In situ visualization of damaged DNA in human sperm by Raman microspectroscopy.’ Human Reproduction 26, № 7: 1641–1649. doi: 10.1093/humrep/der122.
- . . ‘An XFEM method for modeling geometrically elaborate crack propagation in brittle materials.’ International Journal for Numerical Methods in Engineering 88: 1042–1065. doi: 10.1002/nme.3211.
- . . ‘Upper bounds on coarsening rates in demixing binary viscous liquids.’ SIAM Journal on Mathematical Analysis 43, № 1: 134. doi: 10.1137/090775142.
submitted / under review
- . Mathematical modeling, analysis and numerical simulations for the influence of heat shock proteins on tumor invasion , .
- . . Mathematical analysis and numerical simulations for a system modeling acid-mediated tumor cell invasion , .
- . . A minimal mathematical model for the dynamics of (TNF-) receptor signaling , .
published
- . . ‘A solver for dynamic PET reconstructions based on forward-backward- splitting.’ Contributed to the ICNAAM 2010, Crete. doi: 10.1063/1.3498318.
- . . ‘Scalable distributed simulation of large dense crowds using the Real-Time Framework (RTF).’ Lecture notes in computer science 6271 LNCS, № PART 1: 572–583.
- . . ‘On the short time asymptotic of the stochastic Allen-Cahn equation.’ Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques 46, № 4: 965–975. doi: 10.1214/09-AIHP333.
- . . ‘Sharp Interface Limit for Invariant Measures of a Stochastic Allen-Cahn Equation.’ Communications on Pure and Applied Mathematics 63, № 8: 1071–1109. doi: 10.1002/cpa.20323.
- . ‘Qualitative behavior of a Keller-Segel model with non-diffusive memory.’ Communications in Partial Differential Equations 35, № 2: 245–274. doi: 10.1080/03605300903473400.
- . . ‘Topological flow structure in a mathematical model for rotation-mediated cell aggregation.’ In Topological Methods in Data Analysis and Visualization - Theory, Algorithms, and Applications, edited by , 193–204. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-642-15014-2_16.
- . ‘A note on nonsimultaneous blow-up for a drift-diffusion model.’ Differential and Integral Equations 23, № 5-6: 451–462. doi: 10.57262/die/1356019306.
- . ‘Homogenization of fiber reinforced brittle materials: The intermediate case.’ Advances in Calculus of Variations 3, № 4: 345–370. doi: 10.1515/ACV.2010.011.
- . . ‘A unified existence and uniqueness theorem for stochastic evolution equations.’ Bulletin of the Australian Mathematical Society 81, № 1: 33–46. doi: 10.1017/S0004972709000677.
- . . ‘An improved maximum allowable transfer interval for $L^p$-stability of networked control systems.’ IEEE Transactions on Automatic Control 55, № 1: 179–184. doi: 10.1109/TAC.2009.2033771.
- . . ‘Taylor expansions of solutions of stochastic partial differential equations with additive noise.’ Annals of Probability 38, № 2: 532–569. doi: 10.1214/09-AOP500.
- . . ‘Taylor expansions of solutions of stochastic partial differential equations.’ Discrete and Continuous Dynamical Systems - Series B 14, № 2: 515–557. doi: 10.3934/dcdsb.2010.14.515.
- . . A New Inflow-Implicit/Outflow-Explicit Finite Volume Method for Solving Variable Velocity Advection Equations , .
- . . A new problem adapted hierarchical model reduction technique based on reduced basis methods and dimensional splitting , .
- . . Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems.
- . . ‘A generic interface for parallel and adaptive scientific computing: Abstraction principles and the DUNE-FEM module.’ Computing 90, № 3-4: 165–196. doi: 10.1007/s00607-010-0110-3.
- . . ‘A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach.’ SIAM Journal on Scientific Computing 32, № 3: 1527–1544. doi: 10.1137/09075946X.
- . . ‘The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift.’ Networks and Heterogeneous Media 5, № 4: 711–744. doi: 10.3934/nhm.2010.5.711.
- . . ‘A mixed finite element method for nonlinear diffusion equations.’ Kinetic and Related Methods 3: 59–83.
- . . ‘On a spatial Solow model with technological diffusion and nonconcave production function.’ Nonlinear Analysis: Real World Applications 11, № 5: 3858–3876. doi: 10.1016/j.nonrwa.2010.01.016.
- . . ‘Bregmanized nonlocal regularization for deconvolution and sparsereconstruction .’ SIAM Journal on Imaging Sciences 3, № 3: 253–276. doi: 10.1137/090746379.
- . ‘A solver for dynamic PET reconstructions based on forward-backward- splitting.’ Contributed to the International Conference on Numerical Analysis and Applied Mathematics 2010, ICNAAM-2010, Rhodes, grc. doi: 10.1063/1.3498318.
- . . ‘A Solver for Dynamic PET Reconstruction based on Forward-Backward Splitting .’ Contributed to the ICNAAM 2010.
- . . ‘Heteroclinic standing waves in defocusing DNLS equations: variational approach via energy minimization.’ Applicable Analysis 89, № 10: 1591–1602. doi: 10.1080/00036811.2010.492504.
- . ‘Estimates on path functionals over Wasserstein spaces.’ SIAM Journal on Mathematical Analysis 42, № 3: 1179–1217. doi: 10.1137/100782693.
- . . ‘Multi-fluid poro-elastic modelling of the CSF infusion test.’ In 6th World Congress of Biomechanics (WCB 2010), IFMBE Proceedings, 362–365.
- . . A Framework for Automated Cell Tracking in Phase Contrast Microscopic Videos based on Normal Velocities , .
- . . ‘Mathematical modeling and simulation of nanopore blocking by precipitation.’ J. Phys.: Cond. Matt. 22: 45401. doi: 10.1088/0953-8984/22/45/454101.
- . . ‘Stability analysis of the inverse transmembrane potential problem in electrocardiography.’ Inverse Problems 26, № 10: 105012. doi: 10.1088/0266-5611/26/10/105012.
- . . ‘A mixed finite element method for nonlinear diffusion equations.’ Kinetic and Related Methods 3: 59–83.
- . . ‘A unified primal-dual algorithm framework based on Bregman iteration.’ J Sci Comp 3.
- . . ‘Infinite harmonic chain with heavy mass.’ Communications on Pure and Applied Analysis 9, № 1: 61–75. doi: 10.3934/cpaa.2010.9.61.
- . . ‘Riemann solvers and undercompressive shocks of convex FPU chains.’ Nonlinearity 23, № 2: 277–304. doi: 10.1088/0951-7715/23/2/004.
- . . ‘Unimodal wavetrains and solitons in convex Fermi-Pasta-Ulam chains.’ Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, № 4: 753–785. doi: 10.1017/S0308210509000146.
- . . ‘Heteroclinic travelling waves in convex FPU-type chains.’ SIAM Journal on Mathematical Analysis 42, № 4: 1483–1504. doi: 10.1137/080743147.
- . ‘Motion correction of cardiac PET using mass-preserving registration.’ Contributed to the 2010 IEEE Nuclear Science Symposium, Medical Imaging Conference, NSS/MIC 2010 and 17th International Workshop on Room-Temperature Semiconductor X-ray and Gamma-ray Detectors, RTSD 2010, Knoxville, TN, usa. doi: 10.1109/NSSMIC.2010.5874418.
- . . Improved Dynamic PET via Kinetic Models and Operator Splitting.
- . . ‘Nonlinear cross-diffusion with size exclusion.’ SIAM Journal on Mathematical Analysis 42, № 6: 2842–2871. doi: 10.1137/100783674.
- . . ‘A continuity equation based optical flow method for cardiac motion correction in 3D PET data.’ In Medical Imaging and Augmented Reality: 5th International Workshop, MIAR 2010, Beijing, China, September 19-20, 2010, Proceedings (Lecture Notes in ... Vision, Pattern Recognition, and Graphics), edited by , 88–97. Heidelberg: Springer. doi: 10.1007/978-3-642-15699-1_10.
- . . ‘On a stochastic reaction-diffusion system modeling pattern formation on seashells.’ JMB 60: 765–796.
- . ‘On a Time-Dependent Fluid-Solid Coupling in 3D with Nonstandard Boundary Conditions. Steps Towards Modeling Blood Flow.’ Acta Applicandae Mathematica 110: 1087–1104.
- . . ‘A Nonparametric Approach to Cell Dispersal.’ Int. J. of Biomathematics and Biostatistics 1: 109–128.
- . . ‘An optimal control model of oil discovery and extraction.’ Applied Mathematics and Computation 217, № 3: 1163–1169. doi: 10.1016/j.amc.2010.03.075.
- . . ‘Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment.’ Mathematical Medicine and Biology 27, № 2: 157–179. doi: 10.1093/imammb/dqp012.
- . . ‘On a time-dependent fluid-solid coupling in 3D with nonstandard boundary conditions: steps towards modeling blood flow.’ Acta Applicandae Mathematicae 110, № 3: 1087–1104. doi: 10.1007/s10440-009-9495-4.
- . . ‘On a stochastic reaction-diffusion system modeling pattern formation on seashells.’ Journal of Mathematical Biology 60, № 6: 765–796. doi: 10.1007/s00285-009-0284-5.
- . . Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation , .
- . . ‘Edge-Preserving Regularization for the Deconvolution of Biological Images in Nanoscopy.’ Contributed to the ICNAAM 2010, Rhodes, Greece. doi: 10.1063/1.3498325.
- . . ‘Confocal Raman microspectroscopy, the future for semen analysis?’ doi: 10.1111/j.1365-2605.2010.01106.x.
accepted / in Press (not yet published)
- . . ‘An Unfitted Discontinuous Galerkin Finite Element Method for Pore Scale Simulations.’ In 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing. Heidelberg: Springer.
- . . ‘Parallel medical image reconstruction: From graphics processors to grids.’ Lecture notes in computer science 5698 LNCS: 457–473.
- . ‘Mass-selection in alignment models with non-deterministic effects.’ Communications in Partial Differential Equations 34, № 5: 419–456. doi: 10.1080/03605300902797171.
- . ‘Simultaneous finite time blow-up in a two species model for chemotaxis.’ Analysis 29, № 3: 317–338. doi: 10.1524/anly.2009.1029.
- . ‘An integro-differential equation model for alignment and orientational aggregation.’ Journal of Differential Equations 246, № 4: 1387–1421. doi: 10.1016/j.jde.2008.11.006.
- . . ‘Traveling wave speeds in rapidly oscillating media.’ Discrete and Continuous Dynamical Systems - Series A 25, № 1: 89–108. doi: 10.3934/dcds.2009.25.89.
- ‘Mathematical biology. Abstracts from the workshop held May 3-9, 2009. Organized by Emmanuele DiBenedetto, Benoit Perthame and Angela Stevens’, edited by . Oberwolfach Reports 6. doi: 10.4171/OWR/2009/24.
- . ‘Multiscale analysis of a prototypical model for the interaction between microstructure and surface energy.’ Interfaces and Free Boundaries 11, № 1: 61–108.
- . ‘Discrete-to-continuum limits for strain-alignment-coupled systems: Magnetostrictive solids, ferroelectric crystals and nematic elastomers.’ Networks and Heterogeneous Media 4, № 4: 667–708. doi: 10.3934/nhm.2009.4.667.
- . . ‘Overcoming the order barrier in the numerical approximation of stochastic partial differential equations with additive space-time noise.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, № 2102: 649–667. doi: 10.1098/rspa.2008.0325.
- . . ‘A random Euler scheme for Carathéodory differential equations.’ Journal of Computational and Applied Mathematics 224, № 1: 346–359. doi: 10.1016/j.cam.2008.05.060.
- . . ‘Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients.’ Numerische Mathematik 112, № 1: 41–64. doi: 10.1007/s00211-008-0200-8.
- . . ‘Pathwise Taylor schemes for random ordinary differential equations.’ BIT Numerical Mathematics 49, № 1: 113–140. doi: 10.1007/s10543-009-0211-6.
- . . ‘Pathwise numerical approximation of SPDEs with additive noise under non-global Lipschitz coefficients.’ Potential Analysis 31, № 4: 375–404. doi: 10.1007/s11118-009-9139-3.
- . . ‘Pathwise convergence of numerical schemes for random and stochastic differential equations.’ In Foundations of computational mathematics, Hong Kong 2008, edited by , 140–161. Cambridge: Cambridge University Press. doi: 10.1017/CBO9781139107068.006.
- . . ‘The numerical approximation of stochastic partial differential equations.’ Milan Journal of Mathematics 77: 205–244. doi: 10.1007/s00032-009-0100-0.
- . . An Unfitted Discontinuous Galerkin Scheme for Micro-scale Simulations and Numerical Upscaling Dissertation thesis, Universität Heidelberg.
- . . ‘An unfitted finite element method using discontinuous Galerkin.’ International Journal for Numerical Methods in Engineering 79, № 12: 1557–1576. doi: 10.1002/nme.2631.
- . . ‘A review of a posteriori error control and adaptivity for approximations of nonlinear conservation laws.’ International Journal for Numerical Methods in Fluids 59, № International Journal for Numerical Methods in Fluids: 333–354. doi: 10.1002/fld.1686.
- . . A-posteriori error estimate for a heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift. , .
- . . ‘Efficient reduced models for parametrized dynamical systems by offline/online decomposition.’
- . . Local Discontinuous Galerkin Verfahren für die Stokes Gleichungen und Homogenisierung in porösen Medien (Diplomarbeit).
- . . ‘Space-adaptive reduced basis simulation for time-dependent problems.’
- . . ‘Reduced Basis Method for Explicit Finite Volume Approximations of Nonlinear Conservation Laws.’ In Hyperbolic problems: theory, numerics and applications. Providence, RI: American Mathematical Society.
- . . ‘The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains.’ Numer. Math. 113: 601–629. doi: 10.1007/s00211-009-0244-4.
- . . ‘Iterative total variation schemes for nonlinear inverse problems.’ Inverse Problems 25.
- . ‘Long-term planning versus short-term planning in the asymptotical location problem.’ ESAIM: Control, Optimisation and Calculus of Variations 15, № 3: 509–524. doi: 10.1051/cocv:2008034.
- . . ‘Analytic solution of the linear unsteady poroelastic equations in a spherically symmetric brain during an infusion test.’ Mathematical Medicine and Biology 26: 25–61.
- . . ‘Geodesics in Shape Space via Variational Time Discretization.’ In 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, 288–302. doi: 10.1007/978-3-642-03641-5_22.
- . . ‘An Elasticity Approach to Principal Modes of Shape Variation.’ In Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, 709–720.
- . . ‘A nonlinear elastic shape averaging approach.’ SIAM Journal on Imaging Sciences 2, № 3: 800–833. doi: 10.1137/080738337.
- . . ‘Cahn-Hilliard inpainting and a generalization for grayvalue image.’ SIAM J. Imag. Sci. 3: 3.
- . . ‘Iterative solution methods.’ In Handbook of Mathematical Methods in Imaging, edited by , .. Düsseldorf: Springer VDI Verlag.
- . . ‘Sensitivity of beamformer source analysis to deficiencies in forward modeling.’ Human Brain Mapping 31: 1907–1927.
- . . ‘Self-similar solutions for fat tails for a coagulation equation with nonlocal drift.’ Comptes Rendus Mathématique 347, № 15-16: 909–914. doi: 10.1016/j.crma.2009.05.006.
- . . ‘Periodic travelling waves in convex Klein-Gordon chains.’ Nonlinear Analysis: Theory, Methods and Applications 71, № 11: 5501–5508. doi: 10.1016/j.na.2009.04.039.
- . . ‘Self-similar solutions for the LSW model with encounters.’ Journal of Differential Equations 247, № 8: 2282–2309. doi: 10.1016/j.jde.2009.07.021.
- . . ‘Bregman-EM-TV Methods with Application to Optical Nanoscopy.’ Contributed to the SSVM 2009, Voss, Norway. doi: 10.1007/978-3-642-02256-2_20.
- . . ‘Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control.’ SIAM J. Imag. Sci. 2, № 4: 1190–1210. doi: 10.1137/080725064.
- . . ‘Parallel medical image reconstruction: From graphics processors to grids.’ Contributed to the 10th International Conference PaCT, Novosibirsk, Russia.
- . . ‘Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries.’ Contributed to the Proceedings of ALGORITMY 2009.
- . . Reduzierte Basis Methoden für ungesättigte Grundwasserströmungen.
- . . ‘Total Variation Processing of Images with Poisson Statistics.’ Contributed to the CAIP 2009, Münster, Deutschland. doi: 10.1007/978-3-642-03767-2_65.
- . . ‘List mode-driven cardiac and respiratory gating in PET.’ Journal of Nuclear Medicine 50, № 5: 674–681. doi: 10.2967/jnumed.108.059204.
- . . ‘List mode-driven cardiac and respiratory gating.’ PET. J. Nucl. Med. 50: 674–681.
- . . ‘A weak solution approach to a reaction-diffusion system modeling pattern formation on seashells.’ MMAS 32: 2267–2286.
- . . ‘Second order sufficient optimality conditions for a control problem with continuous and bang-bang control components: Riccati approach.’ In System modeling and optimization, 411–429. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-642-04802-9_24.
- . . ‘Sufficient conditions and sensitivity analysis for optimal bang-bang control problems with state constraints.’ In System modeling and optimization, 82–99. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-642-04802-9_4.
- . . ‘On optimal delivery of combination therapy for tumors.’ Mathematical Biosciences 222, № 1: 13–26. doi: 10.1016/j.mbs.2009.08.004.
- . . ‘Optimal control problems with delays in state and control variables subject to mixed control-state constraints.’ Optimal Control Applications and Methods 30, № 4: 341–365. doi: 10.1002/oca.843.
- . . ‘Detection of intensity and motion edges within optical flow via multidimensional control.’ SIAM Journal on Imaging Sciences 2, № 4: 1190–1210. doi: 10.1137/080725064.
- . . ‘A weak solution approach to a reaction-diffusion system modeling pattern formation on seashells.’ Mathematical Methods in the Applied Sciences 32, № 17: 2267–2286. doi: 10.1002/mma.1133.
- . ‘Partial differential equations and non-diffusive structures.’ Nonlinearity 21, № 12: T283–T289. doi: 10.1088/0951-7715/21/12/T04.
- . . ‘A new $hp$-adaptive DG scheme for conservation laws based on error control .’ In Hyperbolic Problems: Theory, Numerics, Applications, edited by , 187–198. Berlin. doi: 10.1007/978-3-540-75712-2_15.
- . . ‘A reduced basis method for evolution schemes with parameter-dependent explicit operators .’ Electronic transactions on numerical analysis 32: 145–161.
- . . ‘Parallel and adaptive simulation of fuel cells in 3d.’ In Computational science and high performance computing III, 69–81. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-540-69010-8_7.
- . . ‘A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part {II}: Implementation and Tests in {DUNE}.’ Computing 82, № 2--3: 121–138. doi: 10.1007/s00607-008-0004-9.
- . . ‘A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part I: Abstract framework.’ Computing 82, № 2--3: 103–119. doi: 10.1007/s00607-008-0003-x.
- . . ‘Modelling in vitro growth of dense root networks.’ Journal of Theoretical Biology 254, № 1: 99–109. doi: 10.1016/j.jtbi.2008.04.014.
- . . ‘Modeling and Simulation of Hairy Root Growth.’ In Mathematics-Key Technology for the Future: Joint Projects Between Universities and Industry 2004-2007, edited by , 101–115. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-540-77203-3_8.
- . . ‘A non-isothermal PEM fuel cell model including two water transport mechanisms in the membrane.’ Journal of Fuel Cell Science and Technology 5, № Journal of Fuel Cell Science and Technology: 5. doi: 10.1115/1.2822884.
- . . ‘Adaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes.’ Contributed to the Finite Volumes for Complex Applications VI Problems & Perspectives: FVCA 6, Prague.
- . . ‘Parallel adaptive simulation of PEM fuel cells.’ In Mathematics – Key Technology for the Future, edited by , 235–249.
- . . ‘Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations.’ M2AN Math. Model. Numer. Anal. 42, № 2: 277–302. doi: 10.1051/m2an:2008001.
- . . ‘A reduced basis method for evolution schemes with parameter-dependent explicit operators.’ Electronic transactions on numerical analysis 32: 145–161.
- . . ‘A Nonlinear Variational Method for Improved Quantification of Myocardial Blood Flow Using Dynamic H215O PET .’ Contributed to the IEEE NSS/MIC 2008, Dresden.
- . . ‘A generalization of Cahn-Hilliard inpainting for gray-value images.’ In PAMM Special Issue: ICIAM 07, 1041905–1041906.
- . . ‘Cahn-Hilliard inpainting and the Willmore functional.’ In PAMM Special Issue: ICIAM 07, 1011209–1011210.
- . . ‘Inverse problems related to ion channels.’ In PAMM Special Issue: ICIAM 07, 1120801–1120802.
- . . ‘A model for an inverse power constitutive law for cerebral compliance.’ Mathematical Medicine and Biology 25: 113–131. doi: 10.1093/imammb/dqn006.
- . . ‘A Globally Covergent Gummel Map for Optimal Dopant Profiling.’ Math. Models Meth. Appl. Sci. 19.
- . . ‘A note on sparse reconstruction methods.’ In J Phys Conference Series, edited by , 012002.
- . . ‘Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions.’ Commun. Math. Sci. 6: 1–28.
- . . ‘Discovering point sources in unknown environments.’ Contributed to the WAFR 2008.
- . . ‘Finite element approximation of elliptic partial differential equations on implicit surfaces.’ Comp. Vis. Sci. .
- . . ‘Finite element based level set methods for higher order flows.’ J. Sci. Comp. 35: 77–98.
- . . ‘Large time behavior of nonlocal aggregation models with nonlinear diffusion.’ Networks and Heterogeneous Media 3: 749–785.
- . . ‘On-/Off-State design of semiconductor doping profiles.’ Commun. Math. Sci. 6: 1021–1041.
- . . ‘Shape from Defocus via Diffusion.’ IEEE Transactions PAMI 30: 518–531.
- . . ‘The Willmore functional and instabilities in the Cahn-Hilliard equation.’ Commun. Math. Sci. 6: 309–329.
- . . ‘Numerical experiments on the modulation theory for the nonlinear atomic chain.’ Physica D: Nonlinear Phenomena 237, № 2: 255–282. doi: 10.1016/j.physd.2007.09.003.
- . . ‘A kinetic model for grain growth.’ Kinetic and Related Models 1, № 4: 591–617. doi: 10.3934/krm.2008.1.591.
- . . ‘Lagrangian and Hamiltonian two-scale reduction.’ Journal of Mathematical Physics 49, № 10: 103505, 42. doi: 10.1063/1.2956487.
- . . „aaa Kantenerkennung im optischen Fluss als mehrdimensionales Steuerungsproblem.“. BTU Cottbus.
- . . Mathematical Models for Pedestrian Motion.
- . . ‘Motion correction in respiratory gated cardiac PET/CT using multi-scale optical flow.’ doi: 10.1007/978-3-540-85990-1_19.
- . . ‘Multi-scale optical flow for respiratory motion correction in cardiac PET/CT.’ Contributed to the MICCAI, New York.
- . ‘On the Time-Dependent Motion of a Viscous Incompressible Fluid Through a Tube with Compliant Walls.’ Studia UBB Mathem LIII: 77–95.
- . . ‘Direct optimization methods for solving a complex state-constrained optimal control problem in microeconomics.’ Applied Mathematics and Computation 204, № 2: 568–579. doi: 10.1016/j.amc.2008.05.035.
- . . ‘Accurate EM-TV algorithm in PET with low SNR.’ Contributed to the IEEE NSS/MIC 2008, Dresden, Deutschland. doi: 10.1109/NSSMIC.2008.4774392.
- . . ‘Time, space, and spectrally resolved studies on J-aggregate interactions in zeolite L nanochannels.’ Journal of the American Chemical Society 130, № 33: 10970–10976. doi: 10.1021/ja801178p.
- . . ‘Initiation of cytoskeletal asymmetry for cell polarization and movement.’ Journal of Theoretical Biology 249, № 2: 278–288. doi: 10.1016/j.jtbi.2007.08.013.
- . ‘The Neumann sieve problem and dimensional reduction: A multiscale approach.’ Mathematical Models and Methods in Applied Sciences 17, № 5: 681–735. doi: 10.1142/S0218202507002078.
- . ‘A note on equi-integrability in dimension reduction problems.’ Calculus of Variations and Partial Differential Equations 29, № 2: 231–238. doi: 10.1007/s00526-006-0065-6.
- . . ‘Pathwise convergent higher order numerical schemes for random ordinary differential equations.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, № 2087: 2929–2944. doi: 10.1098/rspa.2007.0055.
- . . ‘Modelling of interfaces in unsaturated porous media.’ Discrete Contin. Dyn. Syst. , № Dynamical Systems and Differential Equations. Proceedings of the 6th AIMSInternational Conference, suppl.: 794–803.
- . . Über die Entscheidbarkeit gewisser Prädikate in der Theorie der C*-Algebren. Münster.
- . . ‘Basis Construction for Reduced Basis Methods by Adaptive Parameter Grids.’
- . . Die Heterogene Mehrskalenmethode f\�r elliptische Differentialgleichungen in perforierten Gebieten.
- . . ‘Guest Editorial for Special Issue on Modelling and Simulation of PEM-FC.’ Journal of Fuel Cell Science and Technology 2007, № Journal of Fuel Cell Science and Technology.
- . . ‘Parallel and adaptive simulaiton of fuel cells in 3D.’
- . . ‘Error control for a class of Runge-Kutta discontinuous Galerkin methods for nonlinear conservation laws.’ SIAM J. Numer. Anal. 45: 514–538.
- . . ‘Inverse problems related to ion channel selectivity.’ SIAM J. Appl. Math. 67: 960–989.
- . . ‘Global weak solutions of non-isothermal front propagation problem.’ Electronic Research Announcements of the American Mathematical Society 13: 46–52. doi: 10.1090/S1079-6762-07-00173-4.
- . . ‘An extension of the Kolmogorov-Avrami formula to inhomogeneous birth-and-growth processes .’, edited by , 63–76. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-540-44446-6_6.
- . . ‘A level set approach to anisotropic flows with curvature regularization.’ J. Comp. Phys. 225: 183–205.
- . . ‘Error estimation for Bregman iterations and inverse scale space methods.’ Computing 81: 109–135.
- . . ‘Inverse total variation flow.’ SIAM Multiscale Mod. Simul. 6: 366–395.
- . . ‘On some geometric inverse problems in linear elasticity.’ Math. Meth. Appl. Sci. 30: 625–647.
- . . Berechnung des optischen Flusses und Kantenerkennung mit Optimierungsmethoden.
- . . Reflektoren in der Ultraschall-Tomographie.
- . . Statistical Filtering of Global Illumination for Computer Graphics , .
- . ‘On the Stationary Interaction of a Navier-Stokes Fluid With an Elastic Tube Wall.’ Applicable Analyis 86: 149–165.
- . . ‘Fluid Flows and Free Boundaries.’ In Reactive Flows, Diffusion and Transport, edited by . Düsseldorf: Springer VDI Verlag.
- . . ‘Equivalence of second order optimality conditions for bang-bang control problems. {II}. Proofs, variational derivatives and representations.’ Control and Cybernetics 36, № 1: 5–45.
- . . ‘On the stationary interaction of a Navier-Stokes fluid with an elastic tube wall.’ Applicable Analysis 86, № 2: 149–165. doi: 10.1080/00036810601108756.
- . . ‘Fluid flows and free boundaries.’ In Reactive flows, diffusion and transport, 5–24. Düsseldorf: Springer VDI Verlag. doi: 10.1007/978-3-540-28396-6_1.
- . . ‘Traveling wave speeds of nonlocally perturbed reaction diffusion equations.’ Asymptotic Analysis 46, № 1: 81–91.
- . . ‘Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit.’ Indiana University Mathematics Journal 55, № 1: 289–316. doi: 10.1512/iumj.2006.55.2677.
- ‘Mathematical biology. Abstracts from the workshop held May 14-20, 2006. Organized by Emmanuele DiBenedetto, Benoit Perthame and Angela Stevens’, edited by . Oberwolfach Reports 3. doi: 10.4171/OWR/2006/24.
- . . ‘The Distributed and Unified Numerics Environment (DUNE).’ In Proc. of the 19th Symposium on Simulation Technique in Hannover, September 12 - 14.
- . . ‘A general object oriented framework for discretizing nonlinear evolution equations.’, 93.
- . . ‘An efficient implementation of an adaptive and parallel grid in DUNE.’, 91.
- . . Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations , .
- . . ‘Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method.’ Math. Comp. 75: 113–150.
- . . Weak solutions of a polymer crystal growth model , .
- . . ‘Surface diffusion including adatoms.’ Comm. Math. Sci. 4: 1–51.
- . . ‘The Keller-Segel model for chemotaxis: linear vs. nonlinear diffusion.’ SIAM J. Math. Anal. 38: 1288–1315.
- . . ‘Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems.’ SIAM Journal on Numerical Analysis 44, № 1: 153–182. doi: 10.1137/040613779.
- . ‘Path functionals over Wasserstein spaces.’ Journal of the European Mathematical Society 8, № 3: 415–434.
- . . ‘Effect of nonlinear permeability in a spherical model of hydrocephalus.’ Mathematical Medicine and Biology 23: 339–361. doi: 10.1093/imammb/dql015.
- . . ‘An axisymmetric and fully 3D poroelastic model for the onset and treatment of hydrocephalus.’ Mathematical Medicine and Biology 23: 363–388. doi: 10.1093/imammb/dql014.
- . . ‘A one-shot approach to topology optimization with stress constraints.’ Contributed to the IUTAM Symposium on Topological Design Optimization of Structures, Machines, and Materials.
- . . ‘An extension of the Avrami-Kolmogorov formula to inhomogeneous birth-and-growth processes.’ Contributed to the Math Everywhere, Milano.
- . . ‘Cartoon extraction based on anisotropic image classification.’ Contributed to the Vision, Modeling, and Visualization Proceedings.
- . Deterministic and Stochastic Modelling in Biomedicine, Economics, and Industry.
- . . ‘Iterative total variation regularization with non-quadratic fidelity.’ J. Math. Imaging Vision 26: 167–184.
- . . ‘Mesoscale averaging of nucleation and growth processes.’ SIAM Multiscale Mod. Simul. 5: 564–592.
- . . ‘Nonlinear inverse scale space methods.’ Commun. Math. Sci. 4: 179–212.
- . . ‘On an aggregation model with long and short range interactions.’ Nonlinear Analysis: Real World Applications 8: 939–958.
- . . ‘Optimization models for semiconductor dopant profiling.’ In Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photons, and Biological Systems, edited by , 91–116. Basel: Birkhäuser Verlag.
- . . ‘Phase-field relaxation of topology optimization with local stress constraints,.’ SIAM J. Control. Optim. 45: 1447–1466.
- . . ‘Micro-macro transition in the atomic chain via Whitham's modulation equation.’ Nonlinearity 19, № 2: 471–500. doi: 10.1088/0951-7715/19/2/013.
- . . ‘On a thermodynamically consistent modification of the Becker-Döring equations.’ Physica D: Nonlinear Phenomena 222, № 1-2: 116–130. doi: 10.1016/j.physd.2006.08.004.
- . . ‘Continuum descriptions for the dynamics in discrete lattices: derivation and justification.’ In Analysis, modeling and simulation of multiscale problems, edited by , 435–466. Düsseldorf: Springer VDI Verlag. doi: 10.1007/3-540-35657-6_16.
- . . ‘Wave trains, solitons and modulation theory in FPU chains.’ In Analysis, modeling and simulation of multiscale problems, edited by , 467–500. Düsseldorf: Springer VDI Verlag. doi: 10.1007/3-540-35657-6_17.
- . . ‘The three-dimensional architecture of the left ventricular myocardium.’ The anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology 288A, № 6: 565–578.
- . ‘On the Stationary Motion of a Stokes Fluid in a Thick Elastic Tube: A 3D/3D Interaction Problem.’ AMUC 75: 95–106.
- . . ‘A Note on an Individual Bioequivalence Setting.’ J. Inequal. Pure Appl. Math. 7: 8.
- . . ‘On {$L^1$}-minimization in optimal control and applications to robotics.’ Optimal Control Applications and Methods 27, № 6: 301–321. doi: 10.1002/oca.781.
- . . ‘Second order optimality conditions for controls with continuous and bang-bang components.’ In Systems, control, modeling and optimization, 297–307. Düsseldorf: Springer VDI Verlag. doi: 10.1007/0-387-33882-9_28.
- . . ‘A note on an individual bioequivalence setting.’ Journal of inequalities in pure and applied mathematics 7, № 3: Article 100, 8 pp. (electronic).
- . . ‘On the stationary motion of a Stokes fluid in a thick elastic tube: a 3D/3D interaction problem.’ Acta Mathematica Universitatis Comenianae 75, № 1: 95–106.
- . . ‘Three-dimensional architecture of the left ventricular myocardium.’ Anatomical Record Part A: Discoveries in Molecular Cellular and Evolutionary Biology 288A, № 6: 565–578. doi: 10.1002/ar.a.20326.
published
- . . ‘Drift-diffusion limits of kinetic models for chemotaxis: A generalization.’ Discrete and Continuous Dynamical Systems - Series B 5, № 2: 319–334. doi: 10.3934/dcdsb.2005.5.319.
- . . ‘Making waves: Pattern formation by a cell-surface-associated signal.’ Trends in Microbiology 13, № 6: 249–252. doi: 10.1016/j.tim.2005.04.002.
- . . ‘Global solutions of nonlinear transport equations for chemosensitive movement.’ SIAM Journal on Mathematical Analysis 36, № 4: 1177–1199. doi: 10.1137/S0036141003431888.
- . . A Discontinuous Galerkin Method for Simulations in Complex Domains , .
- . . ‘Solving partial differential equations in complicated domains.’ Oberwolfach Reports 4.
- . . ‘A new stable discontinuous Galerkin approximation for non-linear conservation laws on adaptively refined grids.’, 1095–1099.
- . . ‘A posterior error estimates for the heterogenoeous mulitscale finite element method for elliptic homogenization problems.’ SIAM Multiscale Mod. Simul. 4, № 1: 88–114.
- . . ‘Error control for approximations of non-linear conservation laws.’, 85–100.
- . . ‘Towards a unified framework for scientific computing.’, 167–174.
- . . ‘A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems.’ Multiscale Model. Simul. 4: 88–114.
- . . ‘A model hierarchy for surface diffusion: the small slope case.’ Contributed to the 5th MATHMOD, Vienna.
- . . ‘A survey on level set methods for inverse problems and optimal design.’ European J. Appl. Math. 16: 263–301.
- . . ‘Greedy algorithms for neural network training with data noise.’ Computing 74: 1–22.
- . . ‘Inverse dopant profiling for highly doped semiconductor devices.’ Contributed to the 5th MATHMOD, Vienna.
- . . ‘Nonlinear inverse scale space methods for image restoration.’ Contributed to the Variational and Level Set Methods 2005.
- . . ‘Numerical simulation of anisotropic surface diffusion with curvature-dependent energy.’ J. Comp. Phys. 203: 602–625.
- . . ‘Projected gradient flows for BV / level set relaxation.’ PAMM 5, № PAMM: 11–14.
- . . ‘Symbolic preprocessing of finite element methods for parameter-dependent geometric differential equations.’ Contributed to the Workshop on Symbolic-Numerical Computation 2005.
- . . ‘An iterative regularization method for total variation based image restoration.’ SIAM Multiscale Modelling and Simulation 4: 460–489.
- . ‘Optimal networks for mass transportation problems.’ ESAIM: Control, Optimisation and Calculus of Variations null, № 11: 88–101. doi: 10.1051/cocv:2004032.
- . . ‘Kinetic schemes for selected initial and boundary value problems.’ In Analysis and numerics for conservation laws, edited by , 203–232. Düsseldorf: Springer VDI Verlag. doi: 10.1007/3-540-27907-5_9.
- . . ‘Equivalence of second order optimality conditions for bang-bang control problems. I. Main results.’ Control and Cybernetics 34, № 3: 927–950.
- . . ‘Optimization methods for the verification of second order sufficient conditions for bang-bang controls.’ Optimal Control Applications and Methods 26, № 3: 129–156. doi: 10.1002/oca.756.
- . . ‘Second order sufficient conditions for optimal control subject to first order state constraints.’ In Control and boundary analysis, 293–304. London: Chapman & Hall.
- . . ‘Marching schemes for inverse acoustic scattering problems.’ Numerische Mathematik 100, № 4: 697–710. doi: 10.1007/s00211-004-0580-3.
submitted / under review
- . . ‘A constructive approach to traveling waves in chemotaxis.’ Journal of Nonlinear Science 14, № 1: 1–25. doi: 10.1007/s00332-003-0548-y.
- . . ‘Towards a Unified Framework for Scientific Computing.’ In Proceedings of the 15th Conference on Domain Decomposition Methods. doi: 10.1007/3-540-26825-1_13.
- . . ‘Finite volume methods: foundation and analysis.’, 439–474.
- . . ‘Higher order finite volume methods on selfadaptive grids for convection dominated reactive transport problems in porous media.’ Comp. Vis. Sci. 7, № 1: 41–51.
- . . ‘Growth of multiple crystals in polymer melts.’ European J. Appl. Math. 15: 347–363.
- . . ‘Incorporating topological derivatives into level set methods.’ J. Comp. Phys. 194: 344–362.
- . . ‘Inverse problem techniques for the design of photonic crystals.’ IEICE Transactions on Electronics 87 C: 258–265.
- . . ‘Level set methods for geometric inverse problems in linear elasticity.’ Inverse Problems 20: 673–696.
- . . ‘Levenberg-Marquardt level set methods for inverse obstacle problems.’ Inverse Problems 20: 673–696.
- . . ‘On inverse problems for semiconductor equations.’ Milan J. Math. 72: 273–314.
- . . ‘Optimal control of polymer morphologies.’ J. Eng. Math. 49: 339–358.
- . . ‘Scene and motion reconstruction from defocused and motion blurred images via anisotropic diffusion.’ Contributed to the ECCV.
- . . ‘Convergence rates of convex variational regularization.’ Inverse Problems 20: 1411–1421.
- . . ‘Kinetic solutions of the Boltzmann-Peierls equation and its moment systems.’ Continuum Mechanics and Thermodynamics 16, № 5: 453–469. doi: 10.1007/s00161-003-0171-z.
- . . ‘Second-order sufficient conditions for state-constrained optimal control problems.’ Journal of Optimization Theory and Applications 123, № 3: 595–617. doi: 10.1007/s10957-004-5725-0.
- . . ‘Second order sufficient conditions for time-optimal bang-bang control.’ SIAM Journal on Control and Optimization 42, № 6: 2239–2263. doi: 10.1137/S0363012902402578.
- . . ‘Minimizing the transition time in lasers by optimal control methods single-mode semiconductor laser with homogeneous transverse profile.’ Physica D: Nonlinear Phenomena 191, № 3-4: 238–260. doi: 10.1016/j.physd.2003.12.002.
- . . ‘The forces generated within the musculature of the left ventricular wall.’ Heart 90, № 2: 200–207. doi: 10.1136/hrt.2003.011650.
- . . Direkte Simulation von Transportprozessen im Boden zur Bestimmung makroskopischer Parameter.
- . . ‘A posteriori error estimates and adaptive methods for hyperbolic and convection dominates parabolic conservation laws.’, 289–306.
- . . ‘Adaptive second order central schemes on unstructured staggered grids.’
- . . ‘Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations.’ Computing 70, № Computing: 181–204.
- . . ‘Fast optimal design of semiconductor devices.’ SIAM J. Appl. Math. 64: 108–126.
- . . ‘Growth and impingement in polymer melts.’ Contributed to the FBP 2002, Trento.
- . . ‘Model reduction for semiconductor inverse dopant profiling.’ Contributed to the 4th IMACS Symposium on Mathematical Modelling, Wien, Österreich.
- . . ‘Model reduction for semiconductor inverse dopant profiling.’ In Proceedings of the 4th IMACS Symposium on Mathematical Modelling, edited by .
- . . ‘A framework for the construction of level set methods for shape optimization and reconstruction.’ Interfaces and Free Boundaries 5: 301–329.
- . . ‘A critical evaluation of results of partial left ventriculectomy.’ Journal of Cardiac Surgery 18, № 3: 225–235. doi: 10.1046/j.1540-8191.2003.02026.x.
- . . ‘The relationship between structure and function: why does reshaping the left ventricle surgically not always result in functional improvement?’ Computers in Biology and Medicine 33, № 3: 185–196. doi: 10.1016/S0010-4825(02)00085-9.
- . . ‘Emerging patterns in a hyperbolic model for locally interacting cell systems.’ Journal of Nonlinear Science 12, № 6: 619–640. doi: 10.1007/s00332-002-0510-4.
- . . ‘A posteriori error estimate for finite volume approximations of convection diffusion problems.’
- . . ‘Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems.’ IMA J. Numer. Anal. 22, № 2: 253–280.
- . . ‘Adaptive finite volume methods for displacement problems in porous media.’ Comp. Vis. Sci. 5, № 2: 95–106.
- . . ‘Local adaptive methods for convection dominated problems.’ International Journal for Numerical Methods in Fluids 40, № 1-2: 79–91.
- . . ‘A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.’ J. Math. Anal. Appl. 275: 439–458.
- . . ‘Analysis of Tikhonov regularization for function approximation by neural networks.’ Neural Networks 16: 79–90.
- . . ‘Data-Driven construction of Sugeno controllers: analytical aspects and new numerical methods.’ Contributed to the 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver.
- . . ‘Inverse doping problems for semiconductor devices.’ Contributed to the Recent Progress in Computational and Applied PDEs.
- . . ‘Iterative regularization of parameter identification problems by SQP methods.’ Inverse Problems 18: 943–970.
- . . ‘Mathematical modelling of the crystallization process of polymers.’ Contributed to the 5th Hellenic Conference on Computer Mathematics and its Applications, Athens.
- . . ‘Mathematical models for polymer crystallization processes.’ In Mathematical modelling for polymer industry, edited by , 167–242. Düsseldorf: Springer VDI Verlag.
- . . ‘Modelling crystallization of polymers in temperature fields.’ ZAMM 82: 51–63.
- . . ‘Modelling multi-dimensional crystallization of polymers in interaction with heat transfer.’ Nonlinear Analysis: Real World Applications 3: 139–160.
- . . ‘Regularized data-driven construction of fuzzy controllers.’ J. Inverse Ill-Posed Problems 10: 319–344.
- . . ‘Tuning of fuzzy systems as an ill-posed problem.’ Contributed to the ECMI 2000, Palermo.
- . . ‘Numerical approximation of an SQP-type method for parameter identification .’ SIAM Journal on Numerical Analysis 40, № 5: 1775–1797. doi: 10.1137/S0036142901389980.
- . . ‘Tuning of fuzzy systems as an ill-posed problem.’ Contributed to the ECMI 2000, Palermo.
- . . ‘Kinetic schemes and initial boundary value problems for the Euler system.’ Transport Theory and Statistical Physics 31, № 1: 1–33. doi: 10.1081/TT-120003009.
- . . ‘Second order sufficient conditions for optimal control problems with free final time: the Riccati approach.’ SIAM Journal on Control and Optimization 41, № 2: 380–403. doi: 10.1137/S0363012900377419.
- . . ‘Variational principles for propagation speeds in inhomogeneous media.’ SIAM Journal on Applied Mathematics 62, № 1: 129–148. doi: 10.1137/s0036139999361148.
- . . ‘A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations.’ Numerische Mathematik 87, № 4: 737–761.
- . . A posteriori error estimates and adaptive methods for convection dominated transport processes.
- . . h-p-Multiresolution Visualization of Adaptive Finite Element Simulations , .
- . . ‘A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations.’ M2AN Math. Model. Numer. Anal. 35: 355–387.
- . . ‘A level set method for inverse problems.’ Inverse Problems 17: 1327–1356.
- . . ‘Error bounds for approximation with neural networks.’ J. Approx. Theory 112: 235–250.
- . . ‘Identification of doping profiles in semiconductor device.’ Inverse Problems 17: 1765–1795.
- . . ‘Iterative regularization of a parameter identification problem occurring in polymer crystallization.’ SIAM J. Numer. Anal. 39, № SIAM J. Numer. Anal.: 1029–1054.
- . . ‘Mathematical modelling and simulation of non-isothermal crystallization of polymers.’ Math. Models and Methods in Appl. Sciences 11: 1029–1054.
- . . ‘Regularization methods for blind deconvolution and blind source separation problems.’ Mathematics of Control, Signals and Systems 14: 358–383.
- . . ‘Stochastic and deterministic simulation of nonisothermal crystallization of polymers .’ Journal of Mathematical Chemistry 30, № 2: 169–193. doi: 10.1023/A:1017923703579.
- . . ‘Second order sufficient conditions and sensitivity analysis for the optimal control of a container crane under state constraints.’ Optimization 49, № 4: 351–368. doi: 10.1080/02331930108844537.
- . . ‘Real-time control of an industrial robot under control and state constraints.’ In Online optimization of large scale systems, 83–92. Düsseldorf: Springer VDI Verlag.
- . . ‘*Sensitivity analysis and real-time control of parametric optimal control problems using nonlinear programming methods.’ In Online optimization of large scale systems, 57–68. Düsseldorf: Springer VDI Verlag.
- . . ‘*Sensitivity analysis and real-time control of parametric optimal control problems using boundary value methods.’ In Online optimization of large scale systems, 17–55. Düsseldorf: Springer VDI Verlag.
- . . ‘*Sensitivity analysis and real-time optimization of parametric nonlinear programming problems.’ In Online optimization of large scale systems, 3–16. Düsseldorf: Springer VDI Verlag.
- . . ‘Sensitivity analysis and real-time control of a container crane under state constraints.’ In Online optimization of large scale systems, 69–82. Düsseldorf: Springer VDI Verlag.
- . . ‘Computational sensitivity analysis for state constrained optimal control problems.’ Annals of Operations Research 101: 75–99. doi: 10.1023/A:1010960221295.
- . . ‘Sensitivity analysis for optimal control problems subject to higher order state constraints.’ Annals of Operations Research 101: 43–73. doi: 10.1023/A:1010956104457.
- . . ‘Optimization techniques for solving elliptic control problems with control and state constraints. {II}. Distributed control.’ Computational Optimization and Applications 18, № 2: 141–160. doi: 10.1023/A:1008774521095.
- . . Mathematical methods in image reconstruction. N/A: Selbstverlag / Eigenverlag. doi: 10.1118/1.1455744.
- . . ‘The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems.’ SIAM Journal on Applied Mathematics 61, № 1: 183–212. doi: 10.1137/S0036139998342065.
- . . ‘A stochastic cellular automaton modeling gliding and aggregation of myxobacteria.’ SIAM Journal on Applied Mathematics 61, № 1: 72–182. doi: 10.1137/S0036139998342053.
- . . ‘Hyperbolic models for chemotaxis in 1-D.’ Nonlinear Analysis: Real World Applications 1, № 3: 409–433. doi: 10.1016/S0362-546X(99)00284-9.
- . . ‘A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multidimensions.’ Math. Comp. 69: 25–39.
- . . ‘Training neural networks with noisy data as an ill-posed problem.’ Adv. Comp. Math 13, № Adv. Comp. Math: 335–354.
- . . ‘Nonlinear programming methods for real-time control of an industrial robot.’ Journal of Optimization Theory and Applications 107, № 3: 505–527. doi: 10.1023/A:1026491014283.
- . . ‘An example for computational sensitivity analysis of state constrained control problems.’ In Parametric optimization and related topics, V (Tokyo, 1997), 25–35. Lausanne: Peter Lang.
- . . ‘Computational sensitivity analysis of state constrained control problems.’ In Optimization, dynamics, and economic analysis, 12–21. Heidelberg: Physica-Verlag.
- . . ‘Solving elliptic control problems with interior point and {SQP} methods: control and state constraints.’ Journal of Computational and Applied Mathematics 120, № 1-2: 175–195. doi: 10.1016/S0377-0427(00)00309-5.
- . . ‘S{QP}-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control.’ Journal of Computational and Applied Mathematics 120, № 1-2: 85–108. doi: 10.1016/S0377-0427(00)00305-8.
- . . ‘Real-time control of robots with initial value perturbations via nonlinear programming methods.’ Optimization 47, № 3-4: 383–405. doi: 10.1080/02331930008844488.
- . . ‘Second order sufficient conditions and sensitivity analysis for optimal multiprocess control problems.’ Control and Cybernetics 29, № 1: 11–31.
- . . ‘Optimization techniques for solving elliptic control problems with control and state constraints. I. Boundary control.’ Computational Optimization and Applications 16, № 1: 29–55. doi: 10.1023/A:1008725519350.
- . . A Procedural Interface for Multiresolutional Visualization of General Numerical Data , .
- . . ‘Adaptive mesh refinement for single and two phase flow problems in porous media.’
- . . ‘Adaptive protection operators in multiresolution scientific visualizations.’ IEEE Transactions on Visualization and Computer Graphics 5, № 1: 74–94.
- . . ‘Mixed finite element-finte volume methods for two-phase flow in porous media.’
- . . ‘On numerical algorithm and interactive visualization for optimal control problems.’ Comp. Visual. Sci. 1, № 4: 221–229.
- . . ‘Inverse problems related to crystallization of polymers.’ Inverse Problems 15, № Inverse Problems: 155–173.
- . . ‘Modelling and parameter-identification in non-isothermal crystallization of polymers.’ Contributed to the EcMI 98, Gothenburg.
- . . ‘Sufficient conditions and sensitivity analysis for economic control problems.’ Annals of Operations Research 88: 3–14. doi: 10.1023/A:1018942732605.
- . . Challenges in Fluid Dynamics.
- . ‘On the Pathwise Uniqueness of Solutions of Stochastic Differential Equations.’ Portugaliae Mathematica 55: 451–456.
- . . ‘Sensitivity analysis and real-time control of nonlinear optimal control systems via nonlinear programming methods.’ In Variational calculus, optimal control and applications (Trassenheide, 1996), 185–196. Basel: Birkhäuser Verlag.
- . . ‘Solution techniques for periodic control problems: a case study in production planning.’ Optimal Control Applications and Methods 19, № 3: 185–203. doi: 10.1002/(SICI)1099-1514(199805/06)19:3<185::AID-OCA627>3.0.CO;2-E.
- . . ‘Sensitivity analysis for state constrained optimal control problems.’ Discrete and Continuous Dynamical Systems - Series A 4, № 2: 241–272.
- . . ‘Convergence of approximations to nonlinear optimal control problems.’ In Mathematical programming with data perturbations, 253–284. New York City: Marcel Dekker Verlag.
- . . ‘Aggregation, blowup, and collapse: The ABC's of taxis in reinforced random walks.’ SIAM Journal on Applied Mathematics 57, № 4: 1044–1081. doi: 10.1137/s0036139995288976.
- . . ‘Aggregation induced by diffusing and non-diffusing media.’ In Dynamics of Cell and Tissue Motion. Mathematics and Biosciences in Interaction., edited by , 183–192. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-0348-8916-2_22.
- . . ‘Convergence of a mixed finite element-finite volume method for the two phase flow in porous media.’ East-West journal of numerical mathematics 5, № 3: 183–210.
- . . ‘Efficient visualization of large-scale data on hierarchical meshes.’
- . . ‘Hierarchical and adaptive visualization on nested grids.’ Computing 59, № Computing: 365–385.
- . ‘The Cauchy Problem for Seismic Wave Propagation.’ Analele Univ. de Vest din Timisoara, Seria Matematica/Informatica XXXV: 299–305.
- . . ‘Simulation of chemotaxis-equations in two space dimensions.’ In Nonlinear Physics of Complex Systems - Current Status and Future Trends, edited by , 363–371. Heidelberg: Springer. doi: 10.1007/BFb0105453.
- . . ‘Trail Following and Aggregation of Myxobacteria.’ Journal of Biological Systems 3, № 4: 1059–1068. doi: 10.1142/S0218339095000952.
- . . ‘A propagation-backpropagation method for ultrasound tomography.’ Inverse Problems 11, № 6: 1225–1232. doi: 10.1088/0266-5611/11/6/007.
- . . ‘Aggregation of Myxobacteria - a many particle system.’ In Proceedings 1st European Conference on the Applications of Mathematics to Medicine & Biology (1990) , edited by , 519–524. Winnipeg: Wuerz Publishing Ltd.
- . . ‘A finite difference method for the inverse scattering problem at fixed frequency.’ In Inverse problems in mathematical physics (Saariselkä, 1992), 157–166. Düsseldorf: Springer VDI Verlag. doi: 10.1007/3-540-57195-7_18.
- . . ‘A model for gliding and aggregation of Myxobacteria.’ In Nonlinear wave processes in excitable media, edited by , 269–276. Luxemburg: Springer Science+Business Media. doi: 10.1007/978-1-4899-3683-7_25.
- . . ‘Simulations of the aggregation and gliding behavior of Myxobacteria.’ In Biological motion, edited by , 548–555. Heidelberg: Springer. doi: 10.1007/978-3-642-51664-1_36.
- . . ‘Differential stability in infinite-dimensional nonlinear programming.’ Applied Mathematics and Optimization 6, № 2: 139–152. doi: 10.1007/BF01442889.
- . . ‘Differential stability in optimal control problems.’ Applied Mathematics and Optimization 5, № 4: 283–295. doi: 10.1007/BF01442559.
- . . ‘First and second order necessary and sufficient optimality conditions for infinite-dimensional programming problems.’ Mathematical Programming 16, № 1: 98–110. doi: 10.1007/BF01582096.
- . . ‘Optimality conditions for the programming problem in infinite dimensions.’ In Optimization and operations research (Proc. Workshop, Univ. Bonn, Bonn, 1977), 261–270. Düsseldorf: Springer VDI Verlag.
- . . ‘Differentiable perturbations of infinite optimization problems.’ In Optimization and operations research (Proc. Workshop, Univ. Bonn, Bonn, 1977), 181–191. Düsseldorf: Springer VDI Verlag.
- . . ‘Second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems.’ In Optimization techniques (Proc. 8th {IFIP} Conf., Würzburg, 1977), Part 2, 13–21. Düsseldorf: Springer VDI Verlag. doi: 10.1007/BFb0006504.
- . . ‘On optimal control problems with bounded state variables and control appearing linearly.’ SIAM Journal on Control and Optimization 15, № 3: 345–362. doi: 10.1137/0315023.
- . . ‘Numerical solution of singular control problems using multiple shooting techniques.’ Journal of Optimization Theory and Applications 18, № 2: 235–257. doi: 10.1007/BF00935706.
- . . ‘Optimale Steuerprozesse mit Zustandsbeschränkungen.’ In Optimization and optimal control (Proc. Conf., Oberwolfach, 1974), 244–260. Düsseldorf: Springer VDI Verlag.
- . . ‘Application of multiple shooting to the numerical solution of optimal control problems with bounded state variables.’ Computing 15, № 2: 105–126. doi: 10.1007/BF02252860.
- . . ‘An example of a continuous junction for a singular control problem of even order.’ SIAM Journal on Control and Optimization 13: 899–903. doi: 10.1137/0313055.