Forschung
Forschungsschwerpunkte
- Numerik Partieller Differentialgleichungen
- Fehlerkontrolle und Adaptivität für Finite Elemente und Finite Volumen Verfahren
- Modellreduktion für parametrisierte partielle Differentialgleichungen
- Entwicklung und Analyse von numerischen Mehrskalenmethoden
- Softwareentwicklung und Wissenschaftliches Rechnen
Publikationen
- . . ‘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.
- . . ‘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.
- . . ‘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, Nr. 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.
- . . ‘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. [accepted / in Press (not yet published)]
- . . ‘Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems.’ SIAM Journal on Scientific Computing 46, Nr. 5: A3205–A3229. doi: 10.1137/23M1613402.
- . Kernel Methods in the Deep Ritz framework: Theory and practice arXiv. doi: 10.48550/arXiv.2410.03503. [submitted / under review]
- . . ‘Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems.’ Computational Science and Engineering 1, Nr. 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.
- . A Parareal algorithm without Coarse Propagator? arXiv. doi: 10.48550/arXiv.2409.02673. [submitted / under review]
- . Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems arXiv. doi: 10.48550/arXiv.2408.15900. [submitted / under review]
- . . ‘Application of an adaptive model hierarchy to parametrized optimal control problems.’ Contributed to the Algoritmy, Podbanske.
- . . ‘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.
- . . ‘A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells.’ European Journal of Applied Mathematics 34, Nr. 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, Nr. 3. doi: 10.1137/22M1481002.
- . DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions arXiv. doi: 10.48550/arXiv.2302.00348. [submitted / under review]
- . . ‘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.
- . . ‘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.
- . Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems arXiv. doi: 10.48550/arXiv.2307.15590. [accepted / in Press (not yet published)]
- . . ‘A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.’ SIAM Journal on Scientific Computing 45, Nr. 3: A1039. doi: 10.1137/22M1493318.
- . . ‘Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery.’ Advances in Computational Mathematics 2022, Nr. 48: 73. doi: 10.1007/s10444-022-09981-z.
- . . ‘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.
- . . ‘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.
- . . ‘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, Nr. 5: 1561–1596.
- . . ‘On the Performance of Machine Learning Methods for Breakthrough Curve Prediction.’ arXiv [physics.flu-dyn] 2204.11719. doi: 10.48550/arXiv.2204.11719. [submitted / under review]
- . . ‘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 model hierarchy for data-augmented training of kernel models for reactive flow.’ In MATHMOD 2022 Discussion Contribution Volume, edited by , 67–68. 17. Aufl. 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.
- . . ‘Dynamic interplay of protrusive microtubule and contractile actomyosin forces drives tissue extension.’ eLife 2022. doi: 10.1101/2022.06.21.496930. [submitted / under review]
- . . ‘Optimal local approximation spaces for parabolic problems.’ Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 20, Nr. 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.
- . . Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition Dissertationsschrift, Universität Münster. N/A: Selbstverlag / Eigenverlag.
- . . ‘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.
- . . ‘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.
- . . ‘Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD.’ arXiv [math.NA] 2111.00129. [submitted / under review]
- . . ‘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.
- . . Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations Dissertationsschrift, Universität Münster. N/A: Selbstverlag / Eigenverlag.
- . . ‘The DUNE Framework: Basic Concepts and Recent Developments.’ Computers & Mathematics with Applications 81: 75–112. doi: 10.1016/j.camwa.2020.06.007.
- . . ‘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, Nr. 1. doi: 10.5334/jors.307/.
- . . ‘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.
- . . ‘Mathematical analysis of transmission properties of electromagnetic meta-materials.’ Networks and Heterogeneous Media 15, Nr. 1: 29–56. doi: 10.3934/nhm.2020002.
- . . ‘Stable and efficient Petrov-Galerkin methods for a kinetic Fokker-Planck equation.’ arXiv 2020. [submitted / under review]
- . . ‘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, Nr. 295. doi: 10.12688/f1000research.23224.1.
- . . ‘Model order reduction framework for problems with moving discontinuities.’ Contributed to the Proceedings of ENUMATH 2019, Egmond aan Zee. [online first]
- . . ‘A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction.’ Contributed to the ENUMATH 2019, Graz. [accepted / in Press (not yet published)]
- . . ‘Parametric model order reduction using pyMOR.’ Contributed to the MODRED 2019, Graz. [accepted / in Press (not yet published)]
- . . ‘Numerical Upscaling of Perturbed Diffusion Problems.’ SIAM Journal on Scientific Computing 2020, Nr. Volume 42, Issue 4: A2014–A2036. doi: 10.1137/19M1278211.
- . . ‘First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: realizability-preserving splitting scheme and numerical analysis.’ arXiv 2019. [submitted / under review]
- . . ‘Cross-Gramian-Based Dominant Subspaces.’ Advances in Computational Mathematics 45, Nr. 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.
- . . ‘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, Nr. 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, Nr. 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.
- . . ‘Advances in Model Order Reduction for Large Scale or Multi-Scale Problems.’ Oberwolfach Reports 16, Nr. 3: 2510–2512. doi: 10.4171/OWR/2019/40.
- . . ‘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 .: Wiley. doi: 10.1002/pamm.201900026.
- . . ‘On Reduced Input-Output Dynamic Mode Decomposition.’ Advances in Computational Mathematics 44, Nr. 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, Nr. 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, Nr. 4: 189–193. doi: 10.1515/dmvm-2018-0058.
- . . ‘Numerical homogenization of H(curl)-problems.’ SIAM J. Numer. Anal. 56, Nr. 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, Nr. 1: 385–411. doi: 10.1137/16M1108820.
- . . Numerical multiscale methods for Maxwell's equations in heterogeneous media Dissertationsschrift, Universität Münster.
- . . Randomisierte lokalisierte Modellreduktion mit Robin-Transferoperator (Masterarbeit).
- . . ‘Model reduction for parameterized systems and inverse problems.’ Oberwolfach Reports 2018, Nr. 39: 2454–2457. doi: 10.4171/OWR/2018/39.
- . . ‘Hierarchical Approximate Proper Orthogonal Decomposition.’ SIAM Journal on Scientific Computing 40, Nr. 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.
- . . ‘Heterogeneous Multiscale Method for the Maxwell equations with high contrast.’ ESAIM Math. Model. Numer. Anal. xx. [accepted / in Press (not yet published)]
- . . ‘Comparison of methods for parametric model order reduction of instationary problems.’ In Model Reduction and Approximation: Theory and Algorithms., edited by , 377–408. 1. Aufl. 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, Nr. 3: 690–692.
- . . Randomized Local Model Order Reduction : arXiv:1706.09179, . [submitted / under review]
- (Eds.): . Model Reduction of Parametrized Systems. 1. Aufl. 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 , –. 2. Aufl. 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, Nr. 1: 21–61. doi: 10.11588/ans.2017.1.28602.
- . . ‘Extending DUNE: The dune-xt modules.’ Archive of Numerical Software 5, Nr. 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.
- . . ‘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.
- . . ‘ArbiLoMod, a Simulation Technique Designed for Arbitrary Local Modifications.’ SIAM Journal on Scientific Computing 39, Nr. 4: A1435–A1465. doi: 10.1137/15M1054213.
- . . ‘Fast Low-Rank Empirical Cross Gramians.’ PAMM 17, Nr. 1: 841–842. doi: 10.1002/pamm.201710388.
- . . Variational crimes in the Localized orthogonal decomposition method (master's thesis).
- . . ‘Numerical homogenization for indefinite H(curl)-problems.’ In Proceedings of Equadiff 2017 Conference, edited by , 137–146.
- . . ‘Localized Orthogonal Decomposition for two-scale Helmholtz-type problems.’ AIMS Mathematics 2, Nr. 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, Nr. 2: 641–677. doi: 10.1051/m2an/2016031.
- . . ‘Analysis of multiscale methods for time-harmonic Maxwell's equations.’ Proc. Appl. Math. Mech. 16, Nr. 1: 559–560. doi: 10.1002/pamm.201610268.
- . . ‘Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.’ AIMS Mathematics 1, Nr. 3: 261--281. doi: 10.3934/Math.2016.3.261.
- . . ‘A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations.’ SIAM J. Numer. Anal. 54, Nr. 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, Nr. 1: 012109.
- . . ‘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. [online first]
- . . ‘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 Dissertationsschrift, Westfälische Wilhelms-Universität Münster.
- . . ‘pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, Nr. 5: S194–S216. doi: 10.1137/15M1026614.
- . . ‘Adaptive Localized Model Reduction.’ Oberwolfach Reports 13, Nr. 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, Nr. 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.
- . . Efficient implementation of the Localized Orthogonal Decomposition method arXiv, . [submitted / under review]
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . ‘Optimal local approximation spaces for component-based static condensation procedures.’ SIAM J. Sci. Comput. 38, Nr. 5: A3318––A3356. doi: 10.1137/15M1009603.
- . . ‘A note on the cross Gramian for non-symmetric systems.’ System Science and Control Engineering 4, Nr. 1: 199–208. doi: 10.1080/21642583.2016.1215273.
- . . L2-estimates for a high order unfitted finite element method for elliptic interface problems : arXiv eprints, . [submitted / under review]
- . . ‘High order unfitted finite element methods on level set domains using isoparametric mappings.’ Comp. Meth. Appl. Mech. Eng. 300, Nr. 1: 716–733. doi: 10.1016/j.cma.2015.12.005.
- . . ‘Analysis of a high order unfitted finite element method for elliptic interface problems.’ arXiv preprint arXiv:1602.02970 1602.02970. [submitted / under review]
- . „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 Dissertationsschrift, RWTH Aachen.
- . . ‘The Localized Reduced Basis Multiscale method for two-phase flows in porous media.’ International Journal for Numerical Methods in Engineering 5, Nr. 102: 1018–1040. doi: 10.1002/nme.4773.
- . . ‘Data-driven combined state and parameter reduction for inverse problems.’ Advances in Computational Mathematics 41, Nr. 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, Nr. 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.
- . . ‘Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems.’ Discrete and Continuous Dynamical Systems - Series S 8, Nr. 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, Nr. 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, Nr. 6: A2865–A2895. doi: 10.1137/151003660.
- . . Numerical methods for kinetic equations (Master's thesis).
- . . ‘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.
- . . ‘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.
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