Research Areas

Institute for Analysis and Numerics

The institute's research focuses on the development and application of analytical and numerical mathematical methods and on mathematical modelling. Particular areas of interest are partial differential equations, multiscale methods, inverse problems, variational calculus, mathematical imaging, mathematical models in the biosciences, dynamical systems, optimization and scientific computing.

AG Wirth: Verallgemeinerte Bezier-Fläche auf einer Riemannschen Mannigfaltigkeit

AG Ohlberger: detailed simulation of a Li-Ion battery model with the software framework DUNE
© AGO

AG Engwer: A solution of the electroencephalography (EEG) forward problem using implicit level set data within an unfitted discontinuous Galerkin scheme.
© A. Nüßing

AG Zeppieri: Crazing in polymers close to the crack-tip

Interdisciplinary cooperations

Strong interdisciplinary connections exist to medicine and biology. In particular, the teams participate actively in the cluster of excellence Cells in Motion, the collaborative research centre 656 Molekulare kardiovaskuläre Bildgebung (MoBil), the European Institute for Molecular Imaging (EIMI), the centre for Developing Mathematics in Interaction (DEMAIN), the Center for Nonlinear Science (CENOS) of the WWU, the Center for Multiscale Theory and Computation (CMTC) and the forum Competence for Computing in Science (CoCoS) at the University of Münster.

Ongoing projects and recent publications

A selection of ongoing projects and recent publications are listed below.

You can find more projects and publications on the webpages of the groups.

Current Projects
- MONTECARLO – Overcoming the curse of dimensionality through nonlinear stochastic algorithms: Nonlinear Monte Carlo type methods for high-dimensional approximation problems (2023 – 2028)
  EU-Project Hosted at University the of Münster: EC Horizon Europe - ERC Consolidator Grant | Project Number: 101045811
- GE4SPDE – Global Estimates for non-linear stochastic PDEs (2022 – 2027)
  EU-Project Hosted at University the of Münster: EC Horizon Europe - ERC Consolidator Grant | Project Number: 101045082
- MaRDI – Mathematical Research Data Initiative - TA2: Scientific Computing (2021 – 2026)
  Subproject in DFG-Joint Project Hosted outside the University of Münster: DFG - National Research Data Infrastructure | Project Number: NFDI 29 /1
- Mathematical analysis of bubble rings in ideal fluids (2024 – 2025)
  Individual Granted Project: DFG - Individual Grants Programme | Project Number: SE 2436/5-1
- InterKI – Interdisziplinäres Lehrprogramm zu maschinellem Lernen und künstlicher Intelligenz (2021 – 2025)
  Individual Granted Project: Federal Ministry of Education and Research | Project Number: 16DHBKI049
- Dynamical systems and irregular gradient flows (2021 – 2025)
  Own Resources Project
- CRC 1450 - A05: Targeting immune cell dynamics by longitudinal whole-body imaging and mathematical modelling (2021 – 2024)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1450/1, A05
- CRC 1450 - A06: Improving intravital microscopy of inflammatory cell response by active motion compensation using controlled adaptive optics (2021 – 2024)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1450/1, A06
- NIH Grant Number: 1 R01 EB 026299-01 – BrainStorm: Highly Extensible Software for Advanced Electrophysiology and MEG/EEG Imaging (since 2019)
  Own Resources Project
- EXC 2044 - C1: Evolution and asymptotics (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - C2: Multi-scale phenomena and macroscopic structures (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - C4: Geometry-based modelling, approximation, and reduction (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - C3: Interacting particle systems and phase transitions (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 – Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure (2019 – 2025)
  Main DFG-Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - B3: Operator algebras & mathematical physics (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- Reconstruction of epilepsy-characteristic sources by means of a simultaneous evaluation of EEG- and MEG- data using calibrated realistic head models (since 2016)
  Own Resources Project
- Modeling and Simulation of TNF receptor clustering (since 2010)
  Own Resources Project
- CiM-IMPRS – Cells in Motion (CiM) Graduate School and International Max Planck Research School - Molecular Biomedicine (since 2010)
  Individual Granted Project: Federal Ministry of Culture and Science of the Federal State of North Rhine-Westphalia
Latest Publications
- Esposito, A, Patacchini, FS, and Schlichting, A. 2024. “On a Class of Nonlocal Continuity Equations on Graphs.” European Journal of Applied Mathematics, № 35 (1): 109–126. doi: 10.1017/S0956792523000128.
- Chevyrev, I., Gerasimovičs, A., and Weber, H. 2024. “Feature Engineering with Regularity Structures.” Journal of Scientific Computing, № 98 (13) doi: 10.1007/s10915-023-02401-4.
- Chandra, Ajay, de Lima Feltes, Guilherme, and Weber, Hendrik. 2024. “A priori bounds for 2-d generalised Parabolic Anderson Model.” arXiv doi: 10.48550/arXiv.2402.05544.
- Grazieschi, Paolo, Matetski, Konstantin, and Weber, Hendrik. 2024. “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.
- Grazieschi, Paolo, Matetski, Konstantin, and Weber, Hendrik. 2024. “Martingale-driven integrals and singular SPDEs.” Probability Theory and Related Fields, № 190: 1063–1120. doi: 10.1007/s00440-024-01311-2.
- Baumann, Lena, and Pirner, Marlies. 2024. “Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions.” in HYP2022 proceedings, edited by Carlos Parés, Manuel Castro, Tomas Morales de Luna and Maria Luz Muñoz-Ruiz. Berlin: Springer Nature.
- Pirner, Marlies. 2024. “A consistent kinetic Fokker-Planck model for gas mixtures.” Journal of Statistical Physics, № 191
- Wenzel, Tizian, Haasdonk, Bernard, Kleikamp, Hendrik, Ohlberger, Mario, and Schindler, Felix. 2024. “Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.” in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I. Lirkov and S. Margenov. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
- Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Biedinger, Christine, Fiedler, Jochen, Reidelbach, Marco, Shehu, Aurela, Schmidt, Burkhard, Koprucki, Thomas, Iglezakis, Dorothea, and Göddeke, Dominik. 2024. “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, Vol. 2048 of Communications in Computer and Information Science, edited by Emmanouel Garoufallou and Fabio Sartori. Heidelberg: Springer. doi: 10.1007/978-3-031-65990-4_14.
- Singh, A, Thale, S, Leibner, T, Lamparter, L, Ricker, A, Nüsse, H, Klingauf, J, Galic, M, Ohlberger, M, and Matis, M. 2024. “Dynamic interplay of microtubule and actomyosin forces drive tissue extension.” Nature Communications, № 15 (1): 3198–3198. doi: 10.1038/s41467-024-47596-8.
- Tim Keil, Mario Ohlberger, and Felix Schindler, Julia Schleuß. 2024. “Local training and enrichment based on a residual localization strategy.” in Proceedings of the Conference Algoritmy 2024, Vol. 8 of Proceedings of the Conference Algoritmy, edited by P Frolkovič, K Mikula and D Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
- Budde, Ilka, Schlichting, André, Ing, David, Schimmelpfennig, Sandra, Kuntze, Anna, Fels, Benedikt, Romac, Joelle M.-J., Swain, Sandip M., Liddle, Rodger A., Stevens, Angela, Schwab, Albrecht, and Pethő, Zoltán. 2024. “Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels.” BioRxiv, № 2024 doi: 10.1101/2023.12.22.572956.
- Holler, Martin, and Wirth, Benedikt. 2024. “Exact reconstruction and reconstruction from noisy data with anisotropic total variation.” SIAM Journal on Mathematical Analysis, № 56 (3): 2938–2967. doi: 10.1137/22M1508571.
- Braunsmann, Juliane, Rajković, Marko, Rumpf, Martin, and Wirth, Benedikt. 2024. “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.
- Holler, Martin, Schlüter, Alexander, and Wirth, Benedikt. 2024. “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.
- Mauritz, Marco, Schmitzer, Bernhard, and Wirth, Benedikt. 2024. “A Bayesian model for dynamic mass reconstruction from PET listmode data.” SIAM Journal on Mathematical Analysis, № 56 (5): 5840–5880. doi: 10.1137/23M161923X.
- Ceci, Stefano, and Seis, Christian. 2024. “On the dynamics of vortices in viscous 2D flows.” Mathematische Annalen, № 388: 1937–1967. doi: 10.1007/s00208-023-02568-z.
- Seis, Christian, and Winkler, Dominik. 2024. “Invariant Manifolds for the Thin Film Equation.” Archive for Rational Mechanics and Analysis, № 248 (2) doi: 10.1007/s00205-024-01968-y.
- Keil, Tim, Ohlberger, Mario, and Schindler, Felix. 2024. “Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.” in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I Lirkov and S Margenov. Berlin: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
- Seis, Christian, and Winkler, Dominik. 2024. “Fine large-time asymptotics for the axisymmetric Navier-Stokes equations.” Journal of Evolution Equations, № 24 72. doi: 10.1007/s00028-024-01001-5.
- Meyer, David, and Seis, Christian. 2024. “Propagation of regularity for transport equations. A Littlewood-Paley approach.” Indiana University Mathematics Journal, № 73 (2): 445–473.
- Choi, Beomjun, and Seis, Christian. 2024. “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.
- Otto, Felix, Sauer, Jonas, Smith, Scott, and Weber, Hendrik. 2024. “A priori bounds for quasi-linear SPDEs in the full sub-critical regime.” Journal of the European Mathematical Society, № online first doi: 10.4171/jems/1574.
- Esquivel, Salvador, and Weber, Hendrik. 2024. “A priori bounds for the dynamic fractional Φ4 model on T3 in the full subcritical regime.” arXiv e-prints doi: arXiv:2411.16536.
- Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. 2024. “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.

Research Areas

Interdisciplinary cooperations

Ongoing projects and recent publications

Current Projects

Latest Publications