| Private Homepage | https://www.uni-muenster.de/AMM/engwer/team/engwer.shtml |
| Research Interests | Numerical methods for partial differential equations Scoientific Computing High-Performance Computing Design and development of numerical software Cut-cell methods Numerical methods for surface PDEs and geometric PDEs Biomedical Applications |
| Topics in Mathematics Münster | T9: Multi-scale processes and effective behaviour T10: Deep learning and surrogate methods |
| Current Publications | • Engwer, Christian; Ohlberger, Mario; Renelt, Lukas Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems. SIAM Journal on Scientific Computing Vol. 46 (5), 2024 online • Engwer,Christian; Ohlberger, Mario; Renelt, Lukas Construction of local reduced spaces for Friedrichs' systems via randomized training. , 2024 online • Medani, Takfarinas; Garcia-Prieto, Juan; Tadel, Francois; Antonakakis, Marios; Erdbrügger, Tim; Höltershinken, Malte; Mead, Wayne; Schrader, Sophie; Joshi, Anand; Engwer, Christian; Wolters, Carsten H.; Mosher, John C.; Leahy, Richard M. Brainstorm-DUNEuro: An integrated and user-friendly Finite Element Method for modeling electromagnetic brain activity. NeuroImage Vol. 267, 2023 online • Renelt, Lukas; Ohlberger, Mario; Engwer, Christian An optimally stable approximation of reactive transport using discrete test and infinite trial spaces. Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related ProblemsSpringer Proceedings in Mathematics & Statistics Vol. 2, 2023 online • Erdbrügger, T.; Westhoff, A.; Höltershinken, M.; Radecke, J.-O.; Buschermöhle,Y.; Buyx, A.; Wallois, F.; Pursiainen, S.; Gross, J.; Lencer, R.; Engwer, C.; Wolters, C.H. CutFEM forward modeling for EEG source analysis. Frontiers in Human Neuroscience Vol. 17, 2023 online • Renelt, Lukas; Ohlberger, Mario; Engwer, Christian An optimally stable approximation of reactive transport using discrete test and infinite trial spaces. Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related ProblemsSpringer Proceedings in Mathematics & Statistics Vol. 2, 2023 online • Bastian P, Blatt M, Dedner A, Dreier N, Engwer C, Fritze R, Gräser C, Kempf D, Klöfkorn R, Ohlberger M, Sander O The DUNE Framework: Basic Concepts and Recent Developments. Computers & Mathematics with Applications Vol. 81, 2021, pp 75-112 online • Streitbürger Florian, Engwer Christian, May Sandra, Nüßing Andreas Monotonicity considerations for stabilized DG cut cell schemes for the unsteady advection equation. , 2021 online • Dreier Nils-Arne, Engwer Christian Strategies for the vectorized Block Conjugate Gradients method. , 2021 online |
| Current Projects | • Interdisziplinäres Lehrprogramm zu maschinellem Lernen und künstlicher Intelligenz The aim of the project is to establish and test a graduated university-wide teaching programme on machine learning (ML) and artificial intelligence (AI). AI is taught as an interdisciplinary cross-sectional topic that has diverse application possibilities in basic research as well as in economy and society, but consequently also raises social, ethical and ecological challenges. The modular teaching program is designed to enable students to build up their AI knowledge, apply it independently and transfer it directly to various application areas. The courses take place in a broad interdisciplinary context, i.e., students from different departments take the courses together and work together on projects. online• BrainStorm: Highly Extensible Software for Advanced Electrophysiology and MEG/EEG Imaging Software grant for integrating DUNEuro (http://www.duneuro.org) into Brainstorm (http://neuroimage.usc.edu/brainstorm) online • EXC 2044 - C1: Evolution and asymptotics In this unit, we will use generalisations of optimal transport metrics to develop gradient flow descriptions of (cross)-diffusion-reaction systems, rigorously analyse their pattern forming properties, and develop corresponding efficient numerical schemes. Related transport-type- and hyperbolic systems will be compared with respect to their pattern-forming behaviour, especially when mass is conserved. Bifurcations and the effects of noise perturbations will be explored. Moreover, we aim to understand defect structures, their stability and their interactions. Examples are the evolution of fractures in brittle materials and of vortices in fluids. Our analysis will explore the underlying geometry of defect dynamics such as gradient descents or Hamiltonian structures. Also, we will further develop continuum mechanics and asymptotic descriptions for multiple bodies which deform, divide, move, and dynamically attach to each other in order to better describe the bio-mechanics of growing and dividing soft tissues. Finally, we are interested in the asymptotic analysis of various random structures as the size or the dimension of the structure goes to infinity. More specifically, we shall consider random polytopes and random trees.For random polytopes we would like to compute the expected number of faces in all dimensions, the expected (intrinsic) volume, and absorption probabilities, as well as higher moments and limit distributions for these quantities. online • EXC 2044 - C2: Multi-scale phenomena and macroscopic structures In multi-scale problems, geometry and dynamics on the micro-scale influence structures on coarser scales. In this research unit we will investigate and analyse such structural interdependence based on topological, geometrical or dynamical properties of the underlying processes. We are interested in transport-dominated processes, such as in the problem of how efficient a fluid can be stirred to enhance mixing, and in the related analytical questions. A major concern will be the role of molecular diffusion and its interplay with the stirring process. High Péclet number flow in porous media with reaction at the surface of the porous material will be studied. Here, the flowinduces pore-scale fluctuations that lead to macroscopic enhanced diffusion and reaction kinetics. We also aim at understanding advection-dominated homogenisation problems in random regimes. We aim at classifying micro-scale geometry or topology with respect to the macroscopic behaviour of processes considered therein. Examples are meta material modelling and the analysis of processes in biological material. Motivated by network formation and fracture mechanics in random media, we will analyse the effective behaviour of curve and free-discontinuity energies with stochastic inhomogeneity. Furthermore, we are interested in adaptive algorithms that can balance the various design parameters arising in multi-scale methods. The analysis of such algorithms will be the key towards an optimal distribution of computational resources for multi-scale problems. Finally, we will study multi-scale energy landscapes and analyse asymptotic behaviour of hierarchical patterns occurring in variational models for transportation networks and related optimal transport problems. In particular, we will treat questions of self-similarity, cost distribution, and locality of the fine-scale pattern. We will establish new multilevel stochastic approximation algorithms with the aim of numerical optimisation in high dimensions. online • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. online | christian.engwer@uni-muenster.de |
| Phone | +49 251 83-35067 |
| FAX | +49 251 83-32729 |
| Room | 120.020 |
| Secretary | Sekretariat Wernke Frau Silvia Wernke Telefon +49 251 83-35052 Fax +49 251 83-32729 Zimmer 120.001 |
| Address | Prof. Dr. Christian Engwer Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Orléans-Ring 10 48149 Münster |
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