Private Homepage | https://www.uni-muenster.de/amm/ohlberger |

Research Interests | Numerical analysis for partial differential equations Error control and adaptivity for finite element and finite volume schemes Model reduction for parametrized partial differential equations Development and analysis of numerical multiscale methods Software development and scientific computing |

Project membershipMathematics Münster | C: Models and ApproximationsC2: Multi-scale phenomena and macroscopic structures C4: Geometry-based modelling, approximation, and reduction |

Current Publications | • Keil Tim, Ohlberger Mario A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 58, 2024 online• Singh A; Thale S; Leibner T; Lamparter L; Ricker A; Nüsse H; Klingauf J; Galic M; Ohlberger M; Matis M Dynamic interplay of microtubule and actomyosin forces drive tissue extension. Nature Communications Vol. 15 (1), 2024, pp 3198 online• Keil Tim, Ohlberger Mario A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 58, 2024 online• Singh A; Thale S; Leibner T; Lamparter L; Ricker A; Nüsse H; Klingauf J; Galic M; Ohlberger M; Matis M Dynamic interplay of microtubule and actomyosin forces drive tissue extension. Nature Communications Vol. 15 (1), 2024, pp 3198 online• Keil Tim, Ohlberger Mario A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems. ESAIM: Mathematical Modelling and Numerical Analysis Vol. 58, 2024 online• Haasdonk B, Kleikamp H, Ohlberger M, Schindler F, Wenzel T A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. SIAM Journal on Scientific Computing Vol. 45 (3), 2023 online• Landstorfer M, Ohlberger M, Rave S, Tacke M A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells. European Journal of Applied Mathematics Vol. 34 (3), 2023 online• Wenzel, Tizian; Haasdonk, Bernard; Kleikamp, Hendrik; Ohlberger, Mario; Schindler, Felix Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling. , 2023 online• Keil Tim, Ohlberger Mario, Schindler Felix Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization. , 2023 online |

Current Projects | • Mathematical Research Data Initiative - TA2: Scientific Computing Driven by the needs and requirements of mathematical research as well as scientific disciplines using mathematics, the NFDI-consortium MaRDI (Mathematical Research Data Initiative) will develop and establish standards and services for mathematical research data.
Mathematical research data ranges from databases of special functions and mathematical objects, aspects of scientific computing such as models and algorithms to statistical analysis of data with uncertainties. It is also widely used in other scientific disciplines due to the cross-disciplinary nature of mathematical methods. online• Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure We will tackle fundamentally important mathematical problems, viewing mathematics as an organic whole with countless interactions. Our research is unified by three major approaches: focusing on the underlying structure of a given problem, taking the geometric viewpoint and studying the relevant dynamics of group or semigroup actions. The theories which we will build will not only solve the problems under consideration but also many others of a similar nature; these theories will also raise exciting new questions. 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 |

E-Mail | mario dot ohlberger at uni-muenster dot de |

Phone | +49 251 83-33775 |

FAX | +49 251 83-32729 |

Room | 120.010 |

Secretary | Sekretariat Wernke Frau Silvia Wernke Telefon +49 251 83-35052 Fax +49 251 83-32729 Zimmer 120.001 |

Address | Prof. Dr. Mario Ohlberger Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |

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