Upcoming Event: Oden Institute Seminar

Inaugural J. Tinsley Oden Distinguished Lecture: Mathematical Challenges in CSE: From Modeling through Analysis to Simulation

Barbara Wohlmuth, Chair, Department of Numerical Analysis, Technical University of Munich (TUM)

Abstract

In this talk, we address several numerical aspects and mathematical challenges in PDE based simulations. High resolution finite element simulations are typically expensive due to, e.g., complex geometries, non-linear material laws or different scales. Additionally data uncertainties are ubiquitous in many application fields, such as subsurface flow, climate prediction or cell growth and the development of novel uncertainty quantification methods is an active field of research. Firstly, we illustrate characteristic challenges on the basis of specific application relevant examples. Secondly, we present ideas how to tackle such challenges algorithmically and provide a rigorous mathematical framework for the numerical analysis based on variational principles and kernel approximations. Thirdly we consider dilute polymers, tumor growth phase-field models and cerebral aneurysms as proto-typical showcases for the application of Faedo--Galerkin approaches in combination with energy estimates and compactness arguments to obtain existence results and of dimension reduced 0d-1d-3d models to obtain algorithmic efficiency. Thirdly we consider dilute polymers and tumor growth phase-field models as proto-typical showcases for the application of Faedo--Galerkin approaches in combination with 
energy estimates and compactness arguments to obtain existence results. In case of coiled cerebral aneurysms, we use dimension reduced 0d-1d-3d models to enhance computational efficiency and in case of fractional non-local operators, we augment the dimension to preserve locality.

Biography

Barbara Wohlmuth is the head of the Chair for Numerical Mathematics at the Technische Universität München (TUM). She studied mathematics in Munich and Grenoble. As a PostDoc, she stayed at the Courant Institute of Mathematical Sciences at New York University and as a visiting professor in France, Hong Kong, and Norway. Barbara Wohlmuth works on the numerical simulation of partial differential equations, in particular, on advanced discretization techniques, multi-scale iterative solvers such as large-scale hybrid multigrid methods, the mathematical modeling of coupled multi-field problems, uncertainty quantification, and many applications areas in biomechanics and porous media. As an author of over 200 scientific publications, she serves on the Editorial Board of several international journals with a special focus on numerical analysis and computational sciences and engineering. Barbara Wohlmuth has been twice elected member of the DFG Review Board 312 for Mathematics and is currently a member of the Bavarian Academy of 
Sciences,  the German National Academy of Sciences Leopoldina, and the European Academy of Sciences. In 2012, she was awarded the prestigious Gottfried Wilhelm Leibniz Prize by the German Research Foundation. At TUM, she acts as the scientific director of the International Graduate School of Science and Engineering with four different interdisciplinary and international funding lines and coordinates qualification programs for PhD and Post-doctoral researchers.