Lecture
Tuesday, 27 March 2018
9:00am - 9:45am
Campus Stuttgart-Vaihingen, Pfaffenwaldring 47
Room V 47.03
From Local Modifications to Global Effects in Finite Element Flow Simulation
We discuss two types of local and computationally inexpensive modifications resulting in finite element approximations of higher accuracy. In case one, we consider a fluid-thermal interaction problem. A local recovery of the discrete flux is performed such that mass conservation on a dual mesh can be guaranteed. The corrected flux enters then into the advective part of the energy equation. To further improve the performance in large scale simulation runs, we use a two-scale time integration scheme in combination with extrapolation techniques and an all-at-once multigrid solver for the flow part Node-wise defined Uzawa type smoothers guarantee level independent convergence rates for the variable V-cycle. In case two, the flowability in the discrete scheme is locally enhanced such that energy can be preserved. A variational crime analysis then guarantees improved convergence rates in case of non-convex domains with a re-entrant corner. All theoretical results are illustrated by a series of simulations.
Biosketch
Barbara Wohlmuth is a leading specialist in the field Computational Mathematics, Numerical Analysis and Scientific Computing. Between 2001 and 2010 she was Full Professor for High Performance Computing at the University of Stuttgart, and since 2010 she has a chair on Numerical Mathematics at the Technical University of Munich. Between 2015 and 2017 she was Magne Espedal Visiting Professor at the University of Bergen in Norway. She is a member of the Bavarian Academy of Sciences and Humanities and the European Academy of Sciences. In 2012 she received the prestigeous Gottfried Wilhelm Leibniz Prize of the DFG. Barbara Wohlmuth is a member of the Scientific Council of INRIA (France) and the ICES Board of Visitors (USA). She serves on numerous editorial boards of highly ranked international journals in mathematics and engineering and on the DFG Review Board 312. She has made significant and lasting contributions to the development and mathematical analysis of numerical algorithms for the approximate solution of partial differential equations that arise in the natural sciences and engineering.
