Date: Thursday, 23rd November, 16:00 – 16:45 excluding informal discussion.
Location: Ravelijn RA 1501.
Speaker: Prof.dr. Markus Bachmayr, Uni Bonn
Title: Sparse and low-rank approximations for parametric and random PDEs
Abstract:
In this talk, we consider methods for the simultaneous approximation of families of PDEs with parameter-dependent coefficients, which leads to high-dimensional problems on the combined spatial and parametric domains. A case of particular interest are problems with anisotropic dependence on countably many parameters, as they arise when uncertain coefficients are modelled as random fields. Two important classes of methods are on the one hand sparse polynomial expansions, and on the other hand low-rank tensor decompositions where problem-adapted basis functions are computed. It turns out that which type of approximation is preferable and which convergence rates and computational complexity of solvers can be achieved depends strongly on the type and structure of the parameter-dependence in the PDE. We give an overview of several illustrative recent results in this direction.
Based on joint works with Albert Cohen, Wolfgang Dahmen, Ron DeVore, Dinh Dung, Giovanni Migliorati, and Christoph Schwab
