4 papers
The Gevrey class implicit mapping theorem with application to UQ of semilinear elliptic PDEs
Helmut Harbrecht, Marc Schmidlin, Christoph Schwab
This article is concerned with a regularity analysis of parametric operator equations with a perspective on uncertainty quantification. We study the regularity of mappings between…
Space-time multilevel quadrature methods and their application for cardiac electrophysiology
Seif Ben Bader, Helmut Harbrecht, Rolf Krause +3
We present a novel approach which aims at high-performance uncertainty quantification for cardiac electrophysiology simulations. Employing the monodomain equation to model the tran…
Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM
Helmut Harbrecht, Marc Schmidlin
Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loa…
Multilevel Methods for Uncertainty Quantification of Elliptic PDEs with Random Anisotropic Diffusion
Helmut Harbrecht, Marc Schmidlin
We consider elliptic diffusion problems with a random anisotropic diffusion coefficient, where, in a notable direction given by a random vector field, the diffusion strength differ…