edoc

Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM

Harbrecht, Helmut and Schmidlin, Marc. (2018) Multilevel quadrature for elliptic problems on random domains by the coupling of FEM and BEM. Preprints Fachbereich Mathematik, 2018 (03).

[img] PDF - Published Version
485Kb

Official URL: https://edoc.unibas.ch/69926/

Downloads: Statistics Overview

Abstract

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 loading. This domain mapping method is quite efficient for theory and practice, since only a single domain discretization is needed. Nonetheless, it is not useful for applying multilevel accelerated methods to efficiently deal with the random parameter. This issues from the fact that the domain discretization needs to be fine enough in order to avoid indefinite diffusion matrices. To overcome this obstruction, we are going to couple the finite element method with the boundary element method. In this article, we verify the required regularity with respect to the random perturbation field, derive the coupling formulation, and show by numerical results that the approach is feasible.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Schmidlin, Marc
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:17 Apr 2019 19:50
Deposited On:28 Mar 2019 09:51

Repository Staff Only: item control page