edoc

Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains

Dölz, Jürgen and Harbrecht, Helmut. (2017) Hierarchical matrix approximation for the uncertainty quantification of potentials on random domains. Preprints Fachbereich Mathematik, 2017 (05).

[img] PDF - Published Version
2031Kb

Official URL: https://edoc.unibas.ch/69943/

Downloads: Statistics Overview

Abstract

Computing statistical quantities of interest of the solution of PDE on random domains is an important and challenging task in engineering. We consider the computation of these quantities by the perturbation approach. Especially, we discuss how third order accurate expansions of the mean and the correlation can numerically be computed. These expansions become even fourth order accurate for certain types of boundary variations. The correction terms are given by the solution of correlation equations in the tensor product domain, which can efficiently be computed by means of $\mathcal{H}$-matrices. They have recently been shown to be an efficient tool to solve correlation equations with rough data correlations, that is, with low Sobolev smoothness or small correlation length, in almost linear time. Numerical experiments in three dimensions for higher order ansatz spaces show the feasibility of the proposed algorithm. The application to a non-smooth domain is also included.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Dölz, Jürgen and Harbrecht, Helmut
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:17 Apr 2019 20:54
Deposited On:28 Mar 2019 09:51

Repository Staff Only: item control page