edoc

Multilevel accelerated quadrature for PDEs with log-normal distributed random coefficient

Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus. (2013) Multilevel accelerated quadrature for PDEs with log-normal distributed random coefficient. Preprints Fachbereich Mathematik, 2013 (18).

[img] PDF - Published Version
3024Kb

Official URL: https://edoc.unibas.ch/70036/

Downloads: Statistics Overview

Abstract

This article is dedicated to multilevel quadrature methods for the rapid solution of stochastic partial differential equations with a log-normal distributed diffusion coefficient. The key idea of these approaches is a sparse grid approximation of the occurring product space between the stochastic and the spatial variable. We develop the mathematical theory and present error estimates for the computation of the solution's statistical moments with focus on the mean and variance. Especially, the present framework covers the multilevel Monte Carlo method and the multilevel quasi Monte Carlo method as special cases. The theoretical findings are supplemented by numerical experiments.
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 Peters, Michael and Siebenmorgen, Markus
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:13 May 2019 05:38
Deposited On:28 Mar 2019 09:52

Repository Staff Only: item control page