edoc

Multilevel Accelerated Quadrature for PDEs with Log-Normally Distributed Diffusion Coefficient

Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus. (2016) Multilevel Accelerated Quadrature for PDEs with Log-Normally Distributed Diffusion Coefficient. SIAM/ASA Journal on Uncertainty Quantification, 4 (1). pp. 520-551.

[img] PDF - Accepted Version
2536Kb

Official URL: http://edoc.unibas.ch/42573/

Downloads: Statistics Overview

Abstract

This article is dedicated to multilevel quadrature methods for the rapid solution of stochastic partial differential equations with a log-normally distributed diffusion coefficient. The key idea of such 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 moments with focus on the mean and the 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. This article is dedicated to multilevel quadrature methods forthe rapid solution of stochastic partial differential equationswith a log-normally distributed diffusion coefficient. The key ideaof such 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 moments with focus on the mean and the 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)
UniBasel Contributors:Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus
Item Type:Article, refereed
Article Subtype:Research Article
e-ISSN:2166-2525
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Last Modified:21 Jun 2018 14:54
Deposited On:20 Sep 2016 13:37

Repository Staff Only: item control page