edoc

On multilevel quadrature for elliptic stochastic partial differential equations

Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus. (2013) On multilevel quadrature for elliptic stochastic partial differential equations. In: Sparse grids and applications. Berlin-Heidelberg, pp. 161-179.

Full text not available from this repository.

Official URL: http://edoc.unibas.ch/dok/A6070669

Downloads: Statistics Overview

Abstract

In this article, we show that the multilevel Monte Carlo method for elliptic stochastic partial differential equations can be interpreted as a sparse grid approximation. By using this interpretation, the method can straightforwardly be generalized to any given quadrature rule for high dimensional integrals like the quasi Monte Carlo method or the polynomial chaos approach. Besides the multilevel quadrature for approximating the solution's expectation, a simple and efficient modification of the approach is proposed to compute the stochastic solution's variance. Numerical results are provided to demonstrate and quantify the approach. In this article, we show that the multilevel Monte Carlo method for elliptic stochastic partial differential equations can be interpreted as a sparse grid approximation.By using this interpretation, the method can straightforwardly be generalized to any given quadrature rule for high dimensional integrals like the quasi Monte Carlo method or the polynomial chaos approach. Besides the multilevel quadrature for approximatingthe solution's expectation, a simple and efficient modification of the approach is proposed to compute the stochastic solution's variance. Numerical results are provided to demonstrate and quantify the approach.
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:Book Section, refereed
Book Section Subtype:Further Contribution in a Book
Bibsysno:Link to catalogue
Publisher:Springer
Note:Also published in: Lecture Notes in Computational Science and Engineering. - Berlin-Heidelberg : Springer. - 88 (2013), S. 161-179 -- Publication type according to Uni Basel Research Database: Book item
Last Modified:13 Apr 2018 06:17
Deposited On:21 Jun 2013 12:23

Repository Staff Only: item control page