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On multilevel quadrature for elliptic stochastic partial differential equations

Harbrecht, Helmut and Peters, Michael and Siebenmorgen, Markus. (2011) On multilevel quadrature for elliptic stochastic partial differential equations. Preprints Fachbereich Mathematik, 2011 (01).

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Abstract

In the present 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.
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 19:35
Deposited On:28 Mar 2019 09:52

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