A Computational Study of Preconditioning Techniques for the Stochastic Diffusion Equation with Lognormal Coefficient
Year: 2022
Author: Eugenio Aulisa, Giacomo Capodaglio, Guoyi Ke
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 2-3 : pp. 220–236
Abstract
We present a computational study of several preconditioning techniques for the GMRES algorithm applied to the stochastic diffusion equation with a lognormal coefficient discretized with the stochastic Galerkin method. The clear block structure of the system matrix arising from this type of discretization motivates the analysis of preconditioners designed according to a field-splitting strategy of the stochastic variables. This approach is inspired by a similar procedure used within the framework of physics based preconditioners for deterministic problems, and its application to stochastic PDEs represents the main novelty of this work. Our numerical investigation highlights the superior properties of the field-split type preconditioners over other existing strategies in terms of computational time and stochastic parameter dependence.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2022-IJNAM-20478
International Journal of Numerical Analysis and Modeling, Vol. 19 (2022), Iss. 2-3 : pp. 220–236
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Stochastic diffusion equation lognormal coefficient stochastic Galerkin method field-split preconditioning geometric multigrid GMRES.