A Computational Study of Preconditioning Techniques for the Stochastic Diffusion Equation with Lognormal Coefficient

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.

Author Details

Eugenio Aulisa

Giacomo Capodaglio

Guoyi Ke