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Volume 19, Issue 2-3
A Computational Study of Preconditioning Techniques for the Stochastic Diffusion Equation with Lognormal Coefficient

Eugenio Aulisa, Giacomo Capodaglio & Guoyi Ke

Int. J. Numer. Anal. Mod., 19 (2022), pp. 220-236.

Published online: 2022-04

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  • 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.

  • Keywords

Stochastic diffusion equation, lognormal coefficient, stochastic Galerkin method, field-split, preconditioning, geometric multigrid, GMRES.

  • AMS Subject Headings

65F08, 65C30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-19-220, author = {Aulisa , EugenioCapodaglio , Giacomo and Ke , Guoyi}, title = {A Computational Study of Preconditioning Techniques for the Stochastic Diffusion Equation with Lognormal Coefficient}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20478.html} }
TY - JOUR T1 - A Computational Study of Preconditioning Techniques for the Stochastic Diffusion Equation with Lognormal Coefficient AU - Aulisa , Eugenio AU - Capodaglio , Giacomo AU - Ke , Guoyi JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 220 EP - 236 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20478.html KW - Stochastic diffusion equation, lognormal coefficient, stochastic Galerkin method, field-split, preconditioning, geometric multigrid, GMRES. AB -

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.

Aulisa , EugenioCapodaglio , Giacomo and Ke , Guoyi. (2022). A Computational Study of Preconditioning Techniques for the Stochastic Diffusion Equation with Lognormal Coefficient. International Journal of Numerical Analysis and Modeling. 19 (2-3). 220-236. doi:
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