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 - <p style="text-align: justify;">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.</p>