Parallel domain decomposition methods for stochastic elliptic equations

Chao Jin

doi:10.1137/060662381

Parallel domain decomposition methods for stochastic elliptic equations

2007-01-01

25

PRE

AI

DOI：10.1137/060662381

Original

Original request for help

Save

Abstract

En 中文

We present parallel Schwarz-type domain decomposition preconditioned recycling Krylov subspace methods for the numerical solution of stochastic elliptic problems, whose coefficients are assumed to be a random field with finite variance. Karhunen-Loeve (KL) expansion and double orthogonal polynomials are used to reformulate the stochastic elliptic problem into a large number of related but uncoupled deterministic equations. The key to an efficient algorithm lies in recycling computed subspaces. Based on a careful analysis of the KL expansion, we propose and test a grouping algorithm that tells us when to recycle and when to recompute some components of the expensive computation. We show theoretically and experimentally that the Schwarz preconditioned recycling GMRES method is optimal for the entire family of linear systems. A fully parallel implementation is provided, and scalability results are reported in the paper.

Keywords:

stochastic elliptic equations

domain decomposition

recycling Krylov subspace method

parallel scalability

Parallel domain decomposition methods for stochastic elliptic equations

Abstract

Journal

Organization