图书馆订阅: Guest
Begell Digital Portal Begell 数字图书馆 电子图书 期刊 参考文献及会议录 研究收集
国际不确定性的量化期刊
影响因子: 4.911 5年影响因子: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.2014007353
pages 333-348

TRUNCATED HIERARCHICAL PRECONDITIONING FOR THE STOCHASTIC GALERKIN FEM

Bedrich Sousedik
Department of Mathematics and Statistics, University of Maryland, Baltimore County, USA
Roger Ghanem
Sony Astani Department of Aerospace and Mechanical Engineering, University of Southern California, 210 KAP Hall, Los Angeles, California 90089, USA

ABSTRACT

Stochastic Galerkin finite element discretizations of partial differential equations with coefficients characterized by arbitrary distributions lead, in general, to fully block dense linear systems.We propose two novel strategies for constructing preconditioners for these systems to be used with Krylov subspace iterative solvers. In particular, we present a variation of the hierarchical Schur complement preconditioner, developed recently by the authors, and an adaptation of the symmetric block Gauss-Seidel method. Both preconditioners take advantage of the hierarchical structure of global stochastic Galerkin matrices, and also, when applicable, of the decay of the norms of the stiffness matrices obtained from the polynomial chaos expansion of the coefficients. This decay allows to truncate the matrix-vector multiplications in the action of the preconditioners. Also, throughout the global matrix hierarchy, we approximate solves with certain submatrices by the associated diagonal block solves. The preconditioners thus require only a limited number of stiffness matrices obtained from the polynomial chaos expansion of the coefficients, and a preconditioner for the diagonal blocks of the global matrix. The performance is illustrated by numerical experiments.


Articles with similar content:

A STOPPING CRITERION FOR ITERATIVE SOLUTION OF STOCHASTIC GALERKIN MATRIX EQUATIONS
International Journal for Uncertainty Quantification, Vol.6, 2016, issue 3
Christophe Audouze , Pär Håkansson, Prasanth B. Nair
A STOCHASTIC COLLOCATION METHOD FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS AND RANDOM INPUTS
International Journal for Uncertainty Quantification, Vol.10, 2020, issue 2
Lijun Yi, Ling Guo
GENERALIZED MULTISCALE FINITE ELEMENT METHODS: OVERSAMPLING STRATEGIES
International Journal for Multiscale Computational Engineering, Vol.12, 2014, issue 6
Michael Presho, Yalchin Efendiev, Guanglian Li, Juan Galvis
TIME-SPACE DOMAIN HIGH-ORDER STAGGERED-GRID FINITE DIFFERENCE METHOD FOR POROUS MEDIA
Journal of Porous Media, Vol.17, 2014, issue 9
Jinghuai Gao, Yijie Zhang
AN ADAPTIVE DOMAIN DECOMPOSITION PRECONDITIONER FOR CRACK PROPAGATION PROBLEMS MODELED BY XFEM
International Journal for Multiscale Computational Engineering, Vol.11, 2013, issue 6
Haim Waisman, Luc Berger-Vergiat