Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
Stochastic analysis
Advances in Engineering Software - Special issue on large-scale analysis, design and intelligent synthesis environments
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Solution of stochastic partial differential equations (spdes) using galerkin method: theory and applications
Shifted Kronecker Product Systems
SIAM Journal on Matrix Analysis and Applications
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Matrix Analysis
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The discretization of linear partial differential equations with random data by means of the stochastic Galerkin finite element method results in general in a large coupled linear system of equations. Using the stochastic diffusion equation as a model problem, we introduce and study a symmetric positive definite Kronecker product preconditioner for the Galerkin matrix. We compare the popular mean-based preconditioner with the proposed preconditioner which—in contrast to the mean-based construction—makes use of the entire information contained in the Galerkin matrix. We report on results of test problems, where the random diffusion coefficient is given in terms of a truncated Karhunen-Loève expansion or is a lognormal random field.