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2015.20: An optimal iterative solver for linear systems arising from SFEM approximation of diffusion equations with random coefficients

2015.20: David Silvester and Pranjal (2015) An optimal iterative solver for linear systems arising from SFEM approximation of diffusion equations with random coefficients.

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Abstract

This paper discusses the design and implementation of efficient solution algorithms for symmetric linear systems associated with stochastic Galerkin approximation of elliptic PDE problems with correlated random data. The novel feature of our iterative solver is the incorporation of error control in the natural "energy" norm in combination with an effective a posteriori estimator for the PDE approximation error. This leads to a robust and optimally efficient stopping criterion: the iteration is terminated as soon as the algebraic error is insignificant compared to the approximation error.

Item Type:MIMS Preprint
Uncontrolled Keywords:Stochastic Galerkin approximation, PDEs with random data, parametric operator equations, a posteriori error analysis, iterative solvers, MINRES, optimal preconditioning
Subjects:MSC 2000 > 35 Partial differential equations
MSC 2000 > 65 Numerical analysis
MIMS number:2015.20
Deposited By:professor david silvester
Deposited On:17 March 2015

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