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

Silvester, David and Pranjal, (2015) An optimal iterative solver for linear systems arising from SFEM approximation of diffusion equations with random coefficients. [MIMS Preprint]

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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 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: professor david silvester
Date Deposited: 17 Mar 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2273

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