Solving Stochastic Collocation Systems with Algebraic Multigrid

Andrew D. Gordon () and Catherine E. Powell ()
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Andrew D. Gordon: University of Manchester, School of Mathematics
Catherine E. Powell: University of Manchester, School of Mathematics

A chapter in Numerical Mathematics and Advanced Applications 2009, 2010, pp 377-385 from Springer

Abstract: Abstract Stochastic collocation methods facilitate the numerical solution of PDEs with random data and give rise to large sequences of linear systems. For elliptic PDEs, algebraic multigrid (AMG) is a robust solver and considered individually, the systems are trivial to solve. The challenge lies in exploiting the systems’ similarities to minimize the cost of solving the entire sequence. We propose an efficient solver that is more robust than other solution strategies in the literature. In particular, we show that it is feasible to use a finely-tuned AMG preconditioner for each system if key set-up information is reused. The method is robust with respect to variations in discretization and statistical parameters for stochastically linear and nonlinear data.

Keywords: Conjugate Gradient; Coarse Grid; Sparse Grid; Elliptic PDEs; Stochastic Collocation (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11795-4_40

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DOI: 10.1007/978-3-642-11795-4_40

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