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Solving Stochastic Collocation Systems with Algebraic Multigrid

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Andrew D. Gordon

    (University of Manchester, School of Mathematics)

  • Catherine E. Powell

    (University of Manchester, School of Mathematics)

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.

Suggested Citation

  • Andrew D. Gordon & Catherine E. Powell, 2010. "Solving Stochastic Collocation Systems with Algebraic Multigrid," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 377-385, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_40
    DOI: 10.1007/978-3-642-11795-4_40
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