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Solving the stochastic steady-state diffusion problem using multigrid
Authors:Elman  Howard; Furnival  Darran
Institution: Department of Computer Science and Institute for Advanced Computer Studies,University of Maryland, College Park, MD 20742, USA
Abstract: Darran Furnival We study multigrid for solving the stochastic steady-state diffusionproblem. We operate under the mild assumption that the diffusioncoefficient takes the form of a finite Karhunen-Loèveexpansion. The problem is discretized using a finite-elementmethodology using the polynomial chaos method to discretizethe stochastic part of the problem. We apply a multigrid algorithmto the stochastic problem in which the spatial discretizationis varied from grid to grid while the stochastic discretizationis held constant. We then show, theoretically and experimentally,that the convergence rate is independent of the spatial discretization,as in the deterministic case, and the stochastic discretization.
Keywords:Karhunen-Loè  ve expansion  multigrid  polynomial chaos
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