Title: Multigrid methods for stationary and timedependent partial differential equations with stochastic coefficients
Authors: Vandewalle, Stefan # ×
Issue Date: 4-Dec-2008
Conference: Computational Engineering Seminar location:Technical University of Darmstadt date:4 December 2008
Abstract: The stochastic finite element method is an important technique for solving certain classes of stochastic partial differential equations (PDEs). This method approximates the solution of the PDE by a generalized polynomial chaos expansion. By using a Galerkin projection in the stochastic dimension, the stochastic PDE is transformed into a coupled
set of deterministic PDEs. A finite element discretization converts this deterministic PDE system into a high dimensional algebraic system. Specialized iterative solvers are required to solve the resulting problem.

In this talk, we shall present an overview of iterative solution approaches. We start from iterative methods based on a block splitting of the system matrices. Next, we extend these methods for use as preconditioner for a Krylov method, and for use as smoother in a multilevel context. Then, the various solvers will be compared based on their convergence properties, computational cost and implementation effort.
Our findings are illustrated by means of two numerical problems. The first one is a steady-state diffusion problem with a discontinuous random field as diffusion coefficient. The second is a deterministic diffusion problem
defined on a random domain.
Publication status: published
KU Leuven publication type: AMa
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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