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A multigrid solver for two-dimensional stochastic diffusion equations

✍ Scribed by O.P. Le Maı̂tre; O.M. Knio; B.J. Debusschere; H.N. Najm; R.G. Ghanem

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
722 KB
Volume
192
Category
Article
ISSN
0045-7825

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✦ Synopsis

Steady and unsteady diffusion equations, with stochastic diffusivity coefficient and forcing term, are modeled in two dimensions by means of stochastic spectral representations. Problem data and solution variables are expanded using the Polynomial Chaos system. The approach leads to a set of coupled problems for the stochastic modes. Spatial finitedifference discretization of these coupled problems results in a large system of equations, whose dimension necessitates the use of iterative approaches in order to obtain the solution within a reasonable computational time. To accelerate the convergence of the iterative technique, a multigrid method, based on spatial coarsening, is implemented. Numerical experiments show good scaling properties of the method, both with respect to the number of spatial grid points and the stochastic resolution level.

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