Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 252, Issue -, Pages 128-141Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2013.06.013
Keywords
Elliptic boundary value problem; Random diffusion; Sparse tensor product approximation; Combination technique
Funding
- Swiss National Science Foundation (SNSF)
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We consider the efficient deterministic solution of elliptic boundary value problems with random diffusion matrix. Assuming random perturbations with known k moments, we derive, to leading order in the random perturbation's amplitude, deterministic equations for k moments of the random solution. The solution's k-th moment satisfies a k-fold tensor product boundary value problem on the k-fold product domain which can efficiently be discretized in sparse tensor product spaces. By defining the complement spaces via Galerkin projections, the related system of linear equations decouples and can be solved by standard multilevel finite element solvers. Numerical results for k = 2 are presented to validate and quantify our theoretical findings. (C) 2013 Elsevier Inc. All rights reserved.
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