Sparse p-version BEM for first kind boundary integral equations with random loading
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2008-03
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Report
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Abstract
We consider the weakly singular boundary integral equation Vu = g(w) on a deterministic smooth closed curve T>R2 with random loading g(w). The statistical moments of g up to order k are assumed to be known. The aim is the efficient deterministic computation of statistical moments MkU:=E, k>1. We derive a deterministic formulation for the kth statistical moment. It is posed in the tensor product Sobolev space and involves the k-fold tensor product operator V(k):=V. The standard full tensor product Galerkin BEM requires O(Nk) unknowns for the kth moment problem, where N is the number of unknowns needed to discretize T. Extending ideas of (?), we develop the p-sparse grid Galerkin BEM to reduce the number of unknowns from O(Nk) to O(N(logN)k-1).
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2008-02
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Seminar for Applied Mathematics, ETH Zurich
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03217 - Künsch, Hans Rudolf (emeritus)
03435 - Schwab, Christoph / Schwab, Christoph
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