کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645824 | 1342066 | 2009 | 15 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Sparse p-version BEM for first kind boundary integral equations with random loading Sparse p-version BEM for first kind boundary integral equations with random loading](/preview/png/4645824.png)
We consider the weakly singular boundary integral equation Vu=g(ω) on a deterministic smooth closed curve Γ⊂R2 with random loading g(ω). Given the kth order statistical moment of g, the aim is the efficient deterministic computation of the kth order statistical moment of u. 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 . 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 Γ. Extending ideas of [V.N. Temlyakov, Approximation of functions with bounded mixed derivative, Proc. Steklov Inst. Math. (1989) vi+121. A translation of Trudy Mat. Inst. Steklov 178 (1986)], we develop the p-Sparse Grid Galerkin BEM to reduce the number of unknowns from O(Nk) to O(N(logN)k−1).
Journal: Applied Numerical Mathematics - Volume 59, Issue 11, November 2009, Pages 2698-2712