Karhunen-Loève approximation of random fields by generalized fast multipole methods
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
On the Acoustic Single Layer Potential: Stabilization and Fourier Analysis
SIAM Journal on Scientific Computing
Sparse second moment analysis for elliptic problems in stochastic domains
Numerische Mathematik
Fast Matrix-Vector Multiplication in the Sparse-Grid Galerkin Method
Journal of Scientific Computing
| Hi-index | 0.00 |
We consider the weakly singular boundary integral equation Vu=g(@w) on a deterministic smooth closed curve @C@?R^2 with random loading g(@w). 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 @?"i"="1^kV. The standard full tensor product Galerkin BEM requires O(N^k) unknowns for the kth moment problem, where N is the number of unknowns needed to discretize @C. 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(N^k) to O(N(logN)^k^-^1).