Physical Sciences and Mathematics Commons^™

Computing The Newton Potential In The Boundary Integral Equation For The Dirichlet Problem Of The Poisson Equation, Wenchao Guan, Ying Jiang, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Evaluating the Newton potential is crucial for efficiently solving the boundary integral equation of the Dirichlet boundary value problem of the Poisson equation. In the context of the Fourier-Garlerkin method for solving the boundary integral equation, we propose a fast algorithm for evaluating Fourier coefficients of the Newton potential by using a sparse grid approximation. When the forcing function of the Poisson equation expressed in the polar coordinates has mth-order bounded mixed derivatives, the proposed algorithm achieves an accuracy of order 𝒪(n^-m log³ n), with requiring 𝒪(n log² n) number of arithmetics for …