Cheinshan Liu1,2, Fajie Wang1,3,*, Wenzheng Qu4,*
CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.3, pp. 351-380, 2018, DOI:10.3970/cmes.2018.114.351
Abstract In this paper we propose a novel two-stage method to solve the three-dimensional Poisson equation in an arbitrary bounded domain enclosed by a smooth boundary. The solution is decomposed into a particular solution and a homogeneous solution. In the first stage a multiple-scale polynomial method (MSPM) is used to approximate the forcing term and then the formula of Tsai et al. [Tsai, Cheng, and Chen (2009)] is used to obtain the corresponding closed-form solution for each polynomial term. Then in the second stage we use a multiple/scale/direction Trefftz method (MSDTM) to find the solution of Laplace equation, of which the… More >
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