Fast Solving the Cauchy Problems of Poisson Equation in an Arbitrary Three-Dimensional Domain  

作　　者：Cheinshan Liu Fajie Wang Wenzheng Qu 

机构地区：[1]Center for Numerical Simulation Software in Engineering and Sciences,College of Mechanics and Materials,Hohai University,Nanjing 211100,China [2]Department of Mechanical and Mechatronic Engineering,National Taiwan Ocean University,Keelung 202-24,Taiwan [3]School of Electromechanic Engineering,Qingdao University,Qingdao 266071,China [4]Institute of Applied Mathematics,Shandong University of Technology,Zibo 255049,China

出　　处：《Computer Modeling in Engineering & Sciences》2018年第3期351-380,共30页工程与科学中的计算机建模（英文）

基　　金：The work described in this paper was supported by the Thousand Talents Plan of China(Grant No.A1211010);the Fundamental Research Funds for the Central Universities(Grant nos.2017B656X14,2017B05714);the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX17_0487);the Natural Science Foundation of Shandong Province of China(Grant No.ZR2017BA003).

摘　　要：In this paper we propose a novel two-stage method to solve the threedimensional 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 directions are uniformly distributed on a unit circle 1,and the scales are determined a priori by the collocation points on boundary.Two examples of 3D data interpolation,and several numerical examples of direct and inverse Cauchy problems in complex domain confirm the efficiency of the MSPM and the MSDTM.

关 键 词：Poisson equation multiple/scale/direction Trefftz METHOD multiple-scale polynomial METHOD IRREGULAR DOMAIN inverse CAUCHY problem 

分 类 号：O17[理学—数学]