POISSON PRECONDITIONING FOR SELF-ADJOINT ELLIPTIC PROBLEMS

作     者：Houde Han Chunxiong Zheng 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing 100084 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2014年第32卷第5期

页      面：560-578页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：The work of the first author was supported by the National Natural Science Foundation of China (91330203). The work of the second author was supported by the National Natural Science Foundation of China (10371218) and the Initiative Scientific Research Program of Tsinghua University 

主　　题：Fast Poisson solver Interface problem Self-adjoint elliptic problem Conjugategradient method. 

摘      要：In this paper, we formulate interface problem and Neumann elliptic boundary value problem into a form of linear operator equations with self-adjoint positive definite op- erators. We prove that in the discrete level the condition number of these operators is independent of the mesh size. Therefore, given a prescribed error tolerance, the classical conjugate gradient algorithm converges within a fixed number of iterations. The main computation task at each iteration is to solve a Dirichlet Poisson boundary value problem in a rectangular domain, which can be furnished with fast Poisson solver. The overall computational complexity is essentially of linear scaling.