Poisson Preconditioning for Self-Adjoint Elliptic Problems

Poisson Preconditioning for Self-Adjoint Elliptic Problems

Year:    2014

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 5 : pp. 560–578

Abstract

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 operators. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1405-m4293

Journal of Computational Mathematics, Vol. 32 (2014), Iss. 5 : pp. 560–578

Published online:    2014-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Fast Poisson solver Interface problem Self-adjoint elliptic problem Conjugate gradient method.