TY - JOUR
T1 - Poisson Preconditioning for Self-Adjoint Elliptic Problems
AU - Houde Han & Chunxiong Zheng
JO - Journal of Computational Mathematics
VL - 5
SP - 560
EP - 578
PY - 2014
DA - 2014/10
SN - 32
DO - http://doi.org/10.4208/jcm.1405-m4293
UR - https://global-sci.org/intro/article_detail/jcm/9904.html
KW - Fast Poisson solver, Interface problem, Self-adjoint elliptic problem, Conjugate
gradient method.
AB - <p style="text-align: justify;">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.</p>