Analyses on the finite difference method by Gibou et al. for Poisson equation

Gangjoon Yoon, Chohong Min

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Gibou et al. in [4] introduced a finite difference method for solving the Poisson equation in irregular domains with the Dirichlet boundary condition. Contrary to its great importance, its properties have not been mathematically analyzed, but have just been numerically observed. In this article, we present two analyses for the method. One proves that its solution is second order accurate, and the other estimates the condition number of its linear system. According to our estimation, the condition number of the unpreconditioned linear system is of size O(1/(h{dot operator}hmin)), and each of Jacobi, SGS, and ILU preconditioned systems is of size O(h-2). Furthermore, our analysis shows that the condition number of MILU is of size O(h-1), the most successful one.

Original languageEnglish
Pages (from-to)184-194
Number of pages11
JournalJournal of Computational Physics
Volume280
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Convergence analysis
  • Finite difference method
  • Poisson equation
  • Preconditioning

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