Schur complement domain decomposition algorithms for spectral methods

Tony Chan*, Danny Goovaerts

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Spectral methods have been using a domain decomposition approach for handling irregular domains. The main focus has been on appropriate matching conditions for the solutions across the subdomain boundaries. In this paper, we propose an efficient method for solving the discrete equations based on solving the Schur complement system for the interface variables. We consider both the Funaro-Maday-Patera weak C1 matching of the solutions on the interfaces and Orszag's exact C1 matching. Numerical results for the model problem show that the condition number of the Schur complement system is of order O(n2). We show how this can be improved to nearly O(1) by a boundary probe preconditioner. We also compare briefly our method and the alternating Neumann-Dirichlet method of Funaro-Quarteroni-Zanolli.

Original languageEnglish (US)
Pages (from-to)53-64
Number of pages12
JournalApplied Numerical Mathematics
Volume6
Issue number1-2
DOIs
StatePublished - Jan 1 1989

Keywords

  • Parallel algorithms
  • domain decomposition
  • partial differential equations
  • preconditioned conjugate gradient
  • spectral methods

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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