Two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method for 2-d problems

T. Tran*, E. P. Stephan

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    We study two-level additive Schwarz preconditioners for the h-p version of the Galerkin boundary element method when used to solve hypersingular integral equations of the first kind, which arise from the Neumann problems for the Laplacian in two dimensions. Overlapping and non-overlapping methods are considered. We prove that the non-overlapping preconditioner yields a system of equations having a condition number bounded by c(1 + logp)2 maxi(1 + logHi/hi) where Hi is the length of the i-th subdomain, hi is the maximum length of the elements in this subdomain, and p is the maximum polynomial degree used. For the overlapping method, we prove that the condition number is bounded by c(1 + logH/δ)2(1 + logp)2 where δ is the size of the overlap and H = maxiHi. We also discuss the use of the non-overlapping method when the mesh is geometrically graded. The condition number in that case is b ounded by c log2 M, where M is the degrees of freedom.

    Original languageEnglish
    Pages (from-to)57-82
    Number of pages26
    JournalComputing (Vienna/New York)
    Volume67
    Issue number1
    DOIs
    Publication statusPublished - 2001

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