A BDDC method for mortar discretizations using a transformation of basis

Hyea Hyun Kim, Maksymilian Dryja, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

A BDDC (balancing domain decomposition by constraints) method is developed for elliptic equations, with discontinuous coefficients, discretized by mortar finite element methods for geometrically nonconforming partitions in both two and three space dimensions. The coarse component of the preconditioner is defined in terms of one mortar constraint for each edge/face, which is the intersection of the boundaries of a pair of subdomains. A condition number bound of the form Cmaxi{(1 + log(Hi/hi)) 2} is established under certain assumptions on the geometrically nonconforming subdomain partition in the three-dimensional case. Here H i and hi are the subdomain diameters and the mesh sizes, respectively. In the geometrically conforming case and the geometrically nonconforming cases in two dimensions, no assumptions on the subdomain partition are required. This BDDC preconditioner is also shown to be closely related to the Neumann-Dirichlet version of the FETI-DP algorithm. The results are illustrated by numerical experiments which confirm the theoretical results.

Original languageEnglish (US)
Pages (from-to)136-157
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume47
Issue number1
DOIs
StatePublished - Nov 10 2008

Keywords

  • BDDC
  • Change of basis
  • Elliptic problems
  • FETI-DP
  • Finite elements
  • Mortar methods
  • Parallel algorithms
  • Preconditioner

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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