An adaptive choice of primal constraints for BDDC domain decomposition algorithms

Juan G. Calvo, Olof B. Widlund

Research output: Contribution to journalArticlepeer-review

Abstract

An adaptive choice for primal spaces based on parallel sums is developed for BDDC deluxe methods and elliptic problems in three dimensions. The primal space, which forms the global, coarse part of the domain decomposition algorithm and which is always required for any competitive algorithm, is defined in terms of generalized eigenvalue problems related to subdomain edges and faces; selected eigenvectors associated to the smallest eigenvalues are used to enhance the primal spaces. This selection can be made automatic by using tolerance parameters specified for the subdomain faces and edges. Numerical results verify the results and provide a comparison with primal spaces commonly used. They include results for cubic subdomains as well as subdomains obtained by a mesh partitioner. Different distributions for the coefficients are also considered with constant coefficients, highly random values, and channel distributions.

Original languageEnglish (US)
Pages (from-to)524-544
Number of pages21
JournalElectronic Transactions on Numerical Analysis
Volume45
StatePublished - 2016

Keywords

  • Adaptive primal constraints
  • BDDC deluxe preconditioners
  • Domain decomposition
  • Elliptic problems

ASJC Scopus subject areas

  • Analysis

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