Balancing domain decomposition by constraints associated with subobjects

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Abstract

A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) is presented. We are able to show that the condition number of the preconditioner is bounded by C(1+log(L∕h))2, where C is a constant, and h and L are the characteristic sizes of the mesh and the subobjects, respectively. As L can be chosen almost freely, the condition number can theoretically be as small as O(1). We will discuss the pros and cons of the preconditioner and its application to heterogeneous problems. Numerical results on supercomputers are provided.

Original languageEnglish
Pages (from-to)93-100
Number of pages8
JournalApplied Mathematics Letters
Volume87
DOIs
Publication statusPublished - 1 Jan 2019
Externally publishedYes

Keywords

  • BDDC
  • FETI-DP
  • Heterogeneous problems
  • Optimal preconditioner
  • Parallel solver

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