Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity

Paulo Goldfeld, Luca F. Pavarino, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Balancing Neumann-Neumann methods are extented to mixed formulations of the linear elasticity system with discontinuous coefficients, discretized with mixed finite or spectral elements with discontinuous pressures. These domain decomposition methods implicitly eliminate the degrees of freedom associated with the interior of each subdomain and solve iteratively the resulting saddle point Schur complement using a hybrid preconditioner based on a coarse mixed elasticity problem and local mixed elasticity problems with natural and essential boundary conditions. A polylogarithmic bound in the local number of degrees of freedom is proven for the condition number of the preconditioned operator in the constant coefficient case. Parallel and serial numerical experiments confirm the theoretical results, indicate that they still hold for systems with discontinuous coefficients, and show that our algorithm is scalable, parallel, and robust with respect to material heterogeneities. The results on heterogeneous general problems are also supported in part by our theory.

Original languageEnglish (US)
Pages (from-to)283-324
Number of pages42
JournalNumerische Mathematik
Volume95
Issue number2
DOIs
StatePublished - Aug 2003

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Discontinuous Coefficients
Elasticity Problem
Linear Elasticity
Mixed Problem
Preconditioner
Balancing
Elasticity
Degree of freedom
Spectral Elements
Mixed Formulation
Schur Complement
Mixed Finite Elements
Domain Decomposition Method
Approximation
Saddlepoint
Condition number
Domain decomposition methods
Interior
Eliminate
Numerical Experiment

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity. / Goldfeld, Paulo; Pavarino, Luca F.; Widlund, Olof B.

In: Numerische Mathematik, Vol. 95, No. 2, 08.2003, p. 283-324.

Research output: Contribution to journalArticle

Goldfeld, Paulo ; Pavarino, Luca F. ; Widlund, Olof B. / Balancing Neumann-Neumann preconditioners for mixed approximations of heterogeneous problems in linear elasticity. In: Numerische Mathematik. 2003 ; Vol. 95, No. 2. pp. 283-324.
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