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A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems
Author(s) -
Rixen Daniel J.,
Farhat Charbel
Publication year - 1999
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19990210)44:4<489::aid-nme514>3.0.co;2-z
Subject(s) - feti , substructure , discretization , domain decomposition methods , finite element method , lagrange multiplier , classification of discontinuities , simple (philosophy) , mathematics , mathematical optimization , computer science , mathematical analysis , structural engineering , engineering , philosophy , epistemology
Several domain decomposition methods with Lagrange multipliers have been recently designed for solving iteratively large‐scale systems of finite element equations. While these methods differ typically by implementational details, they share in most cases the same substructure based preconditioners that were originally developed for the FETI method. The success of these preconditioners is due to the fact that, for homogeneous structural mechanics problems, they ensure a computational performance that scales with the problem size. In this paper, we address the suboptimal behaviour of these preconditioners in the presence of material and/or discretization heterogeneities. We propose a simple and virtually no‐cost extension of these preconditioners that exhibits scalability even for highly heterogeneous systems of equations. We consider several intricate structural analysis problems, and demonstrate numerically the optimal performance delivered by the new preconditioners for problems with discontinuities. Copyright © 1999 John Wiley & Sons, Ltd.