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A study on the lumped preconditioner and memory requirements of FETI and related primal domain decomposition methods
Author(s) -
Fragakis Yannis
Publication year - 2007
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/nme.2154
Subject(s) - preconditioner , domain decomposition methods , feti , dual (grammatical number) , computer science , decomposition , domain (mathematical analysis) , mathematics , parallel computing , mathematical optimization , computational science , algebra over a field , algorithm , finite element method , engineering , iterative method , mathematical analysis , chemistry , pure mathematics , structural engineering , art , literature , organic chemistry
In recent years, domain decomposition methods (DDMs) have emerged as advanced solvers in several areas of computational mechanics. In particular, during the last decade, in the area of solid and structural mechanics, they reached a considerable level of advancement and were shown to be more efficient than popular solvers, like advanced sparse direct solvers. The present contribution follows the lines of a series of recent publications on the relationship between primal and dual formulations of DDMs. In some of these papers, the effort to unify primal and dual methods led to a family of DDMs that was shown to be more efficient than the previous methods. The present paper extends this work, presenting a new family of related DDMs, thus enriching the theory of the relations between primal and dual methods, with the primal methods, which correspond to the dual DDM that uses the lumped preconditioner. The paper also compares the numerical performance of the new methods with that of the previous ones and focuses particularly on memory requirement issues related to the use of the lumped preconditioner, suggesting a particularly memory‐efficient formulation. Copyright © 2007 John Wiley & Sons, Ltd.