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Mesh partitioning for implicit computations via iterative domain decomposition: Impact and optimization of the subdomain aspect ratio
Author(s) -
Farhat Charbel,
Maman Nathan,
Brown Gregory W.
Publication year - 1995
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.1620380608
Subject(s) - domain decomposition methods , feti , computer science , computation , mathematical optimization , scalability , convergence (economics) , algorithm , mesh generation , iterative method , rate of convergence , discretization , finite element method , mathematics , key (lock) , structural engineering , mathematical analysis , computer security , database , engineering , economics , economic growth
Optimal domain decomposition methods have emerged as powerful iterative algorithms for parallel implicit computations. Their key preprocessing step is mesh partitioning, where research has focused so far on the automatic generation of load‐balanced subdomains with minimum interface nodes. In this paper, we emphasize the importance of the subdomain aspect ratio as a mesh partitioning factor, and highlight its impact on the convergence rate of an optimal domain decomposition based iterative method. We also present a fast optimization algorithm for improving the aspect ratio of existing mesh partitions, and illustrate it with several examples from fluid dynamics and structural mechanics applications. For a stiffened shell problem decomposed by the optimal Recursive Spectral Bisection scheme and solved by the FETI method, this optimization algorithm is shown to improve the solution time by a factor equal to 1·54 and to restore numerical scalability.