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Finite element matrices in congruent subdomains and their effective use for large‐scale computations
Author(s) -
Suzuki Atsushi,
Tabata Masahisa
Publication year - 2005
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.1248
Subject(s) - affine transformation , finite element method , computation , domain decomposition methods , solver , stiffness matrix , matrix (chemical analysis) , mathematics , homogeneous space , computer science , pure mathematics , algebra over a field , algorithm , geometry , mathematical optimization , structural engineering , engineering , materials science , composite material
The structure of finite element matrices in congruent subdomains is studied. When a domain has a form of symmetries and/or periodicities, it is decomposed into a union of congruent subdomains, each of which is an image of a reference subdomain by an affine transformation with an orthogonal matrix whose components consist of ‐1, 0, and 1. Stiffness matrices in subdomains are expressed by one in the reference subdomain with renumbering indices and changing signs corresponding to the orthogonal matrices. The memory requirements for a finite element solver are reduced by the domain decomposition, which is useful in large‐scale computations. Reducing rates of memory requirements to store matrices are reported with examples of domains. Both applicability and limitations of the algorithm are discussed with an application to the Earth's mantle convection problem. Copyright © 2005 John Wiley & Sons, Ltd.