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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: F. Magoulès
Chapter 9

Finite Element Matrices in Congruent Subdomains and some Techniques for Practical Problems

A. Suzuki and M. Tabata

Faculty of Mathematics, Kyushu University, Fukuoka, Japan

Full Bibliographic Reference for this chapter
A. Suzuki, M. Tabata, "Finite Element Matrices in Congruent Subdomains and some Techniques for Practical Problems", in F. Magoulès, (Editor), "Substructuring Techniques and Domain Decomposition Methods", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 9, pp 229-266, 2010. doi:10.4203/csets.24.9
Keywords: finite element matrices, congruent subdomains, domain decomposition, orthogonal transformation, orthogonal projection, iterative solver.

This chapter shows computational techniques for finite element equations with fewer memory requirements. Domains having a class of symmetry are dealt with. Introducing domain decomposition into a union of congruent subdomains, we can reproduce finite element matrices in subdomains from the one in a reference subdomain. Orthogonal projections are used to treat essential boundary conditions and periodic boundary conditions, which make the domain decomposition independent of boundary conditions. These techniques drastically reduce required memory to store finite element matrices.

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