The SAS Domain Decomposition Method for Structural Analysis
Chen, Hsin-Chu
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https://hdl.handle.net/2142/69594
Description
Title
The SAS Domain Decomposition Method for Structural Analysis
Author(s)
Chen, Hsin-Chu
Issue Date
1988
Doctoral Committee Chair(s)
Sameh, Ahmed H.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Abstract
A new domain decomposition method for the efficient and parallelizable numerical handling of plate bending and three dimensional elasticity problem is developed via the discovery of two special classes of matrices. The first class of matrices, say $A\in{\cal C}\sp{n\times n}$, has the relation A = P A P and the second, the counterpart of the first class of matrices A, say $B\in{\cal C}\sp{n\times n}$, satisfies the relation B = $-$P B P where P is some symmetrical signed permutation matrix. Also introduced are four special classes of linear vector subspaces which are closely related to this approach. Two of these four subspaces contain vectors as their elements and the other two consist of matrices as their elements.
This new approach has its origin in the idea of the traditional symmetrical and antisymmetrical approach and that of generalized coordinate transformations. It can be viewed physically as a special domain decomposition method, which takes advantage of the symmetry or partial symmetry of a physical problem. This approach is, therefore, referred to as the symmetrical and antisymmetrical (SAS) domain decomposition method, or simply the SAS approach. The SAS domain decomposition method is a very efficient approach for problems which are symmetrically discretizable. The application of this method in conjunction with other domain decomposition techniques to problems which cannot be symmetrically discretized is still promising, although the advantage over the non-SAS approach is not as great as that for symmetrical problems.
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