Domain decomposition method with hybrid approximations applied to solve problems of elasticity

To solve two-dimensional boundary-value problems of elasticity, two iteration algorithms of the domain decomposition method are proposed: parallel Neumann–Neumann and sequential Dirichlet–Neumann. They are based on the hybrid boundary–finite-element approximations. The algorithms are proved to conve...

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Bibliographic Details
Published in:International applied mechanics Vol. 44; no. 11; pp. 1213 - 1222
Main Authors: Grigorenko, A. Ya, Dyyak, I. I., Prokopyshin, I. I.
Format: Journal Article
Language:English
Published: Boston Springer US 01.11.2008
Subjects:
Algorithms
Applications of Mathematics
Approximation
Boundaries
Boundary value problems
Classical Mechanics
Domain decomposition methods
Elasticity
Mathematical analysis
Optimization
Physics
Physics and Astronomy
domain decomposition method
parallel Neumann–Neumann algorithm
finite-element method
direct boundary-element method
sequential Dirichlet–Neumann algorithm
plane problems of elasticity
ISSN:1063-7095, 1573-8582
Online Access:Get full text
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Summary:To solve two-dimensional boundary-value problems of elasticity, two iteration algorithms of the domain decomposition method are proposed: parallel Neumann–Neumann and sequential Dirichlet–Neumann. They are based on the hybrid boundary–finite-element approximations. The algorithms are proved to converge. The optimal parameters are selected using the minimum-residual and steepest-descent methods. Some plane problems of elasticity are solved as examples, and stationary and nonstationary iteration algorithms in these examples are analyzed for efficiency
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ISSN:1063-7095
1573-8582
DOI:10.1007/s10778-009-0147-1