An Iterative Procedure with Interface Relaxation for Domain Decomposition Methods

A domain decomposition method for second-order elliptic problems is considered. An iterative procedure that reduces the problem to a sequence of mixed boundary value problems on each subdomain is proposed. At each iteration, a relaxation is accomplished at the subdomain interfaces. In several circum...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1988-12, Vol.25 (6), p.1213-1236
Main Authors: Funaro, Daniele, Quarteroni, Alfio, Zanolli, Paola
Format: Article
Language:English
Subjects:
Approximation
Boundary value problems
Decomposition
Decomposition methods
Degrees of polynomials
Error rates
Exact sciences and technology
Experiments
Interfaces
Iterative methods
Mathematical functions
Mathematical procedures
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, miscellaneous problems
Polynomials
Sciences and techniques of general use
Spectral methods
Textual collocation
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Summary:A domain decomposition method for second-order elliptic problems is considered. An iterative procedure that reduces the problem to a sequence of mixed boundary value problems on each subdomain is proposed. At each iteration, a relaxation is accomplished at the subdomain interfaces. In several circumstances, a value of the relaxation parameter that yields exact convergence in a finite number of iterations is explicitly found. Moreover, when such a value is not available, an appropriate strategy for the automatic selection of the relaxation parameter at each iteration is indicated and analyzed. This iterative method is then applied to the spectral collocation approximation of the differential problem. The same kind of convergence results are proven. Many numerical experiments show the effectiveness of the method proposed here.
ISSN:0036-1429
1095-7170
DOI:10.1137/0725069