Generalized Schwarz splittings

A classic mathematical technique, the Schwarz Alternating Method (SAM), has recently attracted much attention from researchers in the field of parallel computations, as well as theoreticians. Its advantages in parallelism, wide applicability and great flexibility in implementation make SAM a competi...

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Bibliographic Details
Published in:SIAM journal on scientific and statistical computing 1992-03, Vol.13 (2), p.573-595
Main Author: Tang, Wei Pai
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Boundary conditions
Decomposition
Eulers equations
Exact sciences and technology
Flexibility
Linear algebra
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
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Summary:A classic mathematical technique, the Schwarz Alternating Method (SAM), has recently attracted much attention from researchers in the field of parallel computations, as well as theoreticians. Its advantages in parallelism, wide applicability and great flexibility in implementation make SAM a competitive choice in parallel computations. However, the computational performance of the classical SAM and its modern extensions strongly depend on the amount of overlap between the neighboring subregions. Introducing a large overlap has changed the image of SAM from an impractical theoretical technique to a rewarding numerical approach. However, the duplication of work in these overlapped regions is undesirable. Reducing the amount of overlap without affecting the speed of convergence has become an important performance issue. Schwarz Splitting (SS) has been proposed as an extension of SAM in numerical linear algebra, and a generalized SS is presented in this paper. The new approach allows utilization of the flexibility of the splitting to further improve convergence speed and complexity. A fast convergence is obtained by choosing a good splitting instead of increasing the overlap. The best performance of our generalized SS is much better than that of a previously recommended SS, in which a large overlap is used. Both convergence analysis and numerical results are presented here.
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0913032