Multiplicative Schwarz algorithms for some nonsymmetric and indefinite problems

Journal Article · Sun Aug 01 04:00:00 EDT 1993 · SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0730049· OSTI ID:5944138

Cai, Xiaochuan ^[1]; Widlund, O B ^[2]

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1. Univ. of Kentucky, Lexington, KY (United States). Dept. of Mathematics
2. New York Univ., NY (United States). Courant Inst. of Mathematical Sciences

The classical Schwarz alternating method has recently been generalized in several directions. This effort has resulted in a number of new powerful domain decomposition methods for elliptic problems, in new insight into multigrid methods, and in the development of a very useful framework for the analysis of a variety of iterative methods. Most of this work has focused on positive definite, symmetric problems. In this paper, a general framework is developed for multiplicative Schwarz algorithms for nonsymmetric and indefinite problems. Several applications are then discussed including two and multilevel Schwarz methods and iterative substructuring algorithms. Some new results on additive Schwarz methods are also presented.

• DOE Contract Number: FG02-88ER25053
• OSTI ID: 5944138
• Journal Information: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal on Numerical Analysis (Society for Industrial and Applied Mathematics); (United States) Vol. 30:4; ISSN 0036-1429; ISSN SJNAAM
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ALGORITHMS
CALCULATION METHODS
FINITE ELEMENT METHOD
ITERATIVE METHODS
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
SYMMETRY
USES