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A restricted additive Schwarz preconditioner for general sparse linear systems. (English) Zbl 0944.65031
The paper introduces a variant of the classical additive Schwarz method and tests it for some problems including indefinite Helmholtz equations in two-dimensional and compressible Euler equation on three-dimensional unstructured meshes. The tests show that the new method is superior to the classical one in terms of iteration counts, CPU time, and communications if it is implemented in parallel on distributed memory computers. A one-level convergence theory is developed for elliptic finite element problems and domain decomposition into stripes.

MSC:
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35L65 Hyperbolic conservation laws
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
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