On the development of PSBLAS-based parallel two-level Schwarz preconditioners
Applied Numerical Mathematics
On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices
Applied Numerical Mathematics
On Hybrid Multigrid-Schwarz Algorithms
Journal of Scientific Computing
Parallel Two-Grid Semismooth Newton-Krylov-Schwarz Method for Nonlinear Complementarity Problems
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
Computational Optimization and Applications
Extending PSBLAS to build parallel schwarz preconditioners
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
The Optimized Schwarz Method with a Coarse Grid Correction
SIAM Journal on Scientific Computing
Performance analysis of parallel Schwarz preconditioners in the LES of turbulent channel flows
Computers & Mathematics with Applications
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Convergence results for the restrictive additive Schwarz (RAS) method of Cai and Sarkis [SIAM J. Sci. Comput.}, 21 (1999), pp. 792--797] for the solution of linear systems of the form Ax = b are provided using an algebraic view of additive Schwarz methods and the theory of multisplittings. The linear systems studied are usually discretizations of partial differential equations in two or three dimensions. It is shown that in the case of A symmetric positive definite, the projections defined by the methods are not orthogonal with respect to the inner product defined by A, and therefore the standard analysis cannot be used here. The convergence results presented are for the class of M-matrices (and more generally for H-matrices) using weighted max norms. Comparison between different versions of the RAS method are given in terms of these norms. A comparison theorem with respect to the classical additive Schwarz method makes it possible to indirectly get quantitative results on rates of convergence which otherwise cannot be obtained by the theory. Several RAS variants are considered, including new ones and two-level schemes.