Schwarz Methods: to Symmetrize or Not to Symmetrize
نویسندگان
چکیده
A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. This paper illustrates why symmetrizing may be a bad idea for linear methods. Numerical examples are presented for a test problem.
منابع مشابه
Schwarz Methods: to Symmetrize or Not to Symmetrize1
SUMMARY A preconditioning theory for Schwarz methods is presented. The theory establishes suucient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive deenite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition...
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