A generalized BPX multigrid framework covering nonnested V-cycle methods
نویسندگان
چکیده
منابع مشابه
A Generalized Bpx Multigrid Framework Covering Nonnested V-cycle Methods
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and...
متن کاملErrata to "A generalized BPX multigrid framework covering nonnested V-cycle methods"
More than a decade ago, Bramble, Pasciak and Xu developed a framework in analyzing the multigrid methods with nonnested spaces or noninherited quadratic forms. It was subsequently known as the BPX multigrid framework, which was widely used in the analysis of multigrid and domain decomposition methods. However, the framework has an apparent limit in the analysis of nonnested V-cycle methods, and...
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Nonnested multigrid methods are shown to be optimal-order solvers for systems of finite element equations arising from elliptic boundary problems in any space dimension. Results are derived for Lagrange-type elements of arbitrary degree.
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We describe and analyze certain V-cycle multigrid algorithms with forms deened by numerical quadrature applied to the approximation of symmetric second order elliptic boundary value problems. This approach can be used for the eecient solution of nite element systems resulting from numerical quadrature as well as systems arising from nite diierence discretizations. The results are based on a reg...
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We consider multigrid methods for symmetric positive definite linear systems. We develop an algebraic analysis of V–cycle schemes with Galerkin coarse grid matrices. This analysis is based on the Successive Subspace Correction convergence theory which we revisit. We reformulate it in a purely algebraic way, and extend its scope of application to, e.g., algebraic multigrid methods. This reformul...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-06-01897-7