Higher-dimensional Nonnested Multigrid Methods
نویسندگان
چکیده
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.
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...
متن کاملOptimal-order Nonnested Multigrid Methods for Solving Finite Element Equations Ii: on Non-quasi-uniform Meshes
Nonnested multigrid methods are proved to be optimal-order solvers for finite element equations arising from elliptic problems in the presence of singularities caused by re-entrant corners and abrupt changes in the boundary conditions, where the multilevel grids are appropriately refined near singularities and are not necessarily nested. Therefore, optimal and realistic finer grids (compared wi...
متن کاملOptimal-order Nonnested Multigrid Methods for Solving Finite Element Equations I: on Quasi-uniform Meshes
We prove that the multigrid method works with optimal computational order even when the multiple meshes are not nested. When a coarse mesh is not a submesh of the finer one, the coarse-level correction usually does not have the a(-, •) projection property and does amplify the iterative error in some components. Nevertheless, the low-frequency components of the error can still be caught by the c...
متن کاملAnalysis of the Full Isoparametric Multigrid Algorithm for a Second Order Elliptic Problem
A second order elliptic problem is investigated in domains with complex geometry. The sequence of nonnested finite element triangulations is generated by higher order curved elements. Convergence analysis of the full nonnested multigrid algorithm is done on the basis of a pure isoparametric approach. A numerical example supporting the considered theory is presented.
متن کامل