The Hierarchical Basis Multigrid Method.
Please always quote using this URN: urn:nbn:de:0297-zib-44
- We derive and analyze the hierarchical basis-multigrid method for solving discretizations of self-adjoint, elliptic boundary value problems using piecewise linear triangular finite elements. The method is analyzed as a block symmetric Gauß- Seidel iteration with inner iterations, but it is strongly related to 2-level methods, to the standard multigrid V-cycle, and to earlier Jacobi-like hierarchical basis methods. The method is very robust, and has a nearly optimal convergence rate and work estimate. It is especially well suited to difficult problems with rough solutions, discretized using highly nonuniform, adaptively refined meshes.
Author: | Randolph Bank, Todd F. Dupont, Harry Yserentant |
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Document Type: | ZIB-Report |
Tag: | adaptive mesh refinement; finite elements; hierarchical basis; multigrid; preconditioned conjugate gradient methods; symmetric Gauss-Seidel |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F10 Iterative methods for linear systems [See also 65N22] |
65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F35 Matrix norms, conditioning, scaling [See also 15A12, 15A60] | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N20 Ill-posed problems | |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods | |
Date of first Publication: | 1987/04/01 |
Series (Serial Number): | ZIB-Report (SC-87-02) |
ZIB-Reportnumber: | SC-87-02 |
Published in: | Appeared in: Numer. Mathematik 52, p.427-458 (1988) |