Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)
  • search hit 2 of 11
Back to Result List

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.

Download full text files

Export metadata

Additional Services

Share in Twitter Search Google Scholar Statistics - number of accesses to the document
Metadaten
Author:Randolph Bank, Todd F. Dupont, Harry Yserentant
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)
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.