18th GAMM-Seminar Leipzig on
Multigrid and related methods for optimization problems

Max-Planck-Institute for Mathematics in the Sciences
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  18th GAMM-Seminar
January, 24th-26th, 2002
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  Abstract Sven Beuchler, Sat, 11.00-11.25 Previous Contents Next  
  Multigrid Solver for the p-Version of the FEM
Sven Beuchler (TU Chemnitz)

From the literature it is known that the conjugate gradient method with domain decomposition preconditioners is one of the most efficient methods for solving systems of linear algebraic equations resulting from p-version finite element discretizations of elliptic boundary value problems. The ingredients of such a preconditioner are a preconditioner for the Schur complement, a preconditioner related to the Dirichlet problems in the subdomains, and an extension operator from the boundaries of the subdomains into their interior. In the case of Poisson's equation, we propose in this talk a preconditioner for the problems in the subdomains which can be interpreted as the stiffness matrix resulting from an h-version finite element discretization of a degenerate operator. For solving the corresponding systems of finite element equations a multi-grid algorithm with a special line smoother is used. We have proved that the convergence rate of the multi-grid method is independent of the discretization parameter. The proof is based on the strengthened Cauchy inequality. The theoretical result is confirmed by numerical examples.

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Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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