21st GAMM-Seminar Leipzig on
Robust Fast Solvers

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  21st GAMM-Seminar
January, 26th-28th, 2005
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  Abstract Johannes Kraus, Thu, 10.00-10.30 Previous Contents Next  
  Algebraic MultiGrid based on Computational Molecules (AMGm): 1. Scalar Elliptic PDEs
Johannes Kraus (RICAM Linz)

This talk deals with a new approach in algebraic multigrid for self-adjoint and positive definite elliptic problems arising from finite-element discretization:

We discuss a kernel-preserving splitting of SPSD element matrices into edge matrices (associated with the topological element edges) and provide a feasible algorithm for their computation. The utilization of these edge matrices, gives rise to alter the concept of 'strong' and 'weak' connections, as it is used in classical AMG. This affects the coarse-grid selection as well as the prolongation. We derive interpolation from a local energy minimization: the 'computational molecules' involved in this process are assembled from edge matrices. Numerical tests show the robustness of the new method (with respect to perturbations of the M-matrix property).


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28.01.2005 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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