Einladung zu einem Vortrag von:
Prof. Josef Schicho und Dr. Johannes Kraus
Universität Linz
Montag, 6. Dezember 2004
13:30 Uhr, HF 136
Algebraic construction of edge matrices with application to AMG
In the first part of this talk we consider the problem of splitting a symmetric positive definite (SPD) stiffness
matrix A arising from finite element discretization into a sum of edge matrices thereby assuming that A is given
as a sum of symmetric positive semidefinite (SPSD) element matrices. We give necessary and sufficient conditions
for the existence of a decomposition into SPSD edge matrices and provide a feasible algorithm for the computation
of edge matrices in case of general SPSD element matrices. In the second part of the talk, we focus on a new approach
in algebraic multigrid (AMG): Based on the knowledge of edge matrices, we discuss how to alter the concept of 'strong'
and 'weak' connections, as it is used for coarse-grid selection in classical AMG. We further derive interpolation
from a local energy minimization rule: the 'computational molecules' involved in this process are assembled from edge
matrices. Numerical tests show the robustness of the new method, which we refer to as AMGm (Algebraic MultiGrid based
on computational molecules).
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