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).