Subspace definition for a multigrid method on unstructured grids

Ludmil Zikatanov
Department of Mathematics
Penn State University

Abstract: The construction of optimal (or nearly optimal) algorithms for solving discrete equations arising from FE discretizations of Poisson equation on unstructured grid will be discussed. As a basic solution procedure a variant of multigrid method is used . The definition of the subspaces needed in the multigrid cycle is based on the adjacency structure of the graph (or its sub-graphs), corresponding to the stiffness matrix. Some possible generalizations to other self-adjoint elliptic problems will be presented.