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.