Hierarchical Matrices for Convection-Dominated Problems

Hierarchical matrices provide a technique to efficiently compute and store explicit approximations to the inverses of stiffness matrices computed in the discretization of partial differential equations. In a previous paper, Le Borne [2003], it was shown how standard H-matrices must be modified in order to obtain good approximations in the case of a convection dominant equation with a constant convection direction. This paper deals with a generalization to arbitrary (non-constant) convection directions. We will show how these H-matrix approximations to the inverse can be used as preconditioners in iterative methods.