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Published in:
2005 | OriginalPaper | Chapter
Hierarchical Matrices for Convection-Dominated Problems
Author : Sabine Le Borne
Published in: Domain Decomposition Methods in Science and Engineering
Publisher: Springer Berlin Heidelberg
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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.