H-matrix Preconditioners in Convection-Dominated Problems

@article{Borne2006HmatrixPI,
title={H-matrix Preconditioners in Convection-Dominated Problems},
author={Sabine Le Borne and Lars Grasedyck},
journal={SIAM J. Matrix Analysis Applications},
year={2006},
volume={27},
pages={1172-1183}
}

Hierarchical matrices provide a data-sparse way to approximate fully populated matrices. In this paper we exploit H-matrix techniques to approximate the LU-decompositions of stiffness matrices as they appear in (finite element or finite difference) discretizations of convectiondominated elliptic partial differential equations. These sparse H-matrix approximations may then be used as preconditioners in iterative methods. Whereas the approximation of the matrix inverse by an H-matrix requiresâ€¦Â CONTINUE READING