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 requires… CONTINUE READING
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