Hierarchical Matrices for Convection-Dominated Problems

  • Sabine Le Borne
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


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.


Domain Decomposition Method Admissibility Condition Sparse Approximate Inverse Hierarchical Matrice FETI Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sabine Le Borne
    • 1
  1. 1.MathematicsTennessee Technological UniversityUSA

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