Direct Schur Complement Method by Hierarchical Matrix Techniques

  • Wolfgang Hackbusch
  • Boris N. Khoromskij
  • Ronald Kriemann
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost \(\mathcal{O}\)(N Γ logq N Γ ) is almost linear in N Γ — the number of degrees of freedom on the interface. As input, we use the Schur complement matrices corresponding to subdomains and represented in the -matrix format. In the case of piecewise constant coefficients these matrices can be computed via the BEM representation with the cost \(\mathcal{O}\)(N Γ logq N Γ ), while in the general case the FEM discretisation leads to the complexity O(N Ω logq N Ω ).


Domain Decomposition Linear Complexity Boundary Integral Operator Interface Equation Calderon Projection 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Wolfgang Hackbusch
    • 1
  • Boris N. Khoromskij
    • 2
  • Ronald Kriemann
    • 2
  1. 1.Max-Planck-Institute for Mathematics in the Sciences (MPI MIS)Leipzig
  2. 2.MPI MISGermany

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