11th GAMM-Workshop on

Multigrid and Hierarchic Solution Techniques


  A. Almendral  
  M. Bader  
  R. Bank  
  M. Bebendorf  
  S. Beuchler  
  D. Braess  
  C. Douglas  
  L. Grasedyck  
  B. Khoromskij  
  R. Kornhuber  
  B. Krukier  
  U. Langer  
  C. Oosterlee  
  G. Pöplau  
  A. Reusken  
  J. Schöberl  
  M.A. Schweitzer  
  S. Serra Capizzano  
  B. Seynaeve  
  D. Smits  
  O. Steinbach  
  R. Stevenson  
  M. Wabro  
  R. Wienands  
  Mario Bebendorf : H-matrix approximation of FE inverses for general elliptic operators

In this talk the efficient H-matrix approximation of FE stiffness matrices in the case of uniformly elliptic operators with $L^\infty$ coefficients will be treated. Unlike operators arising from boundary element methods for which the H-matrix theory has been extensively developed the inverses of these operators do not benefit from the smoothness of the kernel function. However, it will be shown that this does not affect the existence of low-rank approximants. Emphasis will be laid on the influence of lower order terms on the efficiency. Numerical examples will show that it is possible to generate the approximate inverse with almost linear complexity.
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