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  
  Lars Grasedyck: rank-adaptive arithmetics for hierarchical matrices

We give a short introduction to the hierarchical matrix structure and corresponding (formatted) arithmetic. The focus is on the factorisation of a large and sparse matrix that stems from an elliptic partial differential equation. We will observe that the hierarchical matrix structure is well suited to store, e.g., the Cholesky factor, but the blockwise rank is quite heterogeneous. The rank-adaptive arithmetic that we present chooses the rank for each block adaptively. Numerical results for the 2d and 3d Laplacian close the talk.
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