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20th GAMM-Seminar Leipzig on
Numerical Methods for Non-Local Operators

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
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  20th GAMM-Seminar
January, 22th-24th, 2004
 
     
  Winterschool on hierarchical matrices  
     
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  Abstract Lars Grasedyck, Sat, 11.30-12.00 Previous Contents Next  
  Adaptive H-matrix Coarsening and H-LU for BEM
Lars Grasedyck (MPI Leipzig)

In this talk we give a brief introduction to the hierarchical matrix format which is used for the efficient storage of BEM stiffness matrices. The basic building block of the format is the cluster tree TI of the index set I which is constructed, e.g., by binary space partitioning. Via the admissiblity condition the block-cluster tree TI x I is built, which describes the subdivision of the matrix into admissible blocks. Each of the admissible blocks is represented by a matrix of low rank.

In the second part of the talk we introduce a coarsening strategy that aims at finding an \emph{optimal} block-cluster tree and thus an optimal admissiblity condition. Optimality can be gained with respect to storage or arithmetic complexity.

In the third part of the talk we use the coarsening procedure and the H-matrix arithmetic in order to define an H-LU preconditioner for BEM stiffness matrices. Complexity estimates for the setup, storage and evaluation of the preconditioner close the talk.
 

 
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Last updated:
30.11.2004 Impressum
 
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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