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

Max-Planck-Institute for Mathematics in the Sciences
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  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
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  Abstract Ronald Kriemann, Sat, 12.20-12.50 Previous Contents Next  
  Parallel H-Matrix Arithmetic for Shared Memory Systems
Ronald Kriemann (MPI Leipzig)

H-matrices allow the usage of the usual matrix arithmetic in an efficient, almost optimal way. A way to further improve the performance of H-matrices is the parallelisation of the underlying algorithms. Of special interest are shared memory systems with a moderate number of processors, i.e. with 2 up to 32 processors. These systems provide a simple and commonly supported programming interface in the form of POSIX-Threads. Furthermore they are widely available, e.g. as workstations or compute-servers.

Online scheduling algorithms are presented for matrix building, matrix multiplication and inversion. These algorithms allow a good or optimal parallel speedup without any knowledge of the actual costs. This property is especially interesting for H-matrices with a fixed accuracy, since the rank and therefore the costs are not known a-priori. For the matrix-vector multiplication an offline scheduling algorithm with an optimal parallel speedup is introduced.

The theoretical results for all parallel algorithms are tested with numerical examples coming from different BEM applications.

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