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 Steffen Börm, Fri, 10.00-10.30 Previous Contents Next  
  H2-Matrices with Adaptive Bases
Steffen Börm (MPI Leipzig)

H2-matrices can be used to find data-sparse representations of the densely populated matrices occurring, e.g., in boundary element methods.

We give a short introduction to the basic concepts of H2-matrices and their application to simple boundary element methods. While these techniques lead to fast algorithms, the corresponding memory requirements are relatively high. In order to avoid this drawback, we present an algorithm that adapts the function systems used in the kernel expansion in order to compress the H2-matrices even further. The algorithm can work ``on the fly'', i.e., there is no need to store the uncompressed matrix.

The original approximation scheme can be shown to converge exponentially if the kernel function satisfies the usual asymptotic smoothness condition. Since the compression methods use only algebraic information, no additional requirements have to be imposed on the kernel function or the geometry in order to preserve exponential convergence.

Numerical experiments with discretizations of Poisson's and Maxwell's equations show that the compression algorithm reduces the memory requirements significantly and also improves the performance of the matrix-vector multiplication that is crucial for most iterative solvers.

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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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