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
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  20th GAMM-Seminar
January, 22th-24th, 2004
  Winterschool on hierarchical matrices  
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  Abstract Stefan Sauter, Fri, 09.00-10.00 Previous Contents Next  
  Classical BEM with linear complexity
Stefan Sauter (University Zürich)

Alternative representations of boundary integral operators corresponding to elliptic boundary value problems will be derived as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing to choose the order of the numerical approximations much lower than for the classical formulations.

Low order discretizations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU-time grow only linearly (without any logarithmic terms) with respect to the number of unknowns.

Numerical experiments will illustrate the performance of the method.

PS: This talk comprises joint work with S. Börm and N. Krzebek.

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