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21st GAMM-Seminar Leipzig on
Robust Fast Solvers

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


     
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  21st GAMM-Seminar
January, 26th-28th, 2005
 
     
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  Abstract Johannes Tausch, Fri, 10.00-10.30 Previous Contents Next  
  A Spectral Method for Integral Formulations of Potential and High-Frequency Scattering Problems
Johannes Tausch (Southern Methodist University)

We discuss a spectral method to reduce the computational complexity associated with boundary integral operators. In this approach the Green's function is replaced by a trigonometric expansion, which is valid globally for all positions of source- and field points. The resulting integral operator can be evaluated efficiently using non-equispaced FFTs. Since in the case of a singular Green's function the convergence rate of the Fourier series is slow, the method is applied to a mollified version of the Green's function. The remainder can be expanded with respect to the mollification parameter and leads to a diagonal operator.

For the integral equations associated with the Laplace equation the mollification parameter and the number of terms in the Fourier series can be chosen such that the scheme is nearly asymptotically optimal. The talk will present some comparisons of this approach and the Fast Multipole Method. Moreover, we will present some applications to high frequency scattering problems.


 

 
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Last updated:
28.01.2005 Impressum
 
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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