M. Feischl, M. Karkulik, D. Praetorius, P. Schaefer:
"Stabile Implementierung der Randelementmethode auf anisotrop verfeinerten Gittern (Supervisor: M. Feischl, M. Karkulik, D. Praetorius)";
Report for Bachelor thesis;
The analytical computation of the entries of the BEM matrices on
strongly anisotropic meshes suffers from cancellation effects. These
lead to artifical instabilities of BEM. In the bachelor thesis, we
propose the use of semi-analytic or fully discrete computation of
the entries instead. We prove that under appropriate admissibility
conditions from the theory of hierarchical matrices, the approximate
matrix converges exponentially fast to the (non-stable) exact matrix.
The proposed numerical quadrature avoids cancellation which is
underlined by numerical experiments.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.