Collection of abstracts 14th GAMM-Seminar Kiel on Concepts of Numerical Software January 23rd to 25th, 1998.

Saturday, January 24th, 1998

Object-oriented implementation of multiscale methods for boundary integral equations

We are developing a object--oriented C++--Code for solving boundary integral equations on manifolds. We realize a matrix compression algorithm working with piecewise linear biorthogonal wavelets with 2 or 4 vanishing moments (higher order wavelets are also possible). The development of suitable wavelets on manifolds and domains is actually a topic of intense research. First suggestions for the construction of such wavelets are realized in our implementation. The aim of our work is to solve integral equations by multiscale methods with complexity O(N).

The three dimensional geometry is given by a parametric surface representation. We use a fully discretized Galerkin multiscale method and therefore we have to evaluate O(N) integrals with sufficient accuracy. Nevertheless it turns out that the computation of these matrix entries is still time--consuming. Our major focus is on appropriate quadrature methods and avoiding as much kernel evaluations as possible.