16. August 2017:

15.00 o'clock,
ARI Seminar Room, Wohllebengasse 12-14 / 1st Floor

Wavelets meet boundary integral equations - Helmut Harbrecht

Wavelets meet boundary integral equations
Helmut Harbrecht, Universität Basel

Solving boundary integral equations by the Galerkin scheme leads
to densely populated system matrices which are often ill conditioned.
Thus, the memory consumption and the computation of the solution
is of at least quadratic complexity. This makes the boundary element
method unattractive for the practical usage. In recent years, algo-
rithms like the Fast Multipole Method and the Panel Clustering have
been developed to reduce the complextity considerably. Another e-
cient method is the wavelet Galerkin scheme: one employs biorthog-
onal wavelet bases with vanishing moments for the discretization of
the given boundary integral equation. The resulting system matrix is
quasi-sparse and can be compressed without loss of accuracy such that
linear over-all complexity is realized. This talk concerns with the prin-
ciples as well as new developments of the wavelet Galerkin scheme for
boundary integral equations, particularly assembling the compressed
system matrix, preconditioning and adaptivity. Numerical experiments
are presented which complement the theory. The matrix compression
does not compromise the accuracy of the Galerkin scheme. However,
we save a factor of storage 100{1000 and accelerate the computing time