16. August 2017:

ARI GUEST TALK

15.00 o'clock,

ARI Seminar Room, Wohllebengasse 12-14 / 1st Floor

**Wavelets meet boundary integral equations****Helmut Harbrecht, Universität Basel****Abstract**

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