Stabilisation of acoustic single layer potential on non-smooth domains
Stefan Sauter (University Zürich)
In our paper, we will propose a general approach for stabilising the single
layer potential for the Helmholtz boundary integral equation and prove its
stability. We will consider Galerkin boundary element discretisations and
analyse their convergence in qualitative way.
Furthemore, we will derive quantitative error bounds for the Galerkin
discretisation which are explicit with respect to the mesh width and
the wave number for the special case that the surface is the unit sphere in
R3. This analysis allows us to choose the stabilisation such
that the (negative) influence of the wave number in the stability and
convergence estimates are minimal.
This talk comprises joint work with A. Buffa, Pavia.