Classical BEM with linear complexity
Stefan Sauter (University Zürich)
Alternative representations of boundary integral operators
corresponding to elliptic boundary value problems will be derived as a
point for numerical approximations as, e.g., Galerkin boundary elements
including numerical quadrature and panel-clustering. These representations
have the advantage that the integrands of the integral operators have a
reduced singular behaviour allowing to choose the order of the numerical
approximations much lower than for the classical formulations.
Low order discretizations for the single layer integral equations as well as
for the classical double layer potential and the hypersingular integral
equation are considered. We will present fully discrete Galerkin boundary
element methods where the storage amount and the CPU-time grow only linearly
(without any logarithmic terms) with respect to the number of unknowns.
Numerical experiments will illustrate the performance of the method.
PS: This talk comprises joint work with S. Börm and N. Krzebek.