Contributions to Books:
M. Löhndorf, J. Melenk:
"Wavenumber-explicit HP-BEM for high frequency scattering";
in: "ASC Report 02/2010",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
For the Helmholtz equation (with wavenumber $k$) and analytic curves or surfaces $\Gamma$
we analyze the Galerkin discretization of classical combined field integral equations
in an $L2$-setting.
We give abstract conditions on the approximation properties of the ansatz space that ensure
stability and quasi-optimality of the Galerkin method. Special attention
is paid to the $hp$-version of the boundary element method ($hp$-BEM). Under the assumption
of polynomial growth of the solution operator we show stability and quasi-optimality of the
$hp$-BEM if the following scale resolution condition is satisfied:
the polynomial degree $p$ is at least $O(\log k)$ and $kh/p$ is bounded by a number that
is sufficiently small, but independent of $k$.
Under this assumption, the constant in the quasi-optimality estimate is independent of $k$.
Numerical examples in 2D illustrate the theoretical results and even suggest that in many cases
quasi-optimality is given under the weaker condition that $kh/p$ is sufficiently small.
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.