AN hp-BEM FOR HIGH FREQUENCY SCATTERING BY CONVEX POLYGONS

Time harmonic acoustic scattering by convex polygons is considered. Standard schemes with piecewise polynomial approximation spaces have a computational cost that grows at least linearly with respect to the wavenumber. Here we extend a h-version Galerkin boundary element method scheme for this problem developed by ChandlerWilde and Langdon to an hp-version of the BEM, for which we demonstrate an exponential convergence rate with respect to the order of the polynomials whilst maintaining only logarithmic dependence on the wavenumber. The question of how to set up the stiffness matrix with work independent of the wavenumber is also addressed.