A High-order Algorithm for Obstacle Scattering in Three Dimensions

Dr. Mahadevan Ganesh

School of Mathematics
University of New South Wales, Austrailia

Abstract:  In this work we describe a high-order fully discrete spectral algorithm for solving the Helmholtz equation exterior to a bounded (sound--soft,  sound--hard or absorbing) obstacle in three  space
dimensions,  with Dirichlet, Neumann or  Robin (impedance) boundary conditions.   We test our algorithm with extensive computational experiments on a variety of three dimensional smooth and non--smooth obstacles with conical singularities. Our tests include the computation of scattered and far fields induced by incident plane waves. Our method is shown to be  very accurate for scattering from surfaces which are globally parameterised by spherical coordinates, and tests show that it performs very much better than several of the well-established fast algorithms for obstacle scattering on a range of such surfaces, even some which are non-smooth. Further, we  prove superalgebraic convergence of the scattered and far fields obtained using our algorithm in the case of smooth scatterers.