Fast multipole accelerated indirect boundary elements for the Helmholtz equation

Abstract

The indirect boundary element method for the Helmholtz equation in three dimensions is of great interest and practical value for many problems in acoustics as it is capable of treating infinitely thin plates and allows coupling of interior and exterior scattering problems. In the present paper we provide a new approach for treatment of boundary integrals, including hypersingular, singular, and nearly singular integrals via analytical expressions for generic boundary conditions on the both sides of the surface. The fast multipole accelerated boundary element solver in Gumerov and Duraiswami (2009) is extended to incorporate the indirect formulation. The new formulation is compared with the analytical solution of scattering off a disk. Previous authors have not provided such comparisons for an extended range of frequencies. The performance of the method and its scalability are investigated. It is demonstrated that problems with hundreds of thousands of boundary elements can be solved efficiently on a personal computer using the present method.