High order local farfield expansions absorbing boundary conditions for multiple scattering

Abstract

In this paper, we derive high order and local absorbing boundary conditions (ABC) for two- and three-dimensional multiple acoustic scattering problems. For this purpose, we employ Karp and Wilcox farfield expansions, which are exact representations of purely outgoing waves in two- and three-dimensions, respectively. We seek solutions of multiple scattering problems for scatterers of arbitrary shape in both homogeneous and locally inhomogeneous media by assuming that each scatterer and its surrounding inhomogeneity (if any) can be well-separated by artificial boundaries from the other scatterers. As a consequence, the computational domain is reduced to the union of relatively small disjoint subdomains bounded in the interior by a scatterer boundary and in the exterior by a circular (2D) or spherical (3D) artificial boundary. The novel ABC is defined at these artificial boundaries by considering continuities of the scattered field and its derivatives at the artificial boundaries and by representing the scattered wave as a superposition of outgoing waves from each subdomain. Finally, we numerically solve the new bounded boundary value problem for numerous examples including complexly shaped obstacles, such as prototype submarines and aircrafts. Accurate results are obtained at relatively low computational cost for problems in both homogeneous and inhomogeneous media.