Null-field BIEM for solving a scattering problem from a point source to a two-layer prolate spheroid

Abstract

In this paper, the acoustic scattering problem from a point source to a two-layer prolate spheroid is solved by using the null-field boundary integral equation method (BIEM) in conjunction with degenerate kernels. To fully utilize the spheroidal geometry, the fundamental solutions and the boundary densities are expanded by using the addition theorem and spheroidal harmonics in the prolate spheroidal coordinates, respectively. Based on this approach, the collocation point can be located on the real boundary, and all boundary integrals can be determined analytically. In real applications of a two-layer prolate spheroidal structure, it can be applied to simulate the kidney-stone biomechanical system. Here, we consider the confocal structure to simulate the kidney-stone system since its analytical solution can be analytically derived. The parameter study for providing some references in the clinical medical treatment is also considered. To check the validity of the null-field BIEM, a special case of the acoustic scattering problem of a point source by a rigid scatterer is also done by setting the density of the inner prolate spheroid to infinity. Results of the present method are compared with those obtained using the commercial finite element software ABAQUS.