Analysis of two-spheres radiation problems by using the null-field integral equation approach

Abstract

In this paper, a system approach, null-field integral equation in conjunction with the degenerate kernel, is used to solve the radiation problem of two spheres. The null-field integral equation instead of the conventional boundary integral equation can avoid the singular and hypersingular integrals. To fully utilize the spherical geometry, the fundamental solutions and the boundary densities are expanded by using degenerate kernels and spherical harmonics in the spherical coordinate, respectively. The main difference between the present approach and the conventional boundary integral equation is that the collocation point can be exactly located on the real boundary owing to introducing the degenerate kernel. The proposed approach is seen as one kind of semi-analytical methods, since the error is attributed from the truncation of spherical harmonics in the implementation. For the single sphere, the present approach can obtain the analytical solution. Finally, a two-spheres radiation problem is given to verify the validity of proposed approach.