Multiple scattering from N spheres

For geometries such as multiple spheres the scattering problem can be solved more efficiently using semi-analytical (spectral) techniques. Here we develop such a method, which in some sense is analytical since it is based on solutions in the form of infinite series. At the same time the method is numerical, since in the simple form presented here, it requires the solution of a large linear system for determining coefficients in the series, to satisfy boundary conditions on multiple spheres. The solution is based on decomposing the contributions of each scatterer to the total field representation of each contribution in the form of a series of spherical multipoles of the Helmholtz equation, and reexpansion of each multipole near the center of each sphere to satisfy the boundary conditions. This procedure produces infinite linear systems in the coefficients of the expansions. This system can be solved numerically by truncation of the series.