Boundary integral equation analysis on the sphere

We present a systematic analysis of the integral operators of potential theory that arise when solving the Helmholtz or Maxwell equations in the exterior (or interior) of a sphere in the frequency domain. After obtaining expressions for the signatures of layer potentials in the spherical harmonic or vector spherical harmonic basis, we turn to a consideration of various integral equations that have been proposed in the literature for problems of acoustic and electromagnetic scattering. The selection of certain parameters in “combined field” and “Calderon-preconditioned” formulations is shown to have a significant impact on condition number, extending earlier work by Kress and others.