Broadband Stable Calderón-Preconditioned Vector-Potential-Only Integral Equations for PEC Scattering

Abstract

We propose a stabilized first-kind, Calderón preconditioned, vector-potential-only integral equation, for scattering at perfect electrical conductors. The method yields accurate low-frequency results for both the vector and the scalar potential, where the scalar potential is computed using the Lorenz gauge in the post-processing. Both the near and far fields can be accurately computed at arbitrarily low frequencies. This is achieved in a post-processing step and is independent of machine and quadrature precision. First, the low-frequency scaling of the degrees of freedom, and the near and far fields, are studied. Next, stabilized methods are derived based on the low-frequency scaling. The tangential trace of the curl of the vector-potential is stabilized leveraging quasi-Helmholtz projectors, while the normal trace of the vector-potential is stabilized with a projector based on the static scalar potential. Numerical experiments are presented showing that the stabilized method shows accurate results even for very low frequencies.