High-order $L^2$-Galerkin schemes for the decoupled potential integral equations

Abstract

We prove Sobolev space well-posedness of the decoupled potential integral equations. Using basic pseudo-differential techniques, discrete stability is obtained for the standard $L^2$-pairing, and we deduce spectral convergence for a high-order scheme employing discontinuous basis functions, or with additional element-wise tangential continuity imposed in the vectorial part of the system. The scheme is shown to be much better conditioned than a mature commercial EFIE/CFIE solver. In many cases appearing almost independent of wavenumber, mesh density, and the order.