Abstract
Traditional integral equation-based models for field scattering start with defining an equivalent current on the surface of an object and then conditions on the tangential components of the fields. These models are restatements of the equivalence theorem. More recent trend has been to develop systems of equations that rely on scalar quantities (both sources and observables). In this paper, we present three different scalar integral equations. The first integral equation is well conditioned at low frequencies, the second is a well-conditioned Fredholm integral equation of the second kind, and the third is a linear combination the first two. We examine the properties of these integral equations using spectral analysis for spherical geometries. Iso-geometric analysis method, developed recently by some of the authors, is used to solve these equations for noncanonical geometries. Numerical examples provided show the spectral properties and performance of the proposed approach for scattering from perfectly conducting objects.
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