A new technique to compute the physical optics (PO) integral is presented. The technique consists of a blind code that computes the different contributions (stationary phase points, end points, etc.) numerically. This technique is based on a decomposition of the surface into small triangles and a fast evaluation of each triangle by means of a deformation of the integration path in the complex plane. This algorithm permits a fast and accurate evaluation of the PO integral for smooth large surfaces. The CPU time is almost independent of frequency.

In the electromagnetics literature, significant attention has been paid to the problem of low-frequency breakdown in the electric field integral equation. By contrast, the magnetic field integral equation is well-conditioned (in simply connected domains) and can be used in the low frequency limit without modification or preconditioning. Reconstruction of the electric field, however, is subject to catastrophic cancellation unless appropriate measure are taken. In this paper, we show that solving an auxiliary (scalar) integral equation for the charge overcomes this form of low frequency breakdown, both in the near and far fields. Moreover, both the current and charge can be discretized using simple piecewise polynomial basis functions on triangulated surfaces. We also analyze an alternative formulation involving magnetic current and charge and illustrate the performance of the methods with several numerical examples.

We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one for the electric field and one for the magnetic field. This permits the derivation of resonance-free Fredholm equations of the second kind that are stable at all frequencies, insensitive to the genus of the scatterers, and invertible for all passive materials including those with negative permittivities or permeabilities. We refer to these as decoupled field integral equations.