Augmented electric‐ and magnetic‐field integral equations

Abstract

Augmented electric‐ and magnetic‐field integral equations, which preserve the basic simplicity, solution capability, and pure electric‐ and magnetic‐field character of Maue's original integral equations, are introduced to eliminate the spurious resonances from the exterior solution of the original integral equations. The exact dependence of the original and augmented integral equations on the geometry of the principal area (self patch) which excludes the singularity of their kernels is also determined, and alternate forms for the integral equations are provided that avoid integrals dependent upon the geometry of the principal area. Numerical results obtained for scattering from the perfectly conducting cube, sphere, and infinite circular cylinder confirm the theoretically predicted result that the augmented integral equations eliminate the spurious resonances for all perfectly conducting scatterers except the sphere.

Dual-surface integral equations in electromagnetic scattering

“…Harmonic time dependence of the form has been suppressed, is the wavenumber, and the free-space Green's function is given by (2) The " " on the integral signs in (1) indicates that a vanishingly small "principal area" isolates the singularity of the Green's function from the surface integration. The form of the EFIE in (1b) is conditional upon the choice of the principal area being a circle with the singular point at its center (or another principal area that is adequately symmetric with respect to the singular point) [12].…”

A study of the augmented EFIE with a Calderón preconditioner

“…It is proven [3] that the normal component of the total electric flux D on the PEC surface is not enforced to equal the induced surface charge density ρ s = ∇ · J /iω in the EFIE solution at (and only at) the internal resonant frequencies, which causes the internal resonance problem of the EFIE. Therefore, this problem can be alleviated by enforcing the boundary conditionn · D = ρ s .…”

“…Although (5) is an over-determined equation, it can be shown to have a unique solution at all frequencies [3], and, therefore, can be solved by using the least-squares method to obtain a unique solution. In the rest of this paper, the first equation in (5), which is the original EFIE, is denoted as TEFIE, and the second equation in (5), which is the augmenting equation, is denoted as NEFIE.…”

“…This choice also allows us to truncate those elements beyond the near-field groups without losing much information of then×L a impedance matrix in its multilevel fast multipole algorithm (MLFMA) implementation since the interaction between source and field points attenuates quickly as their distance increases. The discretization of (6) is similar to those described in [1] and [3], and will not be discussed in this paper.…”

“…Although the internal resonance can be avoided, the accuracy of the solution is compromised because of the introduction of the MFIE. In this paper, the augmented EFIE (AEFIE) [3] is adopted to remove the internal resonance corruption while preserving the pure electric-field characteristics and hence the accuracy, and then preconditioned with the Calderón preconditioner to improve its convergence. Several numerical examples show that the Calderón preconditioned AEFIE can indeed eliminate the internal resonance effectively and converge fast.…”