Applications of Gauge Theories to Enhance Numerical Solutions of Mixed Potential Integral Equations.

摘要

The mixed potential electric field integral equation (MPIE) method is a widely used numerical method in wave scattering analysis. The MPIE and all other classical Maxwell equation scattering methods involving the scalar and vector potentials are based on the Lorentz gauge. In this report we analyze a series of waveguiding and scattering problems formulated by enforcing the Coulomb gauge. Coulomb gauge Green's functions are derived for a rectangular waveguide, free space, a cylinder and a wedge. With the MPIE method the currents on a scatterer are shown to be gauge independent. Comparisons are therefore made between the computation times necessary for calculating the current on a straight thin wire and arbitrary scatterers in the presence of a circular conducting cylinder and conducting wedge. Conclusions are drawn concerning the utility of the Coulomb gauge as compared to the Lorentz and other gauges. (kr)