A Weak-Form Combined Source Integral Equation with Explicit Inversion of the Combined-Source Condition

TL;DR

This paper introduces a novel technique for accelerating the solution of the combined source integral equation (CSIE) in electromagnetic scattering, improving convergence and accuracy over classical methods.

Contribution

The paper presents an explicit inversion method of the weak-form combined-source condition to enhance iterative solution efficiency of CSIE.

Findings

Reduced iteration count for convergence

Improved accuracy in high-precision simulations

Outperforms classical CFIE in numerical tests

Abstract

The combined source integral equation (CSIE) for the electric field on the surface of a perfect electrically conducting scatterer can be discretized very accurately with lowest-order Rao-Wilton-Glisson basis and testing functions if the combined-source (CS) condition is enforced in weak form. We introduce a technique to accelerate the iterative solution for this kind of CSIE. It is demonstrated that the iterative solution of the equation system can be performed very efficiently by explicitly inverting the weak-form CS condition in any evaluation of the forward operator. This reduces the number of unknowns and results in improved convergence behavior at negligible, linear cost. Numerical results demonstrate that the new CSIE outperforms the classical CFIE for high-accuracy simulations.