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

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.