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GCSIE: An efficient formulation for RCS computation

The Surface Integral Equation is one of the most used methods in the simulation of electromagnetic problems. Its implementation combined with a fast multipole algorithm (MLFMM) and iterative solvers leads efficient and accurate methods for the analysis of radar cross section (RCS) for a target. But the effectiveness of iterative methods depends on the conditioning of linear systems. It is therefore absolutely crucial to have either effective preconditioners or integral formulations inherently well-conditioned. A research, based on the generalization of a combined sources integral equation (GCSIE) using a regularizing operator, was initiated in 1998 at ONERA. The main idea is to try to incorporate into the formalism, some information on the solution that could be extracted, by the asymptotic theories (physical or mathematics). Thus, the GCSIE equation depends on the choice of an operator whose mission is to better approximate the admittance of the diffracting body. In the limiting case, where this approximation is exact, the operator becomes the identity. GCSIE combines therefore both a mathematical analysis and a physical approach of the diffraction phenomena. Although complex and difficult to implement, they allow reformulating the problem of wave propagation with an equation inherently well-conditioned: for instance, RCS computation of a sphere with 2.6 million unknowns needs less than an hour (on a single core). GCSIE shows also excellent performance for industrial cases: a military aircraft with payloads details and antennas (f=4.0GHz and 5 million unknowns) is treated in less than four hours (on a single core). Actually, we will show that the GCSIE is truly a well-conditioned equation more powerful than the classical EFIE and CFIE equations to solve PEC problems.