OPTIMIZATION OF THE METHOD OF AUXILIARY SOURCES FOR 3D SCATTERING PROBLEMS BY USING GENERALIZED IMPEDANCE BOUNDARY CONDITIONS AND LEVEL SET TECHNIQUE

Abstract

The method of auxiliary sources (MAS) presents a promising alternative to methods based on discretization, currently used for solving scattering problems. The optimal choice of the auxiliary surface and the proper allocation of radiation centers play a crucial role in ensuring accuracy and stability of the MAS. This approach is considered an open issue and can be investigated numerically. In this paper, we propose a systematic and fully automated technique leading to determine the optimal parameters of the MAS for arbitrary shaped obstacles (partially or fully penetrable) for scattering problems. Solving scattering problems with an optimal compromise between accuracy and computational resources has been a requirement of many engineering fields such as inverse problems, microwave imaging, Radar cross section computing and EMC. Numerical techniques based on rigorous formulation like the method of moments (MOM), TLM or FDTD provide accurate results, however in many cases, the computational cost is assessed as prohibitive. The mesh-free methods like the method of auxiliary sources state an auspicious alternative to these techniques. The MAS is a numerical method which was originally developed by a Georgian research group for solving scattering and radiation electromagnetic problems (1-3). The fundamental idea of the MAS is the interchange of boundary conditions and differential equation, which excludes the singularities of the integral equation by shifting the auxiliary sources contour relative to integration one (4). The scattered field is expanded in terms of the fundamental solutions of Helmholtz-equation (5). The boundary value problem is solved by imposing the boundary condition at the scattering surface in the same manner as the standard surface integral methods. Previous researches (6-8) have shown that the appropriate choice of the auxiliary surface and the location of radiation centers is decisive to achieve efficiency of the MAS. The optimal choice of the MAS parameters (auxiliary surface, radiation centers) remains an open issue probed by several scientific manuscripts (9-11, 20, 25). The distribution of the auxiliary sources strongly affects the accuracy and the convergence of the numerical solution, it is shown that to ensure the MAS efficiency, the auxiliary surface should enclose the scattered field singularities as tightly as possible (12, 13, 26). The standard placement of the auxiliary sources is based on empirical conventions and on the caustic hypothesis. As a result, the optimal distribution of the auxiliary sources, for a predefined accuracy is achieved by try-and- error processes or by determining the corresponding caustic surfaces (8, 21-24). These approaches are analytically feasible only when treating problems with canonical geometries (sphere, ellipsoid or infinite plan . . . ). The localization of scattered field singularities for arbitrary-shaped objects is the prevailing breakdown point of the MAS. The salient feature of the proposed technique is the replacement of