Numerical Optimization of the Method of Auxiliary Sources by Using Level Set Technique

Abstract

Abstract-It is well-known that the choice of the auxiliary surface and the arrangement of radiation centers play a decisive role for ensuring accuracy and stability of the method of auxiliary sources (MAS). Using level set technique, a numerical scheme is proposed to determine the optimal location and amplitudes of the auxiliary sources for threedimensional scattering problems.

Optimization of the Method of Auxiliary Sources for 3d Scattering Problems by Using Generalized Impedance Boundary Conditions and Level Set Technique

“…The scattered field has phase centers located in the ellipsoid foci's region [8]. The Figure 5 shows the auxiliary surface evolution at 0, 23, 50 and 70 iterations.…”

“…So, the accuracy is not automatically adjustable, the only degree of freedom is the auxiliary sources' amplitudes. Generally, The standard MAS is based on empirical rules and on the caustic concept leading to the following recommendation [8]: The distance d between the physical surface Γ and the auxillary surface S should satisfy the condition d < R min , where R min is the minimal radius of positive curvature of the surface Γ. Several numerical methods have been proposed to overcome these constraints for the case of two-dimensional scattering problems, such as [9,10].…”

“…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][7][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 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-anderror processes or by determining the corresponding caustic surfaces [8,[21][22][23][24]. These approaches are analytically feasible only when treating problems with canonical geometries (sphere, ellipsoid or infinite plan .…”