Deep-Shadow Producing Multipole Kernels for the Efficient MoM Solution of Large Impenetrable Scatterers

The integral-equation kernel in a standard Method-of-Moments (MoM) procedure consists of the free-space Green’s function leading to a dense system of linear equations. The rank of the corresponding matrix blocks describing interaction between different parts of the scatterer scales linearly and even quadratically with the electrical size of the scatterer in two- and three-dimensional cases, respectively. Such behavior may make the scattering problem intractable for large geometries. As has been shown in [1], [2] for the two- and three-dimensional cases, respectively, for impenetrable scatterers a modification of the integral equation kernels can be employed to obtain a significantly lower rank of the matrix blocks, thus making the whole MoM matrix compressible. Basically, this rank-reduction is achieved by introducing a shadow-producing structure or shadow-producing sources in a region which is in the original set-up occupied by the impenetrable scatterer. Thus, the interaction between one MoM source point and those lying in the shadow region can be neglected. In the present contribution, we will investigate the use of a multipole expansion to produce the shadow. This approach allows a systematic analysis of the performance as a function of the different available parameters such as the location of the multipole origin, the shadow angle, the degree of the multipole expansion etc. Preliminary numerical outcomes including comparisons to recent results obtained by other methods will be presented.