The method of auxiliary sources for scattering by layered media with parallel algorithmic implementations

Scattering of electromagnetic waves by a cylinder with a radially inhomogeneous refractive index is investigated. This problem finds applications in the analysis of antennas, lenses and coatings, in biomedical engineering, in electromagnetic shielding as well as in subsurface exploration. The refractive index distribution can be approximated by a piecewise constant function corresponding to a layered scatterer with a sufficiently large number of layers. In this work, the scattering problem of the respective layered scatterer is solved by the Method of Auxiliary Sources (MAS). It is shown that the MAS matrix is a block matrix composed of circulant blocks. This fact enables the development of an efficient inversion algorithm, thus, yielding accurate results in a significantly reduced computational time compared to standard methods. Then, the inversion algorithm is parallelized leading to a further important decrease in the computational time dependent on the number of utilized threads. Numerical results are presented exhibiting the accuracy of the MAS scheme as well as the CPU time reduction for the serial and the parallel versions of the developed algorithm. A discrete Luneburg-lens cylinder with a large number of layers is tested and it is demonstrated that the attained boundary conditions error remains below acceptable thresholds.