The MFS for Electromagnetic Scattering by a Layered Chiral Object

The scattering of time-harmonic electromagnetic waves by a layered chiral obstacle is considered. The direct scattering problem is formulated. Surface vector potentials in terms of the dyadic fundamental solutions of the differential operators governing the problem are defined. The Method of Fundamental Solutions (MFS) is applied in order to approximate the sought for solution by finite linear combinations in terms of the dyadic fundamental solutions for singularities placed on auxiliary surfaces outside the domain of the solution and for unknown vector coefficients determined by the conditions on the scatterer’s surfaces. A system of vector functions containing the tangential components of the columns of the dyadic fundamental solutions is constructed. Completeness and linear independence of the constructed system is proven on the surfaces of the scatterer using the defined surface vector potentials. It is concluded that the approximation of the solution by the finite linear combinations is reduced to the approximation of the boundary data. The corresponding MFS approximations of the far-field data are constructed. Imposing the transmission conditions to a finite number of collocation points on the surfaces of the scatterer transforms the problem to an algebraic linear system whose solution determines the unknown vector coefficients. Numerical results obtained by the implementation of the method are presented for the case of a two-layered chiral sphere embedded in a chiral medium.