The MFS for a Mixed Electromagnetic Scattering Problem in Chiral Media

A mixed electromagnetic scattering problem by an impenetrable body in a chiral medium is considered and formulated in terms of the electric fields. The vector spaces used as well as the fundamental solution of the differential operator governing the problem are defined. The Method of Fundamental Solutions (MFS) is applied in order to approximate the electric scattered field by a finite linear combination of fundamental solutions for singularities placed on an auxiliary surface in the interior of the scatterer and for unknown vector coefficients defined via the boundary conditions. A system of vector functions in terms of the columns of the dyadic fundamental solution is defined. Completeness and linear independence for the constructed system in the appropriate spaces of the boundary surface are proven. Conclusion that the approximation of the solution is reduced to the approximation of the boundary data by finite subsets of the constructed system with respect to the corresponding norms is stated within a Theorem. A collocation method is applied for the determination of the unknown coefficients which reduces the problem to a linear algebraic system. Numerical results for the case of a spherical scatterer embedded in a chiral medium are presented based on a model and the corresponding matlab code of our previous work.