The method of fundamental solutions for scattering of electromagnetic waves by a chiral object

Abstract

The scattering of a time-harmonic electromagnetic wave by a penetrable chiral obstacle in an achiral environment is considered. The method of fundamental solutions is employed in order to obtain numerically the solution of the problem using fundamental solutions in dyadic form. Surface vector potentials in terms of dyadic fundamental solutions together with the associated boundary integral operators are defined and their regularity properties are presented. Based on the dependence of the solution to the boundary data, appropriate systems of functions containing elements of dyadic fundamental solutions on the surface of the scatterer are constructed. Completeness and linear independence for these systems are proved with the usage of surface vector potentials. Using the transmission conditions, the scattering problem is transformed into a linear algebraic system with a coefficient matrix which consists of chiral and achiral blocks.

Keywords:

• Method of fundamental solutions
• chiral medium
• boundary integral equations
• surface vector potentials
• dyadic

2020 Mathematics Subject Classifications:

• 35P25
• 47A40
• 78A40

Disclosure statement

No potential conflict of interest was reported by the author(s).