A 3-D Boundary Element Source Method for Anisotropic Objects Embedded in Isotropic Background Medium

We present a method based on boundary elements that can solve the problem of an arbitrarily shaped anisotropic body immersed in a homogeneous isotropic medium. The method solves the problem directly without transforming it into an isotropic one. We study an anisotropic permittivity, conductivity, and permeability and show that the electric and magnetic field equations are in accordance with the electromagnetic duality principle. We assess the accuracy of the method on an anisotropic dielectric sphere placed in a uniform electric field compared to both analytical and finite element solution. Due to the duality, the results are also valid for the other two cases. We achieve a mean relative error of less than 0.45 % within a sphere concerning both reference solutions. The normalized root mean square error outside a sphere is under 0.05 % and 0.6 % in relation to the analytical and finite element solution, respectively. The method can be used for solving inverse problems when determining anisotropic parameters based on field measurements.