Transformation media for finite element solution of multi-scale electromagnetic boundary value problems

This paper presents coordinate transformation techniques for solving multi-scale electromagnetic boundary value problems involving fine geometrical features. The major purpose of this study is to get rid of fine mesh and to allow uniform and easy-to-generate meshes in the finite element solution of the multi-scale problems by introducing metamaterial regions into the computational domain. The permittivity and permeability parameters of the metamaterial are obtained by utilizing the coordinate transformation technique, which is based on the form-invariance property of Maxwell´s equations. The medium where the coordinate transformation is applied is equivalent to an anisotropic medium whose parameters are determined by the Jacobian of the transformation. Several numerical simulations are illustrated in the context of finite element solution of electromagnetic scattering problems.