Transformation media for efficient numerical modeling of finite methods

In this paper, we design and demonstrate various transformation media for the development of numerical models for efficient solution of electromagnetic boundary value problems via finite methods. The governing idea is to alter the computational domain of the finite methods by making use of a suitable transformation media, and hence to devise efficient numerical simulation tools that provide uniform and easy-to-generate meshes and less number of unknowns. Below, we first discuss the form-invariance property of Maxwell´s equations, and formulate the constitutive parameters of a transformation medium under a general coordinate transformation. Afterwards, we present each technique in each sub-section together with representative numerical simulations performed by the finite element method (FEM) and the finite difference time domain method (FDTD).