Domain compression via anisotropic metamaterials designed by coordinate transformations

We introduce a spatial coordinate transformation technique to compress the excessive white space (i.e. free-space) in the computational domain of finite methods. This approach is based on the form-invariance property of Maxwell's equations under coordinate transformations. Clearly, Maxwell's equations are still satisfied inside the transformed space, but the medium turns into an anisotropic medium whose constitutive parameters are determined by the coordinate transformation. The proposed technique can be employed to reduce the number of unknowns especially in high-frequency applications wherein a finite method requires an electrically-large computational domain. After developing the analytical background of this technique, we report some numerical results for finite element simulations of electromagnetic scattering problems.