Analytical Derivation of Ellipsoid Conformal Perfectly Matched Layers for Electromagnetic Simulations

The 3-D ellipsoid conformal perfectly matched layer (PML) is proposed and realized by the discontinuous Galerkin time-domain (DGTD) method. The interface between free space and the PML region is an ellipsoid in this scheme. The analytical formulas are derived from differential geometry. The numerical results show that compared with planar-PML, the ellipsoid-PML (EPML) avoids the corner problem and provides an efficient absorbing boundary condition for the DGTD simulation. Meanwhile, this new EPML scheme has higher accuracy than that of the old EPML scheme that we proposed.