Cartesian Grid Mapper: Transformation Media for Modeling Arbitrary Curved Boundaries With Cartesian Grids

A transformation electromagnetics-based approach is presented to facilitate the use of fixed Cartesian grids for modeling arbitrarily shaped (convex or nonconvex) curved boundaries in finite methods. The basic idea is to design transformation media adapted to the Cartesian grid by using the duality between the material parameters of the media and the coordinate transformation that maps the points of the Cartesian grid to the points on the original curved boundary. Such a transformation medium is named Cartesian grid mapper, and its main mission is to create an illusion to make the Cartesian grid behave like a conformal grid over the curved boundary. The techniques are validated via the results of some numerical simulations.