Anisotropic Locally Conformal Perfectly Matched Layer for Higher Order Curvilinear Finite-Element Modeling

Abstract

A perfectly matched layer (PML) method is proposed for electrically large curvilinear meshes based on a higher order finite-element modeling paradigm and the concept of transformation electromagnetics. The method maps the non-Maxwellian formulation of the locally conformal PML to a purely Maxwellian implementation using continuously varying anisotropic and inhomogeneous material parameters. An approach to the implementation of a conformal PML for higher order meshes is also presented, based on a method of normal projection for PML mesh generation around an already existing convex volume mesh of a dielectric scatterer, with automatically generated constitutive material parameters. Once the initial mesh is generated, a PML optimization method based on gradient descent is implemented to most accurately match the PML material parameters to the geometrical interface. The numerical results show that the implementation of a conformal PML in the higher order finite-element modeling paradigm dramatically reduces the reflection error when compared to traditional PMLs with piecewise constant material parameters. The ability of the new PML to accurately and efficiently model scatterers with a large variation in geometrical shape and those with complex material compositions is demonstrated in examples of a dielectric almond and a continuously inhomogeneous and anisotropic transformation-optics cloaking structure, respectively.