Analytical derivation of a conformal perfectly matched absorber for electromagnetic waves

Abstract

We present an analytical deri¨ation of a 3-D conformal ( ) perfectly matched layer PML for mesh termination in general orthogo-nal cur¨ilinear coordinates. The deri¨ation is based on the analytic continuation to complex space of the normal coordinate to the mesh termination. The resultant fields in the complex space do not obey Maxwell's equations. Howe¨er, it is demonstrated that, through simple field transformations, a new set of fields can be introduced so that they obey Maxwell's equations for an anisotropic medium with properly chosen constituti¨e parameters depending on the local radii of cur¨ature. The formulation presented here reco¨ers, as particular cases, the pre¨iously proposed Cartesian, cylindrical, and spherical PMLs. A pre¨iously ( ) employed anisotropic quasi-PML for conformal terminations is shown to be the large radius of cur¨ature approximation of the anisotropic conformal PML deri¨ed herein.

Parametric finite elements, exact sequences and perfectly matched layers

“…In the series of papers [10][11][12], Teixeira and Chew showed that an appropriate change of field variables (analogous to Piola transforms for H(curl)-and H(div)-conforming fields) combined with complex coordinate stretching leads to Maxwellian PML for general curvilinear coordinates and anisotropic linear media. A similar approach was used for elastic wave propagation in [13,14], where the H(div)-conforming Piola transform was applied to the stress tensor.…”

Differential form approach to the analysis of electromagnetic cloaking and masking

“…The derivation of this metamaterial blueprint has close analogy with the derivation of Maxwellian perfectly matched layers (PMLs) for conformal boundaries [18]. This is because the latter can be derived in the various coordinate systems by applying a complex coordinate stretching (i.e., complexification on the metric of space) and the above metric invariance [10], [18].…”

Simple Methods to Raise the Robustness and Efficiency of the Incomplete Cholesky Preconditioners for Fem Simulation of Electromagnetic Problems

“…To truncate the computational domain, the wave port is filled with perfectly matched layers (PMLs) [20], which can be conveniently interpreted as a diagonal anisotropic medium. The PMLs are backed with perfectly electric conductor (PEC) or absorbing boundary conditions (ABCs).…”