Comparison of Finite Difference and Mixed Finite Element Methods for Perfectly Matched Layer Models (Communications in Computational Physics, 2007)
We consider the anisotropic uniaxial formulation of the perfectly matchedlayer (UPML) model for Maxwell's equations in the time domain. We present and analyze a mixed finite element method for the discretization of the UPML in the timedomain to simulate wave propagation on unbounded domains in two dimensions. Onrectangles the spatial discretization uses bilinear finite elements for the electric fieldand the lowest order Raviart-Thomas divergence conforming elements for the magnetic field. We use a centered finite difference method for the time discretization. Wecompare the finite element technique presented to the finite difference time domainmethod (FDTD) via a numerical reflection coefficient analysis. We derive the numerical reflection coefficient for the case of a semi-infinite PML layer to show consistencybetween the numerical and continuous models, and in the case of a finite PML to studythe effects of terminating the absorbing layer. Finally, we demonstrate the effectivenessof the mixed finite element scheme for the UPML by a numerical example and providecomparisons with the split field PML discretized by the FDTD method. In conclusion,we observe that the mixed finite element scheme for the UPML model has absorbingproperties that are comparable to the FDTD method.