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This lecture presents the perfectly matched layer (PML) absorbing boundary condition (ABC) used to simulate free space when solving the Maxwell equations with such finite methods as the finite difference time domain (FDTD) method or the finite element method. The frequency domain and the time domain equations are derived for the different forms of PML media, namely the split PML, the CPML, the NPML, and the uniaxial PML, in the cases of PMLs matched to isotropic, anisotropic, and dispersive media. The implementation of the PML ABC in the FDTD method is presented in detail. Propagation and reflection of waves in the discretized FDTD space are derived and discussed, with a special emphasis on the problem of evanescent waves. The optimization of the PML ABC is addressed in two typical applications of the FDTD method: first, wave-structure interaction problems, and secondly, waveguide problems. Finally, a review of the literature on the application of the PML ABC to other numerical techniques of electromagnetics and to other partial differential equations of physics is provided. In addition, a software package for computing the actual reflection from a FDTD-PML is provided. It is available here.
Table des matières
Introduction.- The Requirements for the Simulation of Free Space and a Review of Existing Absorbing Boundary Conditions.- The Two-Dimensional Perfectly Matched Layer.- Generalizations and Interpretations of the Perfectly Matched Layer.- Time Domain Equations for the PML Medium.- The PML ABC for the FDTD Method.- Optmization of the PML ABC in Wave-Structure Interaction and Waveguide Problems.- Some Extensions of the PML ABC.
A propos de l'auteur
Jean-Pierre Berenger has been with the Centre d'Analyse de D ¿efense (formerly Laboratoire ¿ Central de l'Armement), Arcueil, France, since 1975. He received a Master in Physics from the Joseph Fourier University, Grenoble, France, in 1973, and a Master in Optical Engineering from the Institut d'Optique Graduate School (formerly Ecole Superieure d'Optique), Paris, ¿ France, in 1975. From 1975 to 1984 he was engaged in applied research in the field of the electromagnetic effects of nuclear bursts. During this period he was the author of the DIFRAC computer code, the first FDTD code developed in France for the calculation of the coupling of the nuclear electromagnetic pulse with objects. During years 1984 to 1988 he was involved in the development of simulation software related to ballistic missiles. From 1989 to 1998 he held a position as expert on the electromagnetic effects of nuclear disturbances. He is currently a manager of prospective studies in the field of command, control, andcommunications. From 1984 to now, Jean-Pierre Berenger has stayed active in numerical electromagnetics, in such topics as the FDTD method, absorbing boundary conditions, and low frequency propagation. Most of his works published in the scientific literature are on the PML absorbing boundary condition and the VLF-LF propagation. In the past fifteen years, he has been an advisor to several laboratories or universities, about the FDTD method and the boundary conditions. He has been also a lecturer on FDTD method in continuing education. He is a senior member of the IEEE, a member of URSI, and a member of the Electromagnetics Academy.
