This book presents the perfectly matched layer (PML) absorbing boundary condition (ABC) used to simulate the surrounding 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 described with details. Propagation and reflection of waves in the discretized FDTD space are derived and discussed, with a special emphasize on the problem of evanescent waves. The optimization of the PML ABC is described for two typical applications of the FDTD method, firstly wave-structure interaction problems, secondly waveguide problems. 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.

Finally, the design of PMLs suited to actual applications is revisited in the context of computers of the 2020's that are, by far, more powerful than the computers of the 1990's when the PML ABC was introduced. A simple and general-purpose method is described to design the PML in this current context.

Describes a simple and general-purpose method for the design of PMLs suitable for the computers of the 2020s Puts an emphasize on evanescent waves which play a crucial role in the design of PMLs for actual applications Presents the different forms of PML absorbing boundary conditions useful in certain methods of solving Maxwell equations

Autorentext

Jean-Pierre Bérenger 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, Paris, France, in 1975. From 1975 to 2013 he was with the Direction Générale de l'Armement (DGA) of the French Ministry of Defense. During years 1975-1988 he was engaged in applied research in the field of the electromagnetic effects of nuclear bursts. From 1988 to 1998 he held a position as an expert on the effects of nuclear bursts on radio communications, and from 1998 to 2013 he was a manager of prospective studies in the field of command, control, and communications. From 2013 to 2023 he was a visiting Professor with the University of Manchester, UK, and from 2013 he has been a consultant on numerical methods and on the electromagnetic effects of nuclear rays. Most of the works published by Jean-Pierre Bérenger in the scientific literature concern the FDTD method, the absorbing boundary conditions, and the propagation of VLF-LF radiowaves over the Earth surface. He was the recipient of the 2013 Medal of URSI-France and of the 2014 John Dellinger Gold Medal of URSI. He is a Fellow of IEEE and URSI.

Inhalt

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.- Optimization of the PML ABC in wave-structure interaction and waveguide problems.- Some extensions of the PML ABC.- Using the PML in the Context of Modern Computers.