Perfectly Matched Layer Pml For Computational Electromagnetics

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Perfectly Matched Layer (PML) for Computational Electromagnetics

Author: Jean-Pierre Bérenger
language: en
Publisher: Morgan & Claypool Publishers
Release Date: 2007
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 at http: //www.morganclaypool.com/page/berenger
Computational Electromagnetics

Author: Thomas Rylander
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-11-06
Computational Electromagnetics is a young and growing discipline, expanding as a result of the steadily increasing demand for software for the design and analysis of electrical devices. This book introduces three of the most popular numerical methods for simulating electromagnetic fields: the finite difference method, the finite element method and the method of moments. In particular it focuses on how these methods are used to obtain valid approximations to the solutions of Maxwell's equations, using, for example, "staggered grids" and "edge elements." The main goal of the book is to make the reader aware of different sources of errors in numerical computations, and also to provide the tools for assessing the accuracy of numerical methods and their solutions. To reach this goal, convergence analysis, extrapolation, von Neumann stability analysis, and dispersion analysis are introduced and used frequently throughout the book. Another major goal of the book is to provide students with enough practical understanding of the methods so they are able to write simple programs on their own. To achieve this, the book contains several MATLAB programs and detailed description of practical issues such as assembly of finite element matrices and handling of unstructured meshes. Finally, the book aims at making the students well-aware of the strengths and weaknesses of the different methods, so they can decide which method is best for each problem. In this second edition, extensive computer projects are added as well as new material throughout. Reviews of previous edition: "The well-written monograph is devoted to students at the undergraduate level, but is also useful for practising engineers." (Zentralblatt MATH, 2007)
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics

Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing