Computational electrodynamics: the finite-difference time-domain method.

*(English)*Zbl 0840.65126
Boston: Artech House. xvii, 599 p. (1995).

The object of this book is to provide a survey of the state of the art in this field which has developed over the past thirty years. There are seventeen chapters and rather than give a detailed account of each the book will be treated as a whole. In the early chapters, the author gives a general introduction to Maxwell’s equations and electromagnetic theory, and a discussion of the scalar wave equation, and indicates how the finite-difference time-domain method (FDTM) may be used to approximate the equations concerned. This is followed by a discussion of the stability problems involved, and a comparison of the numerical and analytical dispersion.

There follow chapters upon the application of the FDTM method to the classical problems of electromagnetic theory with treatments of such problems as wave guides, scattering and the Sommerfeld radiation condition. There is a discussion of a number of different kinds of non-ideal media and of a soliton. Following on this, the importance of detailed localised modification to the cell size is indicated for fine structures and boundaries with awkward shapes.

The last third of the book has a number of co-authors whose names should in fairness be mentioned here (S. T. Barnard, S. D. Gedney, T. G. Jürgens, F. S. Lansing, M. J. Picket-May, G. W. Saewert, E. T. Thiele). This part opens with a treatment of spatial grids which are of analytically awkward shapes, following upon which is a discussion of the appreciation of FDTM to bodies of revolution, where it is possible to simplify the problem by the use of Fourier series, and of the utility of the method in circuit theory, including the conditions under which the method may be applied to transistors and other nonlinear circuit elements. There follow treatments of a number of simple types of antenna, and of concepts such as radar cross-section, penetration and lasers: a particular interest of the author, biological tissue structures is also considered. The book closes with a brief discussion of algorithms for vector and microprocessor computers. In addition to the treatments of the classical time dependent Maxwell equations, there are, in a number of places in the book, mentions of special relativity, and some attention is paid also to frequency dependent systems and the associated Fourier analysis.

Every chapter contains a number of references and suggestions for supplementary reading, over 400 in the whole book, and many chapters also contain exercises. There are a large number of figures scattered throughout the book giving the results of calculations. In many of these there is a comparison with experimental results, and, in nearly all cases, the agreement is good. There are also a number of colour plates associated with various problems. The printing is excellent and the text reads well. The book can be strongly recommended.

There follow chapters upon the application of the FDTM method to the classical problems of electromagnetic theory with treatments of such problems as wave guides, scattering and the Sommerfeld radiation condition. There is a discussion of a number of different kinds of non-ideal media and of a soliton. Following on this, the importance of detailed localised modification to the cell size is indicated for fine structures and boundaries with awkward shapes.

The last third of the book has a number of co-authors whose names should in fairness be mentioned here (S. T. Barnard, S. D. Gedney, T. G. Jürgens, F. S. Lansing, M. J. Picket-May, G. W. Saewert, E. T. Thiele). This part opens with a treatment of spatial grids which are of analytically awkward shapes, following upon which is a discussion of the appreciation of FDTM to bodies of revolution, where it is possible to simplify the problem by the use of Fourier series, and of the utility of the method in circuit theory, including the conditions under which the method may be applied to transistors and other nonlinear circuit elements. There follow treatments of a number of simple types of antenna, and of concepts such as radar cross-section, penetration and lasers: a particular interest of the author, biological tissue structures is also considered. The book closes with a brief discussion of algorithms for vector and microprocessor computers. In addition to the treatments of the classical time dependent Maxwell equations, there are, in a number of places in the book, mentions of special relativity, and some attention is paid also to frequency dependent systems and the associated Fourier analysis.

Every chapter contains a number of references and suggestions for supplementary reading, over 400 in the whole book, and many chapters also contain exercises. There are a large number of figures scattered throughout the book giving the results of calculations. In many of these there is a comparison with experimental results, and, in nearly all cases, the agreement is good. There are also a number of colour plates associated with various problems. The printing is excellent and the text reads well. The book can be strongly recommended.

Reviewer: Ll.G.Chambers (Bangor)

##### MSC:

65Z05 | Applications to the sciences |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

78M20 | Finite difference methods applied to problems in optics and electromagnetic theory |

35Q60 | PDEs in connection with optics and electromagnetic theory |

78-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |