### Abstract

Introduction The finite difference time domain method, usually referred to as the FDTD, is a particular implementation of a general class of methods known as finite difference techniques. The FDTD is so widely used in the CEM community that, although finite difference methods cover a wide spectrum of complexity and accuracy, it is the FDTD which is almost always implied in CEM when finite differences are mentioned. Finite difference methods are numerical methods in which derivatives are directly approximated by finite difference quotients. The general class of such methods is the most intuitive numerical approach, and was the first to be extensively developed by the scientific computing community. To this day, it probably remains the most universally applicable numerical technique and the one most widely used for scientific computation. As just discussed, for dynamic problems in CEM, the most popular is the FDTD. The opening discussion in this chapter will discuss finite differences in general, before moving on to the specifics of the FDTD. At this point, a general comment about the philosophy underlying the mathematical treatment of the computational algorithms in this book would be in order. Although we endeavor not to be “sloppy” mathematically, the emphasis in this book is in presenting well-known methods for well-known problems in CEM, rather than on the basic mathematical requirements of the methods, as one would expect to find in an applied mathematics text, for instance.

Original language | English (US) |
---|---|

Title of host publication | Computational Electromagnetics for RF and Microwave Engineering, Second Edition |

Publisher | Cambridge University Press |

Pages | 32-73 |

Number of pages | 42 |

ISBN (Print) | 9780511778117, 9780521518918 |

DOIs | |

State | Published - Jan 1 2010 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Computational Electromagnetics for RF and Microwave Engineering, Second Edition*(pp. 32-73). Cambridge University Press. https://doi.org/10.1017/CBO9780511778117.006

**The finite difference time domain method : A one-dimensional introduction.** / Davidson, David B.; Aberle, James.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Computational Electromagnetics for RF and Microwave Engineering, Second Edition.*Cambridge University Press, pp. 32-73. https://doi.org/10.1017/CBO9780511778117.006

}

TY - CHAP

T1 - The finite difference time domain method

T2 - A one-dimensional introduction

AU - Davidson, David B.

AU - Aberle, James

PY - 2010/1/1

Y1 - 2010/1/1

N2 - Introduction The finite difference time domain method, usually referred to as the FDTD, is a particular implementation of a general class of methods known as finite difference techniques. The FDTD is so widely used in the CEM community that, although finite difference methods cover a wide spectrum of complexity and accuracy, it is the FDTD which is almost always implied in CEM when finite differences are mentioned. Finite difference methods are numerical methods in which derivatives are directly approximated by finite difference quotients. The general class of such methods is the most intuitive numerical approach, and was the first to be extensively developed by the scientific computing community. To this day, it probably remains the most universally applicable numerical technique and the one most widely used for scientific computation. As just discussed, for dynamic problems in CEM, the most popular is the FDTD. The opening discussion in this chapter will discuss finite differences in general, before moving on to the specifics of the FDTD. At this point, a general comment about the philosophy underlying the mathematical treatment of the computational algorithms in this book would be in order. Although we endeavor not to be “sloppy” mathematically, the emphasis in this book is in presenting well-known methods for well-known problems in CEM, rather than on the basic mathematical requirements of the methods, as one would expect to find in an applied mathematics text, for instance.

AB - Introduction The finite difference time domain method, usually referred to as the FDTD, is a particular implementation of a general class of methods known as finite difference techniques. The FDTD is so widely used in the CEM community that, although finite difference methods cover a wide spectrum of complexity and accuracy, it is the FDTD which is almost always implied in CEM when finite differences are mentioned. Finite difference methods are numerical methods in which derivatives are directly approximated by finite difference quotients. The general class of such methods is the most intuitive numerical approach, and was the first to be extensively developed by the scientific computing community. To this day, it probably remains the most universally applicable numerical technique and the one most widely used for scientific computation. As just discussed, for dynamic problems in CEM, the most popular is the FDTD. The opening discussion in this chapter will discuss finite differences in general, before moving on to the specifics of the FDTD. At this point, a general comment about the philosophy underlying the mathematical treatment of the computational algorithms in this book would be in order. Although we endeavor not to be “sloppy” mathematically, the emphasis in this book is in presenting well-known methods for well-known problems in CEM, rather than on the basic mathematical requirements of the methods, as one would expect to find in an applied mathematics text, for instance.

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