Washington State University, 2015. - 403 pp.Книга основана на курсе лекций, которые автор читал в School of Electrical Engineering and Computer Science Washington State University. Курс посвящен изложению метода конечных разностей во временно́й области (англ. Finite Difference Time Domain, FDTD) — одному из наиболее популярных методов численной электродинамики, основанному на дискретизации уравнений Максвелла, записанных в дифференциальной форме.Метод конечных разностей является основным для моделирования самых разных радиоволновых и оптических приложений. Он с успехом применяется для решения широкого спектра задач: от моделирования сверхдлинных электромагнитных волн и микроволн (например для изучения сигнатурной радиолокации, расчёта характеристик антенн, разработки беспроводных устройств связи, в том числе цифровых) до решения задач в оптическом диапазоне (фотонные кристаллы, наноплазмоника, солитоны и биофотоника).
В настоящее время существует порядка 30 коммерческих программ FDTD, а также проекты с открытым исходным кодом.Цель этой книги - дать читателю объем знаний, необходимый для написания быстрого и эффективного кода, реализующего FDTD, на языке Си. В книге изложены основы электродинамики, теоретические основы FDTD, алгоритмы двухмерного и трехмерного FDTD, способы программной оптимизации на основе распараллеливания вычислений и многопоточности. Изложение сопровождается примерами программных блоков на языке Си.Содержание
A simple overview of some of the errors inherent in digital computation.
Introduction
Finite Precision
Symbolic Manipulation
Brief Review of Electromagnetics.
Introduction
Coulomb’s Law and Electric Field
Electric Flux Density
Static Electric Fields
Gradient, Divergence, and Curl
Laplacian
Gauss’s and Stokes’ Theorems
Electric Field Boundary Conditions
Conductivity and Perfect Electric Conductors
Magnetic Fields
Magnetic Field Boundary Conditions
Summary of Static Fields
Time Varying Fields
Summary of Time-Varying Fields
Wave Equation in a Source-Free Region
One-Dimensional Solutions to the Wave Equation
Introduction to the Finite-Difference Time-Domain Method: FDTD in 1D.
Introduction
The Yee Algorithm
Update Equations in 1D
Computer Implementation of a One-Dimensional FDTD Simulation
Bare-Bones Simulation
PMC Boundary in One Dimension
Snapshots of the Field
Additive Source
Terminating the Grid
Total-Field/Scattered-Field Boundary
Inhomogeneities
Lossy Material
Improving the FDTD Code.
Introduction
Arrays and Dynamic Memory Allocation
Macros
Structures
Improvement Number One
Modular Design and Initialization Functions
Improvement Number Two
Compiling Modular Code
Improvement Number Three
Scaling FDTD Simulations to Any Frequency.
Introduction
Sources
Gaussian Pulse
Harmonic Sources
The Ricker Wavelet
Mapping Frequencies to Discrete Fourier Transforms
Running Discrete Fourier Transform (DFT)
Real Signals and DFT’s
Amplitude and Phase from Two Time-Domain Samples
Conductivity
Transmission Coefficient for a Planar Interface
Transmission through Planar Interface
Measuring the Transmission Coefficient Using FDTD
Introduction
The Advection Equation
Terminating the Grid
Implementation of a First-Order ABC
ABC Expressed Using Operator Notation
Second-Order ABC
Implementation of a Second-Order ABC
Dispersion, Impedance, Reflection, and Transmission.
Introduction
Dispersion in the Continuous World
Harmonic Representation of the FDTD Method
Dispersion in the FDTD Grid
Numeric Impedance
Analytic FDTD Reflection and Transmission Coefficients
Reflection from a PEC
Interface Aligned with an Electric-Field Node
Two-Dimensional FDTD Simulations.
Introduction
Multidimensional Arrays
Two Dimensions: TMz Polarization
TMz Example
The TFSF Boundary for TMz Polarization
TMz TFSF Boundary Example
TEz Polarization
PEC’s in TEz and TMz Simulations
TEz ExampleThree-Dimensional FDTD.
Introduction
3D Arrays in C
Governing Equations and the 3D Grid
3D Example
TFSF Boundary
TFSF Demonstration
Unequal Spatial Steps
Dispersive Material.
Introduction
Constitutive Relations and Dispersive Media
Drude Materials
Lorentz Material
Debye Material
Debye Materials Using the ADE Method
Drude Materials Using the ADE Method
Magnetically Dispersive Material
Piecewise Linear Recursive Convolution
PLRC for Debye Material
Perfectly Matched Layer.
Introduction
Lossy Layer, 1D
Lossy Layer, 2D
Split-Field Perfectly Matched Layer
Un-Split PML
FDTD Implementation of Un-Split PML
Acoustic FDTD Simulations.
Introduction
Governing FDTD Equations
Two-Dimensional Implementation
Parallel Processing.
Threads
Thread Examples
Message Passing Interface
Open MPI Basics
Rank and Size
Communicating Between Processes
Near-to-Far-Field Transformation.
Introduction
The Equivalence Principle
Vector Potentials
Electric Field in the Far-Field
Simpson’s Composite Integration
Collocating the Electric and Magnetic Fields: The Geometric Mean
NTFF Transformations Using the Gemoetric Mean
Double-Slit Radiation
Scattering from a Circular Cylinder
Scattering from a Strongly Forward-Scattering Sphere
Appendices
Miscellaneous material including a PostScript primer that has very little to do with FDTD, but I have found it useful at times to have my code directly draw output in PostScript so that I can visualize what is happening in the grid.
Construction of Fourth-Order Central Differences
Generating a Waterfall Plot and Animation
Rendering and Animating Two-Dimensional Data
Notation
PostScript Primer
Introduction
The PostScript File
PostScript Basic Commands
