Lawrence N. Dworsky

Introduction to Numerical Electrostatics Using MATLAB (eBook, PDF)

• Format: PDF

Produktbeschreibung

Readers are guided step by step through numerous specific problems and challenges, covering all aspects of electrostatics with an emphasis on numerical procedures. The author focuses on practical examples, derives mathematical equations, and addresses common issues with algorithms. Introduction to Numerical Electrostatics contains problem sets, an accompanying web site with simulations, and a complete list of computer codes. * Computer source code listings on accompanying web site * Problem sets included with book * Readers using MATLAB or other simulation packages will gain insight as to the inner workings of these packages, and how to account for their limitations * Example computer code is provided in MATLAB * Solutions Manual * The first book of its kind uniquely devoted to the field of computational electrostatics

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 464
• Erscheinungstermin: 18. Februar 2014
• Englisch
• ISBN-13: 9781118755716
• Artikelnr.: 40515074

Autorenporträt

LAWRENCE N. DWORSKY earned his PhD and BEE in Electrical Engineering at New York University and his Masters of Electrical Engineering at Princeton University. He was an Assistant Professor of Mathematics at Union Community College and an Assistant Professor of Electrical Engineering at Columbia University. From 1974 until 2002, Dr Dworsky served on the technical staff of Motorola, Inc. He has 39 issued U.S. Patents and has authored numerous technical articles. This is his fourth book.

Inhaltsangabe

Preface xi Introduction xiii Acknowledgments xv 1 A Review of Basic
Electrostatics 1 1.1 Charge, Force, and the Electric Field 1 1.2 Electric
Flux Density and Gauss's Law 5 1.3 Conductors 7 1.4 Potential, Gradient,
and Capacitance 10 1.5 Energy in the Electric Field 16 1.6 Poisson's and
Laplace's Equations 18 1.7 Dielectric Interfaces 20 1.8 Electric Dipoles 24
1.9 The Case for Approximate Numerical Analysis 27 2 The Uses of
Electrostatics 33 2.1 Basic Circuit Theory 33 2.2 Radio Frequency
Transmission Lines 41 2.3 Vacuum Tubes and Cathode Ray Tubes 44 2.4 Field
Emission and the Scanning Electron Microscope 47 2.5 Electrostatic Force
Devices 48 2.6 Gas Discharges and Lighting Devices 49 3 Introduction to the
Method of Moments Technique for Electrostatics 51 3.1 Fundamental Equations
51 3.2 A Working Equation Set 55 3.3 The Single-Point Approximation for
Off-Diagonal Terms 56 3.4 Exact Solutions for the Diagonal Term and
In-Plane Terms 57 3.5 Approximating Lij 61 4 Examples using the Method of
Moments 67 4.1 A First Modeling Program 67 4.2 Input Data File Preparation
for the First Modeling Program 68 4.3 Processing the Input Data 71 4.4
Generating the Lij Array 73 4.5 Solving the System and Examining Some
Results 73 4.6 Limits of Resolution 76 4.7 Voltages and Fields 78 4.8
Varying the Geometry 82 5 Symmetries, Images and Dielectrics 89 5.1
Symmetries 89 5.2 Images 90 5.3 Multiple Images and the Symmetric Stripline
95 5.4 Dielectric Interfaces 102 5.5 Two-Dimensional Cross Sections of
Uniform Three-Dimensional Structures 108 5.6 Charge Profiles and Current
Bunching 113 5.7 Cylinder between Two Planes 116 6 Triangles 123 6.1
Introduction to Triangular Cells 123 6.2 Right Triangles 124 6.3
Calculating Lii (Self ) Coefficients 125 6.4 Calculating Lij for i 6 not
equal j 127 6.5 Basic Meshing and Data Formats for Triangular Cell MoM
Programs 127 6.6 Using MATLAB to Generate Triangular Meshings 135 6.7
Calculating Voltages 139 6.8 Calculating the Electric Field 141 6.9
Three-Dimensional Structures 143 6.10 Charge Profiles 152 7 Summary and
Overview 159 7.1 Where We Were, Where We're Going 159 8 The Finite
Difference Method 163 8.1 Introduction and a Simple Example 163 8.2 Setting
Up and Solving a Basic Problem 165 8.3 The Gauss-Seidel (Relaxation)
Solution Technique 172 8.4 Charge, Gauss's Law, and Resolution 175 8.5
Voltages and Fields 177 8.6 Stored Energy and Capacitance 178 9 Refining
the Finite Difference Method 183 9.1 Refined Grids 183 9.2 Arbitrary
Conductor Shapes 189 9.3 Mixed Dielectric Regions and a New Derivation of
the Finite Difference Equation 194 9.4 Example: Structure with a Dielectric
Interface 195 9.5 Axisymmetric Cylindrical Coordinates 196 9.6 Symmetry
Boundary Condition 205 9.7 Duality, and Upper and Lower Bounds to Solutions
for Transmission Lines 207 9.8 Extrapolation 214 9.9 Three-Dimensional
Grids 217 10 Multielectrode Systems 227 10.1 Multielectrode Structures 227
10.2 Utilizing Superposition 229 10.3 Utilizing Symmetry 230 10.4 Circuital
Relations and a Caveat 230 10.5 Floating Electrodes 232 11 Probabilistic
Potential Theory 237 11.1 Random Walks and the Diffusion Equation 237 11.2
Voltage at a Point from Random Walks 239 11.3 Diffusion 246 11.4
Variable-Step-Size Random Walks 249 11.5 Three-Dimensional Structures 260
12 The Finite Element Method (FEM) 265 12.1 Introduction 265 12.2 Solving
Laplace's Equation by Minimizing Stored Energy 266 12.3 A Simple
One-Dimensional Example 267 12.4 A Very Simple Finite Element Approximation
271 12.5 Arbitrary Number of Lines Approximation 274 12.6 Mixed Dielectrics
278 12.7 A Quadratic Approximation 279 12.8 A Simple Two-Dimensional FEM
Program 282 13 Triangles and Two-Dimensional Unstructured Grids 289 13.1
Introduction 289 13.2 Aside: The Area of a Triangle 290 13.3 The
Coefficient Matrix 291 13.4 A Simple Example 293 13.5 A Two-Dimensional
Triangular Mesh Program 296 14 A Zoning System and Some Examples 303 14.1
General Introduction 303 14.2 Introduction to gmsh 304 14.3 Translating the
gmsh.msh File 308 14.4 Running the FEM Analysis 319 14.5 More gmsh Features
and Examining the Electric Field 320 14.6 Multiple Electrodes 324 15 Some
FEM Topics 329 15.1 Symmetries 329 15.2 A Symmetry Example, Including a
Two-Sided Capacitance Estimate 330 15.3 Axisymmetric Structures 337 15.4
The Graded-Potential Boundary Condition 348 15.5 Unbounded Regions 352 15.6
Dielectric Materials 364 16 FEM in Three Dimensions 375 16.1 Creating
Three-Dimensional Meshes 375 16.2 The FEM Coefficient Matrix in Three
Dimensions 384 16.3 Parsing the gmsh Files and Setting Boundary Conditions
386 16.4 Open Boundaries and Cylinders in Space 392 17 Electrostatic Forces
399 17.1 Introduction 399 17.2 Electron Beam Acceleration and Control 400
17.3 The Electrostatic Relay (Switch) 408 17.4 Electrets and
Piezoelectricity: An Overview 414 17.5 Points on a Sphere 415 Problems 419
Appendix Interfacing with Other Languages 423 Index 431

Rezensionen

"The author well organized fundamental theories on electrostatics and also presented numerical examples, in which typical numerical methods, e.g., finite difference method, finite element method, and method of moment, are introduced and demonstrated by Matlab." (Zentralblatt MATH, 1 October 2014)