Missing picture

Introduction to Numerical Electrostatics Using Matlab©

John Wiley..... 2014


Table of Contents

Chapter Section Title Page
Prefacexi
1 A Review Of Basic Electrostatics 1
1.1Charge, Force And The Electric Field1
1.2Electric Flux Density And Gauss' Law5
1.3Conductors 7
1.4Potential, Gradient And Capacitance 10
1.5Energy In The Electric Field 16
1.6Summations 17
1.7Poisson's and Laplace's Equations 18
1.8Dielectric Interfaces 20
1.9The Case For Approximate Numerical Analysis 27
Problems 29
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2 The Uses Of Electrostatics 33
2.1Basic Circuit Theory 33
2.2Radio Frequency Transmission Lines 41
2.3Vacuum Tubes and Cathode Ray Tubes 44
2.4Field Emission And The Scanning Electron Microscope 47
2.5Electrostatic Force Devices 48
2.6Gas Discharges And Lighting Devices 49
Problems 50
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3 Introduction To The Method Of Moments Technique For Electrostatics 51
3.1 Fundamental Equations 51
3.2A Working Equation Set 55
3.3The Single Point Approximation For Off-Diagonal Terms 56
3.4Exact Solutions For Diagonal And In-Plane Terms 57
3.5Approximating Li,j 61
Problems 64
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4 Examples Using The Method Of Moments 67
4.1A First Modeling Program 67
4.2Input Data File Preparation For The First Modeling Program 68
4.3Processing The Input Data 71
4.4Generating The Li,j Array 73
4.5Solving The System And Examining Some Results 73
4.6Limits Of Resolution 76
4.7Voltages And Fields 78
4.8Varying The Geometry 82
Problems 87
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5 Symmetries, Images And Dielectrics 89
5.1Symmetries 89
5.2Images 90
5.3Multiple Images And The Symmetric Stripline 95
5.4Dielectric Interfaces 102
5.5Two-Dimensional Cross Sections Of Three-Dimensional Structures 108
5.6Charge Profiles And Current Bunching 113
5.7Cylinder Between Two Planes 116
Problems 121
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6 Triangles 123
6.1Introduction To Triangular Cells 123
6.2Right Triangles 124
6.3Calculating Li,i (Self) Coefficients 125
6.4Calculating Li,j 127
6.5Basic Meshing And Data Formats For Triangular Cell MOM Programs 127
6.6Using Matlab To Generate Triangular Meshings 135
6.7Calculting Voltages 139
6.8Calculating The Electric Field 141
6.9Three-Dimensional Structures 143
6.10Charge Profiles 152
Problems 156
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7 Summary And Overview 159
7.1Where We Were, Where We Are Going 159
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8 The Finite Difference Method 163
8.1Introduction And A Simple Example 163
8.2Setting Up And Solving A Basic Problem 165
8.3The Gauss-Seidel (Relaxation) Solution Technique 172
8.4Charge, Gauss' Law, Resolution 175
8.5Voltages And Fields 177
8.6Stored Energy And Capacitance 178
Problems 178
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9 Refining The Finite Difference Method 183
9.1Refined Grids 183
9.2Arbitrary Conductor Shapes 189
9.3Mixed Dielectric Regions And A New Derivation Of The Finite Difference Equation 195
9.4Example: Structure With A Dielectric Interface 112
9.5AxiSymmetric Cylindrical Coordinates 196
9.6Symmetry Boundardy Conditions 205
9.7Duality, Upper And Lower Bounds To Solutions For Transmission Lines 207
9.8Extrapolation 214
9.9Three-Dimensional Grids 217
Problems 223
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10 Multielectrode Systems 227
10.1Multielectrode Structures 227
10.2Utilizing Superposition 229
10.3Utilitizing Symmetry 230
10.4Circuital Relations And A Caveat 230
10.5Floating Electrodes 232
Problems 234
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11 Probabilistic Potential Theory 237
11.1Random Walks And The Diffusion Equation 237
11.2Potential At A Point From Random Walks 239
11.3Diffusion 246
11.4Variable Step Size Random Walks 249
11.5Three-Dimensional Structures 260
Problems 216
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12 The Finite Element Method 261
12.1Introduction 265
12.2Solving Laplace's Equation By Minimizing Stored Energy 266
12.3A Simple One Dimensional Example 267
12.4A Very Simple Finite Element Approximation 271
12.5Arbitrary Number Of Lines Approximation 274
12.6Mixed Dielectrics 278
12.7A Quadratic Approximation 279
12.8A Simple Two-Dimensional FEM Program 282
Problems 287
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13 Triangles And Two-Dimensional Unstructured Grids 289
13.1Introduction 289
13.2Aside: The Area Of A Triangle 290
13.3The Coefficient Matrix 291
13.4A Simple Example 293
13.5A Two-Dimensional Triangular Mesh Program 296
Problems 300
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14 A Zoning System And Some Examples 303
14.1General Introduction 303
14.2Introduction To gmsh 304
14.3Translating The gmsh File 308
14.4Running The FEM Analysis 319
14.5More gmsh Features And Examining The Electric Field 320
14.6Multiple Electrodes 324
Problems 327
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15 Some FEM Topics 329
15.1Symmetries 329
15.2A Symmetry Example, Including A Two-Sided Capacitance Estimate 330
15.3Axisymmetric Structures 337
15.4The Graded Potetial Boundary Condition 348
15.5Unbounded Regions 352
15.6Dielectric Material 364
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Problems 371
16 FEM In Three-Dimensions 375
16.1Creating Three-Dimensional Meshes 375
16.2The FEM Coefficient Matrix In Three Dimensions 384
16.3Parsing The gmsh Files And Setting The Boundary Conditions 386
16.4Open Boundaries And Cylinders In Space 392
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Problems 396
17 Electrostatic Forces 401
17.1Introduction 401
17.2Electron Beam Acceleration And Control 402
17.3The Electrostatic Relay 410
17.4Electrets And Piezoelectricity: An Overview 416
17.5Points On A Sphere 417
Problems 421
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Appendix: Interfacing With Other Languages425
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Index 430