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"The first of its kind uniquely devoted to the field of computational electrostatics, this book dives headfirst into the actual problems that engineers are expected to solve using method of moment (MoM), finite difference, and finite element techniques. Readers are guided step by step through specific problems and challenges, covering all aspects of electrostatics with an emphasis on numerical procedures. Focusing on practical examples, mathematical equations, and common issues with algorithms, this is an ideal text for students in engineering, physics, and electrostatics--and working engineers and physicists"--
Table des matières
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
Commentaire
"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)
