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Introduction to Numerical Electrostatics Using MATLAB

Book Description

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

  • Table of Contents

    1. Cover
    2. Title page
    3. Copyright page
    4. Preface
    5. Introduction
    6. Acknowledgments
    7. 1 A Review of Basic Electrostatics
      1. 1.1 Charge, Force, and the Electric Field
      2. 1.2 Electric Flux Density and Gauss’s Law
      3. 1.3 Conductors
      4. 1.4 Potential, Gradient, and Capacitance
      5. 1.5 Energy in the Electric Field
      6. 1.6 Poisson’s and Laplace’s Equations
      7. 1.7 Dielectric Interfaces
      8. 1.8 Electric Dipoles
      9. 1.9 The Case for Approximate Numerical Analysis
      10. Problems
    8. 2 The Uses of Electrostatics
      1. 2.1 Basic Circuit Theory
      2. 2.2 Radio Frequency Transmission Lines
      3. 2.3 Vacuum Tubes and Cathode Ray Tubes
      4. 2.4 Field Emission and the Scanning Electron Microscope
      5. 2.5 Electrostatic Force Devices
      6. 2.6 Gas Discharges and Lighting Devices
    9. 3 Introduction to the Method of Moments Technique for Electrostatics
      1. 3.1 Fundamental Equations
      2. 3.2 A Working Equation Set
      3. 3.3 The Single-Point Approximation for Off-Diagonal Terms
      4. 3.4 Exact Solutions for the Diagonal Term and In-Plane Terms
      5. 3.5 Approximating L<sub xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0">i,j</sub>
      6. Problems
    10. 4 Examples Using the Method of Moments
      1. 4.1 A First Modeling Program
      2. 4.2 Input Data File Preparation for the First Modeling Program
      3. 4.3 Processing the Input Data
      4. 4.4 Generating the Li,j Array
      5. 4.5 Solving the System and Examining Some Results
      6. 4.6 Limits of Resolution
      7. 4.7 Voltages and Fields
      8. 4.8 Varying the Geometry
      9. Problems
    11. 5 Symmetries, Images, and Dielectrics
      1. 5.1 Symmetries
      2. 5.2 Images
      3. 5.3 Multiple Images and the Symmetric Stripline
      4. 5.4 Dielectric Interfaces
      5. 5.5 Two-Dimensional Cross Sections of Uniform Three-Dimensional Structures
      6. 5.6 Charge Profiles and Current Bunching
      7. 5.7 Cylinder Between Two Planes
      8. Problems
    12. 6 Triangles
      1. 6.1 Introduction to Triangular Cells
      2. 6.2 Right Triangles
      3. 6.3 Calculating L<sub xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0">i,i</sub> (Self) Coefficients (Self) Coefficients
      4. 6.4 Calculating L<sub xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0">i,j</sub> FOR i &#8800;j FOR i ≠j
      5. 6.5 Basic Meshing and Data Formats for Triangular Cell MoM Programs
      6. 6.6 Using MATLAB to Generate Triangular Meshings
      7. 6.7 Calculating Voltages
      8. 6.8 Calculating the Electric Field
      9. 6.9 Three-Dimensional Structures
      10. 6.10 Charge Profiles
      11. Problems
    13. 7 Summary and Overview
      1. 7.1 Where We Were, Where We’re Going
    14. 8 The Finite Difference Method
      1. 8.1 Introduction and a Simple Example
      2. 8.2 Setting up and Solving a Basic Problem
      3. 8.3 The Gauss–Seidel (Relaxation) Solution Technique
      4. 8.4 Charge, Gauss’s Law, and Resolution
      5. 8.5 Voltages and Fields
      6. 8.6 Stored Energy and Capacitance
      7. Problems
    15. 9 Refining the Finite Difference Method
      1. 9.1 Refined Grids
      2. 9.2 Arbitrary Conductor Shapes
      3. 9.3 Mixed Dielectric Regions and a New Derivation of the Finite Difference Equation
      4. 9.4 Example: Structure with a Dielectric Interface
      5. 9.5 Axisymmetric Cylindrical Coordinates
      6. 9.6 Symmetry Boundary Condition
      7. 9.7 Duality, and Upper and Lower Bounds to Solutions for Transmission Lines
      8. 9.8 Extrapolation
      9. 9.9 Three-Dimensional Grids
      10. Problems
    16. 10 Multielectrode Systems
      1. 10.1 Multielectrode Structures
      2. 10.2 Utilizing Superposition
      3. 10.3 Utilizing Symmetry
      4. 10.4 Circuital Relations and a Caveat
      5. 10.5 Floating Electrodes
      6. Problems
    17. 11 Probabilistic Potential Theory
      1. 11.1 Random Walks and the Diffusion Equation
      2. 11.2 Voltage at a Point from Random Walks
      3. 11.3 Diffusion
      4. 11.4 Variable-Step-Size Random Walks
      5. 11.5 Three-Dimensional Structures
      6. Problems
    18. 12 The Finite Element Method (FEM)
      1. 12.1 Introduction
      2. 12.2 Solving Laplace’s Equation by Minimizing Stored Energy
      3. 12.3 A Simple One-Dimensional Example
      4. 12.4 A Very Simple Finite Element Approximation
      5. 12.5 Arbitrary Number of Lines Approximation
      6. 12.6 Mixed Dielectrics
      7. 12.7 A Quadratic Approximation
      8. 12.8 A Simple Two-Dimensional FEM Program
      9. Problems
    19. 13 Triangles and Two-Dimensional Unstructured Grids
      1. 13.1 Introduction
      2. 13.2 Aside: The Area of a Triangle
      3. 13.3 The Coefficient Matrix
      4. 13.4 A Simple Example
      5. 13.5 A Two-Dimensional Triangular Mesh Program
      6. Problems
    20. 14 A Zoning System and Some Examples
      1. 14.1 General Introduction
      2. 14.2 Introduction to gmsh
      3. 14.3 Translating the gmsh.msh File
      4. 14.4 Running the FEM Analysis
      5. 14.5 More gmsh Features and Examining the Electric Field
      6. 14.6 Multiple Electrodes
      7. Problems
    21. 15 Some FEM Topics
      1. 15.1 Symmetries
      2. 15.2 A Symmetry Example, Including a Two-Sided Capacitance Estimate
      3. 15.3 Axisymmetric Structures
      4. 15.4 The Graded-Potential Boundary Condition
      5. 15.5 Unbounded Regions
      6. 15.6 Dielectric Materials
      7. Problems
    22. 16 FEM in Three Dimensions
      1. 16.1 Creating Three-Dimensional Meshes
      2. 16.2 The FEM Coefficient Matrix in Three Dimensions
      3. 16.3 Parsing the gmsh Files and Setting Boundary Conditions
      4. 16.4 Open Boundaries and Cylinders in Space
      5. Problems
    23. 17 Electrostatic Forces
      1. 17.1 Introduction
      2. 17.2 Electron Beam Acceleration and Control
      3. 17.3 The Electrostatic Relay (Switch)
      4. 17.4 Electrets and Piezoelectricity: an Overview
      5. 17.5 Points on a Sphere
      6. Problems
    24. A Interfacing with Other Languages
    25. Index
    26. Eula