Description
Book SynopsisProvides a detailed and systematic description of the Method of Moments (Boundary Element Method) for electromagnetic modeling at low frequencies and includes hands-on, application-based MATLAB modules with user-friendly and intuitive GUI and a highly visualized interactive output.
Includes a full-body computational human phantom with over 120 triangular surface meshes extracted from the Visible Human Project Female dataset of the National library of Medicine and fully compatible with MATLAB and major commercial FEM/BEM electromagnetic software simulators.
This book covers the basic concepts of computational low-frequency electromagnetics in an application-based format and hones the knowledge of these concepts with hands-onMATLABmodules. The book is divided into five parts. Part 1 discusses low-frequency electromagnetics, basic theory of triangular surface mesh generation, and computational human phantoms. Part
Table of Contents
PREFACE xi
ACKNOWLEDGMENTS xv
ABOUT THE COMPANION WEBSITE xvii
PART I LOW-FREQUENCY ELECTROMAGNETICS.COMPUTATIONAL MESHES.COMPUTATIONAL PHANTOMS 1
1 Classification of Low-Frequency Electromagnetic Problems. Poisson and Laplace Equations in Integral Form 3
Introduction 3
1.1 Classification of Low-Frequency Electromagnetic Problems 4
1.2 Poisson and Laplace Equations Boundary Conditions and Integral Equations 18
References 30
2 Triangular Surface Mesh Generation and Mesh Operations 35
Introduction 35
2.1 Triangular Mesh and its Quality 36
2.2 Delaunay Triangulation. 3D Volume and Surface Meshes 46
2.3 Mesh Operations and Transformations 56
2.4 Adaptive Mesh Refinement and Mesh Decimation 75
2.5 Summary of MATLAB® Scripts 81
References 85
3 Triangular Surface Human Body Meshes for Computational Purposes 89
Introduction 89
3.1 Review of Available Computational Human Body Phantoms and Datasets 92
3.2 Triangular Human Body Shell Meshes Included with the Text 96
3.3 VHP-F Whole-Body Model Included with the Text 108
References 126
PART II ELECTROSTATICS OF CONDUCTORS AND DIELECTRICS. DIRECT CURRENT FLOW 131
4 Electrostatics of Conductors. Fundamentals of the Method of Moments. Adaptive Mesh Refinement 133
Introduction 133
4.1 Electrostatics of Conductors. MoM (Surface Charge Formulation) 134
4.2 Gaussian Quadratures. Potential Integrals. Adaptive Mesh Refinement 147
4.3 Summary of MATLAB® Modules 162
References 167
5 Theory and Computation of Capacitance. Conducting Objects in External Electric Field 169
Introduction 169
5.1 Capacitance Definitions: Self-Capacitance 170
5.2 Capacitance of Two Conducting Objects 180
5.3 Systems of Three Conducting Objects 188
5.4 Isolated Conducting Object in an External Electric Field 196
5.5 Summary of MATLAB® Modules 204
References 212
6 Electrostatics of Dielectrics and Conductors 215
Introduction 215
6.1 Dielectric Object in an External Electric Field 216
6.2 Combined Metal–Dielectric Structures 229
6.3 Application Example: Modeling Charges in Capacitive Touchscreens 239
6.4 Summary of MATLAB® Modules 245
References 253
7 Transmission Lines: Two-Dimensional Version of the Method of Moments 257
Introduction 257
7.1 Transmission Lines: Value of the Electrostatic Model—Analytical Solutions 258
7.2 The 2D Version of the MoM for Transmission Lines 273
7.3 Summary of MATLAB® Modules 284
References 287
8 Steady-State Current Flow 289
Introduction 289
8.1 Boundary Conditions. Integral Equation. Voltage and Current Electrodes 290
8.2 Analytical Solutions for DC Flow in Volumetric Conducting Objects 300
8.3 MoM Algorithm for DC Flow. Construction of Electrode Mesh 311
8.4 Application Example: EIT 320
8.5 Application Example: tDCS 327
8.6 Summary of MATLAB® Modules 336
References 341
PART III LINEAR MAGNETOSTATICS 347
9 Linear Magnetostatics: Surface Charge Method 349
Introduction 349
9.1 Integral Equation of Magnetostatics: Surface Charge Method 350
9.2 Analytical versus Numerical Solutions: Modeling Magnetic Shielding 358
9.3 Summary of MATLAB® Modules 367
References 369
10 Inductance. Coupled Inductors. Modeling of a Magnetic Yoke 371
Introduction 371
10.1 Inductance 372
10.2 Mutual Inductance and Systems of Coupled Inductors 385
10.3 Modeling of a Magnetic Yoke 404
10.4 Summary of MATLAB® Modules 415
References 421
PART IV THEORY AND APPLICATIONS OF EDDY CURRENTS 423
11 Fundamentals of Eddy Currents 425
Introduction 425
11.1 Three Types of Eddy Current Approximations 426
11.2 Exact Solution for Eddy Currents without Surface Charges Created by Horizontal Loops of Current 440
11.3 Exact Solution for a Sphere in an External AC Magnetic Field 453
11.4 A Simple Approximate Solution for Eddy Currents in a Weakly Conducting Medium 460
11.5 Summary of MATLAB® Modules 464
References 470
12 Computation of Eddy Currents via the Surface Charge Method 473
Introduction 473
12.1 Numerical Solution in a Weakly Conducting Medium with External Magnetic Field 474
12.2 Comparison with FEM Solutions from Maxwell 3D of ANSYS: Solution Convergence 481
12.3 Eddy Currents Excited by a Coil 488
12.4 Summary of MATLAB® Modules 497
References 504
PART V NONLINEAR ELECTROSTATICS 507
13 Electrostatic Model of a pn-Junction: Governing Equations and Boundary Conditions 509
Introduction 509
13.1 Built-in Voltage of a pn-Junction 510
13.2 Complete Electrostatic Model of a pn-Junction 533
References 545
14 Numerical Simulation of pn-Junction and Related Problems: Gummel’s Iterative Solution 547
Introduction 547
14.1 Iterative Solution for Zero Bias Voltage 548
14.2 Numerical Solution for the Electric Field Region 560
14.3 Analytical Solution for the Diffusion Region: Shockley Equation 579
14.4 Summary of MATLAB® Modules 587
References 588
INDEX 591
