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

<p><b>Sergey N. Makarov</b> is a Professor in the Department of Electrical and Computer Engineering at Worcester Polytechnic Institute (WPI).</p> <p><b>Gregory M. Noetscher</b> is a Senior Research Electrical Engineer at the U.S. Army Natick Soldier Research, Development and Engineering Center (NSRDEC) in Natick, MA.</p> <p><b>Ara Nazarian</b> is an Assistant Professor of Orthopaedic Surgery, Harvard Medical School, Center for Advanced Orthopaedic Studies, Beth Israel Deaconess Medical Center (BIDMC).</p>

<p><b>Provides 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.</b></p> <p><b>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.  </b></p> <p>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-on MATLAB^® modules. 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 2 covers electrostatics of conductors and dielectrics, and direct current flow. Linear magnetostatics is analyzed in Part 3. Part 4 examines theory and applications of eddy currents. Finally, Part 5 evaluates nonlinear electrostatics. Application examples included in this book cover all major subjects of low-frequency electromagnetic theory. In addition, this book includes complete or summarized analytical solutions to a large number of quasi-static electromagnetic problems. Each Chapter concludes with a summary of the corresponding MATLAB^® modules.</p> <ul> <li>Combines fundamental electromagnetic theory and application-oriented computation algorithms in the form of stand alone MATLAB^® modules</li> <li>Makes use of the three-dimensional Method of Moments (MoM) for static and quasistatic electromagnetic problems</li> <li>Contains a detailed full-body computational human phantom from the Visible Human Project^® Female, embedded implant models, and a collection of homogeneous human shells </li> </ul> <p><i>Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using</i> MATLAB^® is a resource for electrical and biomedical engineering students and practicing researchers, engineers, and medical doctors working on low-frequency modeling and bioelectromagnetic applications.</p> <p><b>Sergey N. Makarov</b> is a Professor in the Department of Electrical and Computer Engineering at Worcester Polytechnic Institute (WPI).</p> <p><b>Gregory M. Noetscher</b> is a Senior Research Electrical Engineer at the U.S. Army Natick Soldier Research, Development and Engineering Center (NSRDEC) in Natick, MA.</p> <b>Ara Nazarian </b>is an Assistant Professor of Orthopaedic Surgery, Harvard Medical School, Center for Advanced Orthopaedic Studies, Beth Israel Deaconess Medical Center (BIDMC).

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