Sergey N. Makarov

Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using MATLAB Sergey N. Makarov

Marc Notes: Includes bibliographical references and index. Jacket Description/Back: 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(R) 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(R) 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-on MATLAB(R) 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(R) modules. Combines fundamental electromagnetic theory and application-oriented computation algorithms in the form of stand alone MATLAB(R) modules Makes use of the three-dimensional Method of Moments (MoM) for static and quasistatic electromagnetic problems Contains a detailed full-body computational human phantom from the Visible Human Project(R) Female, embedded implant models, and a collection of homogeneous human shells "Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using" MATLAB(R) is a resource for electrical and biomedical engineering students and practicing researchers, engineers, and medical doctors working on low-frequency modeling and bioelectromagnetic applications. Sergey N. Makarov is a Professor in the Department of Electrical and Computer Engineering at Worcester Polytechnic Institute (WPI). Gregory M. Noetscher is a Senior Research Electrical Engineer at the U. S. Army Natick Soldier Research, Development and Engineering Center (NSRDEC) in Natick, MA. Ara Nazarian is an Assistant Professor of Orthopaedic Surgery, Harvard Medical School, Center for Advanced Orthopaedic Studies, Beth Israel Deaconess Medical Center (BIDMC). Table of Contents: PREFACE xiACKNOWLEDGMENTS xvABOUT THE COMPANION WEBSITE xviiPART I LOW-FREQUENCY ELECTROMAGNETICS. COMPUTATIONAL MESHES. COMPUTATIONAL PHANTOMS 11 Classification of Low-Frequency Electromagnetic Problems. Poisson and Laplace Equations in Integral Form 3Introduction 31.1 Classification of Low-Frequency Electromagnetic Problems 41.2 Poisson and Laplace Equations Boundary Conditions and Integral Equations 18References 302 Triangular Surface Mesh Generation and Mesh Operations 35Introduction 352.1 Triangular Mesh and its Quality 362.2 Delaunay Triangulation. 3D Volume and Surface Meshes 462.3 Mesh Operations and Transformations 562.4 Adaptive Mesh Refinement and Mesh Decimation 752.5 Summary of MATLAB(R) Scripts 81References 853 Triangular Surface Human Body Meshes for Computational Purposes 89Introduction 893.1 Review of Available Computational Human Body Phantoms and Datasets 923.2 Triangular Human Body Shell Meshes Included with the Text 963.3 VHP-F Whole-Body Model Included with the Text 108References 126PART II ELECTROSTATICS OF CONDUCTORS AND DIELECTRICS. DIRECT CURRENT FLOW 1314 Electrostatics of Conductors. Fundamentals of the Method of Moments. Adaptive Mesh Refinement 133Introduction 1334.1 Electrostatics of Conductors. MoM (Surface Charge Formulation) 1344.2 Gaussian Quadratures. Potential Integrals. Adaptive Mesh Refinement 1474.3 Summary of MATLAB(R) Modules 162References 1675 Theory and Computation of Capacitance. Conducting Objects in External Electric Field 169Introduction 1695.1 Capacitance Definitions: Self-Capacitance 1705.2 Capacitance of Two Conducting Objects 1805.3 Systems of Three Conducting Objects 1885.4 Isolated Conducting Object in an External Electric Field 1965.5 Summary of MATLAB(R) Modules 204References 2126 Electrostatics of Dielectrics and Conductors 215Introduction 2156.1 Dielectric Object in an External Electric Field 2166.2 Combined Metal-Dielectric Structures 2296.3 Application Example: Modeling Charges in Capacitive Touchscreens 2396.4 Summary of MATLAB(R) Modules 245References 2537 Transmission Lines: Two-Dimensional Version of the Method of Moments 257Introduction 2577.1 Transmission Lines: Value of the Electrostatic Model--Analytical Solutions 2587.2 The 2D Version of the MoM for Transmission Lines 2737.3 Summary of MATLAB(R) Modules 284References 2878 Steady-State Current Flow 289Introduction 2898.1 Boundary Conditions. Integral Equation. Voltage and Current Electrodes 2908.2 Analytical Solutions for DC Flow in Volumetric Conducting Objects 3008.3 MoM Algorithm for DC Flow. Construction of Electrode Mesh 3118.4 Application Example: EIT 3208.5 Application Example: tDCS 3278.6 Summary of MATLAB(R) Modules 336References 341PART III LINEAR MAGNETOSTATICS 3479 Linear Magnetostatics: Surface Charge Method 349Introduction 3499.1 Integral Equation of Magnetostatics: Surface Charge Method 3509.2 Analytical versus Numerical Solutions: Modeling Magnetic Shielding 3589.3 Summary of MATLAB(R) Modules 367References 36910 Inductance. Coupled Inductors. Modeling of a Magnetic Yoke 371Introduction 37110.1 Inductance 37210.2 Mutual Inductance and Systems of Coupled Inductors 38510.3 Modeling of a Magnetic Yoke 40410.4 Summary of MATLAB(R) Modules 415References 421PART IV THEORY AND APPLICATIONS OF EDDY CURRENTS 42311 Fundamentals of Eddy Currents 425Introduction 42511.1 Three Types of Eddy Current Approximations 42611.2 Exact Solution for Eddy Currents without Surface Charges Created by Horizontal Loops of Current 44011.3 Exact Solution for a Sphere in an External AC Magnetic Field 45311.4 A Simple Approximate Solution for Eddy Currents in a Weakly Conducting Medium 46011.5 Summary of MATLAB(R) Modules 464References 47012 Computation of Eddy Currents via the Surface Charge Method 473Introduction 47312.1 Numerical Solution in a Weakly Conducting Medium with External Magnetic Field 47412.2 Comparison with FEM Solutions from Maxwell 3D of ANSYS: Solution Convergence 48112.3 Eddy Currents Excited by a Coil 48812.4 Summary of MATLAB(R) Modules 497References 504PART V NONLINEAR ELECTROSTATICS 50713 Electrostatic Model of a pn-Junction: Governing Equations and Boundary Conditions 509Introduction 50913.1 Built-in Voltage of a pn-Junction 51013.2 Complete Electrostatic Model of a pn-Junction 533References 54514 Numerical Simulation of pn-Junction and Related Problems: Gummel's Iterative Solution 547Introduction 54714.1 Iterative Solution for Zero Bias Voltage 54814.2 Numerical Solution for the Electric Field Region 56014.3 Analytical Solution for the Diffusion Region: Shockley Equation 57914.4 Summary of MATLAB(R) Modules 587References 588INDEX 591Publisher Marketing: 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(R) 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(R) Female dataset of the National library of Medicine and fully compatible with MATLAB(R) 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-on MATLAB(R) 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(R) modules. Combines fundamental electromagnetic theory and application-oriented computation algorithms in the form of stand alone MATLAB(R) modules Makes use of the three-dimensional Method of Moments (MoM) for static and quasistatic electromagnetic problems Contains a detailed full-body computational human phantom from the Visible Human Project(R) Female, embedded implant models, and a collection of homogeneous human shells "Low-Frequency Electromagnetic Modeling for Electrical and Biological Systems Using" "MATLAB(R)" is a resource for electrical and biomedical engineering students and practicing researchers, engineers, and medical doctors working on low-frequency modeling and bioelectromagnetic applications.

Contributor Bio:  Makarov, Sergey N SERGEY N. MAKAROV is an associate professor in the ECE Department at Worcester Polytechnic Institute.