{"product_id":"theory-and-computation-of-electromagnetic-fields-in-layered-media-isbn-9781119763192","title":"Theory and Computation of Electromagnetic Fields in Layered Media","description":"\u003cp\u003e\u003cb\u003eExplore the algorithms and numerical methods used to compute electromagnetic fields in multi-layered media\u003c\/b\u003e  \u003c\/p\u003e\u003cp\u003eIn \u003ci\u003eTheory and Computation of Electromagnetic Fields in Layered Media\u003c\/i\u003e, two distinguished electrical engineering researchers deliver a detailed and up-to-date overview of the theory and numerical methods used to determine electromagnetic fields in layered media. The book begins with an introduction to Maxwell’s equations, the fundamentals of electromagnetic theory, and concepts and definitions relating to Green’s function. It then moves on to solve canonical problems in vertical and horizontal dipole radiation, describe Method of Moments schemes, discuss integral equations governing electromagnetic fields, and explains the Michalski-Zheng theory of mixed-potential Green’s function representation in multi-layered media.  \u003c\/p\u003e\u003cp\u003eChapters on the evaluation of Sommerfeld integrals, procedures for far field evaluation, and the theory and application of hierarchical matrices are also included, along with:  \u003c\/p\u003e\u003cul\u003e   \u003cli\u003eA thorough introduction to free-space Green’s functions, including the delta-function model for point charge and dipole current\u003c\/li\u003e   \u003cli\u003eComprehensive explorations of the traditional form of layered medium Green’s function in three dimensions\u003c\/li\u003e   \u003cli\u003ePractical discussions of electro-quasi-static and magneto-quasi-static fields in layered media, including electrostatic fields in two and three dimensions\u003c\/li\u003e   \u003cli\u003eIn-depth examinations of the rational function fitting method, including direct spectra fitting with VECTFIT algorithms\u003c\/li\u003e  \u003c\/ul\u003e  \u003cp\u003ePerfect for scholars and students of electromagnetic analysis in layered media, \u003ci\u003eTheory and Computation of Electromagnetic Fields in Layered Media\u003c\/i\u003e will also earn a place in the libraries of CAD industry engineers and software developers working in the area of computational electromagnetics. \u003c\/p\u003e\u003cp\u003eAbout the Authors xvii\u003c\/p\u003e \u003cp\u003eForeword xix\u003c\/p\u003e \u003cp\u003ePreface xxi\u003c\/p\u003e \u003cp\u003eAcknowledgments xxiii\u003c\/p\u003e \u003cp\u003eAcronyms xxv\u003c\/p\u003e \u003cp\u003eIntroduction xxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Foundations of Electromagnetic Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Maxwell Equations 2\u003c\/p\u003e \u003cp\u003e1.2 Curl–Curl Equations for the Electric and Magnetic Fields 6\u003c\/p\u003e \u003cp\u003e1.3 Boundary Conditions 7\u003c\/p\u003e \u003cp\u003e1.4 Poynting Theorem 11\u003c\/p\u003e \u003cp\u003e1.5 Vector and Scalar Potentials 15\u003c\/p\u003e \u003cp\u003e1.6 Quasi-Electrostatics. Scalar Potential. Capacitance 19\u003c\/p\u003e \u003cp\u003e1.7 Quasi-Magnetostatics 21\u003c\/p\u003e \u003cp\u003e1.8 Theory of DC and AC Circuits as a Limiting form of Maxwell Equations 31\u003c\/p\u003e \u003cp\u003e1.9 Conclusions 35\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Green’s Functions in Free Space 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 1D Green’s Function 37\u003c\/p\u003e \u003cp\u003e2.2 3D Green’s Function Expansion in Cartesian Coordinates 41\u003c\/p\u003e \u003cp\u003e2.3 3D Green’s Function in Cylindrical Coordinates 44\u003c\/p\u003e \u003cp\u003e2.4 Physical Interpretation of Conical Waves Forming Sommerfeld Identity 46\u003c\/p\u003e \u003cp\u003e2.5 Integral Field Representation Using Green’s Function 50\u003c\/p\u003e \u003cp\u003e2.6 Field Decomposition into TE- and TM-waves in Cartesian Coordinates 51\u003c\/p\u003e \u003cp\u003e2.7 Free-space Dyadic Green’s Functions of Electric and Magnetic Fields 54\u003c\/p\u003e \u003cp\u003e2.8 Conclusions 59\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Equivalence Principle and Integral Equations in Layered Media 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Quasi-Electrostatics Reciprocity Relations in Layered Media 62\u003c\/p\u003e \u003cp\u003e3.2 Equivalence Principle for the External Electrostatic Field in Layered Media 63\u003c\/p\u003e \u003cp\u003e3.3 Integral Equation of Electrostatics for Metal Object in Layered Media 68\u003c\/p\u003e \u003cp\u003e3.4 Integral Equation of Electrostatics for Disjoint Metal and Dielectric Objects in Layered Media 70\u003c\/p\u003e \u003cp\u003e3.5 Integral Equation of Electrostatics for Metal and Dielectric Objects Sharing a Common Boundary and Situated in Layered Media 74\u003c\/p\u003e \u003cp\u003e3.6 Integral Equation of Electrostatics for Dielectric Objects Sharing a Common Boundary and Situated in Layered Media 77\u003c\/p\u003e \u003cp\u003e3.7 Integral Equations of Quasi-Magnetostatics for Wires in Layered Media 81\u003c\/p\u003e \u003cp\u003e3.8 Full-Wave Reciprocity Relations in Layered Media 85\u003c\/p\u003e \u003cp\u003e3.9 Integral Representations of Electromagnetic Fields via Equivalence Principle 91\u003c\/p\u003e \u003cp\u003e3.10 Electric Field Integral Equation (EFIE) for PEC Object in Layered Medium 105\u003c\/p\u003e \u003cp\u003e3.11 Magnetic Field Integral Equation (MFIE) for PEC Object 106\u003c\/p\u003e \u003cp\u003e3.12 Coupled EFIEs for Penetrable Object 110\u003c\/p\u003e \u003cp\u003e3.13 Coupled MFIEs for Penetrable Object 111\u003c\/p\u003e \u003cp\u003e3.14 Muller, PMCHWT, and CFIE Formulations for Penetrable Object 113\u003c\/p\u003e \u003cp\u003e3.15 Volume Integral Equation 115\u003c\/p\u003e \u003cp\u003e3.16 Single-Source Integral Field Representations and Integral Equations 118\u003c\/p\u003e \u003cp\u003e3.17 Conclusions 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Canonical Problems of Vertical and Horizontal Dipoles Radiation in Layered Media 121\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 The Electromagnetics of Dipole Currents in Open Planar Multi-layered Media 121\u003c\/p\u003e \u003cp\u003e4.2 Sommerfeld Problem: Vertical Electric Dipole Above Half-Space 122\u003c\/p\u003e \u003cp\u003e4.3 Vertical Magnetic Dipole in Layered Media 126\u003c\/p\u003e \u003cp\u003e4.4 Vertical Magnetic Dipole (VMD) in 3-Layer Medium 128\u003c\/p\u003e \u003cp\u003e4.5 Horizontal Electric Dipole in Layered Media 134\u003c\/p\u003e \u003cp\u003e4.6 Integration Paths of Complex Plane k\u003csub\u003eρ\u003c\/sub\u003e 151\u003c\/p\u003e \u003cp\u003e4.7 Conclusions 158\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Computation of Fields Via Integration Along Branch Cuts 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Transformation of SIP to Integrals Along Banks of Branch Cuts 159\u003c\/p\u003e \u003cp\u003e5.2 Parametrization of the Path Along Branch Cut Banks Under 2π√-Convention 165\u003c\/p\u003e \u003cp\u003e5.3 Parametrization of the Path Along Branch Cut Banks Under π∕2√ Convention 169\u003c\/p\u003e \u003cp\u003e5.4 Surface Waves 171\u003c\/p\u003e \u003cp\u003e5.5 Conclusions 187\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Computation of Fields Via Integration Along Steepest Descent Path 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Definition of Integrand and Spherical Wave SDP S\u003csub\u003e1\u003c\/sub\u003e 192\u003c\/p\u003e \u003cp\u003e6.2 Saddle Point on Plane k\u003csub\u003eρ\u003c\/sub\u003e and SDP in Its Vicinity 193\u003c\/p\u003e \u003cp\u003e6.3 Parametrization of Spherical Wave SDP S\u003csub\u003e1\u003c\/sub\u003e 196\u003c\/p\u003e \u003cp\u003e6.4 Crossing Point k\u003csub\u003eρ\u003c\/sub\u003e = k\u003csub\u003e1\u003c\/sub\u003e\/sin θ on the SDP S\u003csub\u003e1 \u003c\/sub\u003e199\u003c\/p\u003e \u003cp\u003e6.5 Case 1: SDP S\u003csub\u003e1\u003c\/sub\u003e Switches Riemann Sheets After Crossing Branch Cut 201\u003c\/p\u003e \u003cp\u003e6.6 Case 2: SDP S\u003csub\u003e1\u003c\/sub\u003e Remains on Same Riemann Sheet After Crossing Branch Cut 209\u003c\/p\u003e \u003cp\u003e6.7 Final Remark on Numerical Integration Along SDP 211\u003c\/p\u003e \u003cp\u003e6.8 Reflected Far Field from Saddle Point: Spherical Wave 212\u003c\/p\u003e \u003cp\u003e6.9 Reflected Far Field from Branch Point: Lateral (Conical) Wave 213\u003c\/p\u003e \u003cp\u003e6.10 Conclusions 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Computation of Fields Via Angular Spectral Representation 221\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Transformation of SIP to a Path on Complex Plane of Angles τ 221\u003c\/p\u003e \u003cp\u003e7.2 Reflected Field as Integral on Complex Plane of Angles τ 224\u003c\/p\u003e \u003cp\u003e7.3 Modification of Integration Path on Angles Plane τ to the SDP 228\u003c\/p\u003e \u003cp\u003e7.4 Accounting for Branch Cut and Surface Wave Poles in Integration Along SDP on Plane τ 229\u003c\/p\u003e \u003cp\u003e7.5 Asymptotic Evaluation of SDP Integrals for k\u003csub\u003e1\u003c\/sub\u003eR ≫ 1 236\u003c\/p\u003e \u003cp\u003e7.6 Conclusions 245\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Fields in Spherical Layered Media 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Scalar Green’s Function in Spherical Coordinates 247\u003c\/p\u003e \u003cp\u003e8.2 Electromagnetic Field in Terms of Debye Potentials 250\u003c\/p\u003e \u003cp\u003e8.3 Radial Electric Dipole (RED) in Spherical Layered Media 253\u003c\/p\u003e \u003cp\u003e8.4 Tangential Electric Dipole (TED) in Spherical Layered Media 258\u003c\/p\u003e \u003cp\u003e8.5 Conclusions 267\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Mixed-Potential Integral Equation 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Mixed-Potential Integral Equations in Free Space 269\u003c\/p\u003e \u003cp\u003e9.2 MPIE Formulation in Layered Medium 274\u003c\/p\u003e \u003cp\u003e9.3 Reduction of 3D Vector Maxwell’s Equations to 1D Scalar Telegraphers Equations 285\u003c\/p\u003e \u003cp\u003e9.4 Telegraphers Equations for Transmission Line Voltages and Currents and Their 1D Green’s Functions 299\u003c\/p\u003e \u003cp\u003e9.5 Relations of 3D Dyadic Green’s Functions to 1D Transmission Line Green’s Functions 300\u003c\/p\u003e \u003cp\u003e9.6 Transmission Line Formulation of Mixed-potential Green’s Function Components in Formulation C 303\u003c\/p\u003e \u003cp\u003e9.7 Closed-form Expressions for Voltages and Currents in General Layered Medium 316\u003c\/p\u003e \u003cp\u003e9.8 Conclusions 336\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Discretization of the MPIE with Shape Functions-based RWG MoM 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 MPIE with Augmented Vector Potential Dyadic Green’s Function 337\u003c\/p\u003e \u003cp\u003e10.2 Current Expansion Over RWG- and Half-RWG (Ramp) Basis Functions 338\u003c\/p\u003e \u003cp\u003e10.3 Representation of MoM Matrix Elements in Terms of Shape Function Interactions 349\u003c\/p\u003e \u003cp\u003e10.4 Delta-gap Port Model and Pertinent Discretization 355\u003c\/p\u003e \u003cp\u003e10.5 Conclusions 364\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Computation of Incident Field from Electric Dipole Situated in the Far Zone 365\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Reciprocity Theorem Application 365\u003c\/p\u003e \u003cp\u003e11.2 The Method of Stationary Phase and Green’s Function Components K\u003csub\u003eA,zz\u003c\/sub\u003e, When Dipole Is Situated in the Top Layer 366\u003c\/p\u003e \u003cp\u003e11.3 Green’s Function Components K\u003csub\u003eA,xx\u003c\/sub\u003e, When Dipole Is Situated in the Top Layer 373\u003c\/p\u003e \u003cp\u003e11.4 Green’s Function Components K\u003csub\u003eA,zt\u003c\/sub\u003e, When Dipole Is Situated in the Top Layer 374\u003c\/p\u003e \u003cp\u003e11.5 Green’s Function Components K\u003csub\u003eA,tz\u003c\/sub\u003e, When Dipole Is Situated in the Top Layer 377\u003c\/p\u003e \u003cp\u003e11.6 Green’s Function Components ∇∇′K\u003csub\u003eφ\u003c\/sub\u003e, When Dipole Is Situated in the Top Layer 379\u003c\/p\u003e \u003cp\u003e11.7 Conclusions 385\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Surface-Volume–Surface Electric Field Integral Equation 387\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Surface–Volume Equivalence Principle Augmented with Single-Source Representations 387\u003c\/p\u003e \u003cp\u003e12.2 SVS-VS-EFIE Formulation: SVS-EFIE Coupled to MPIE and VIE 390\u003c\/p\u003e \u003cp\u003e12.3 Method of Moments Discretization of SVS-S-V-EFIE Operators 395\u003c\/p\u003e \u003cp\u003e12.4 Conclusions 415\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Electromagnetic Analysis with Method of Moments in Shielded Layered Media 417\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 The Electromagnetics of Dipole Fields in Shielded Planar Multi-layered Media 417\u003c\/p\u003e \u003cp\u003e13.2 Electric and Magnetic Field Dyadic Green’s Functions in Shielded Layered Media 420\u003c\/p\u003e \u003cp\u003e13.3 Electric Field Integral Equation 429\u003c\/p\u003e \u003cp\u003e13.4 Spectral Domain Method of Moment Discretization on Manhattan Grid 430\u003c\/p\u003e \u003cp\u003e13.5 Space-Domain Method of Moments with Manhattan Gridded Discretization 444\u003c\/p\u003e \u003cp\u003e13.6 Conclusions 451\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Method of Weighted Averages (Mosig–Michalski Extrapolation Algorithm) 453\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 453\u003c\/p\u003e \u003cp\u003e14.2 Classic First-Order Weighted Average Approximation 461\u003c\/p\u003e \u003cp\u003e14.3 Recursive Weighted Average Algorithm 466\u003c\/p\u003e \u003cp\u003e14.4 Conclusions 492\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Extraction of Quasi-Static Images 493\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 493\u003c\/p\u003e \u003cp\u003e15.2 Prioritized Ray Tracing Algorithm 494\u003c\/p\u003e \u003cp\u003e15.3 Static Images for Voltages and Currents 504\u003c\/p\u003e \u003cp\u003e15.4 Static Image Contributions to Green’s Function Components in the Michalski–Zheng’s Mixed-Potential Form: Source and Observer Points are in the Same Layer 509\u003c\/p\u003e \u003cp\u003e15.5 Static Image Contributions to Green’s Function Components in the Michalski–Zheng’s Mixed-\u003c\/p\u003e \u003cp\u003eMixed-Potential Form: Source Point Layer Is Below Observer Point Layer 529\u003c\/p\u003e \u003cp\u003e15.6 Static Image Contributions to Green’s Function Components in the Michalski–Zheng’s Mixed-Potential Form: Source Point Layer Is Above Observer Point Layer 537\u003c\/p\u003e \u003cp\u003e15.7 Conclusions 542\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Discrete Complex Image Method 545\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 545\u003c\/p\u003e \u003cp\u003e16.2 Complex Exponentials Fitting 547\u003c\/p\u003e \u003cp\u003e16.3 Single-level DCIM 551\u003c\/p\u003e \u003cp\u003e16.4 Two-level DCIM 553\u003c\/p\u003e \u003cp\u003e16.5 Conclusions 555\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Extraction of Singular Integrals from MoM Reaction Integrals and Their Analytic Evaluation 557\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Source Point and the Observation Point Are in the Same Layer 558\u003c\/p\u003e \u003cp\u003e17.2 Source Layer Below Observation Layer 563\u003c\/p\u003e \u003cp\u003e17.3 Source Layer Above Observation Layer 565\u003c\/p\u003e \u003cp\u003e17.4 Conclusions 566\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Methods Based on Rational Function Approximation of Green’s Function Spectra 567\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Rational Function Fitting Method (RFFM) 568\u003c\/p\u003e \u003cp\u003e18.2 Spectral Differential Equations Approximation Method (SDEAM) for Vector Potential Green’s Function 575\u003c\/p\u003e \u003cp\u003e18.3 SDEAM for Mixed-Potential Green’s Functions 580\u003c\/p\u003e \u003cp\u003e18.4 Higher-Order SDEAM Solutions and Their Error Bounds 592\u003c\/p\u003e \u003cp\u003e18.5 Dependence on Number of Terms on Radial Distance ρ 593\u003c\/p\u003e \u003cp\u003e18.6 SDEAM for Spherical Layered Media 593\u003c\/p\u003e \u003cp\u003e18.7 Advantages of High-Order SDEAM for Spherical Layered Media 599\u003c\/p\u003e \u003cp\u003e18.8 Conclusions 600\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Multivalued Complex Functions, Branch Cuts, and Riemann Surfaces 601\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Multivalued Complex Functions, Branches, Branch Points, and Branch Cuts 601\u003c\/p\u003e \u003cp\u003eA.1.1 Contour Mapping from Plane k\u003csub\u003eρ\u003c\/sub\u003e to Plane k\u003csub\u003ez\u003c\/sub\u003e 608\u003c\/p\u003e \u003cp\u003eA.1.2 Branch Cut Method for Ensuring Analyticity of Multifunctions 611\u003c\/p\u003e \u003cp\u003eA.1.3 Riemann Surface Representation of Multifunctions 613\u003c\/p\u003e \u003cp\u003eA.1.4 Practical Considerations for Evaluation of ̇√k\u003csup\u003e2\u003c\/sup\u003e − k\u003csub\u003eρ\u003c\/sub\u003e\u003csup\u003e2\u003c\/sup\u003e Directly Versus as a Product √\u003ci\u003ek − k\u003csub\u003eρ\u003c\/sub\u003e\u003c\/i\u003e√\u003ci\u003ek + k\u003csub\u003eρ\u003c\/sub\u003e \u003c\/i\u003e618\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Evaluation of Singular Integrals 621\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB.1 Evaluation Over Triangles of Integrals Containing e\u003csup\u003e−ιkR\u003c\/sup\u003e∕R Green’s Function 621\u003c\/p\u003e \u003cp\u003eB.2 Evaluation Over Triangles of Integrals Containing Product of e\u003csup\u003e−ιkR\u003c\/sup\u003e∕R Green’s Function and a Linear Function 635\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Reduction of Cos–Cos Series to DFT 643\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eC.1 Cos–Cos Series Rearrangement 643\u003c\/p\u003e \u003cp\u003eC.2 Casting Cos–Cos Series into DFT Form 645\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix D Properties of Vector Potential and Its Derivatives Near a Sheet of Current 647\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eD.1 Vector Potential Near Small Disk σ 647\u003c\/p\u003e \u003cp\u003eD.2 Tangential Derivative of the Vector Potential 649\u003c\/p\u003e \u003cp\u003eD.3 Second Tangential Derivative of the Vector Potential 649\u003c\/p\u003e \u003cp\u003eD.4 Normal Derivative of Vector Potential 650\u003c\/p\u003e \u003cp\u003eD.5 Mixed Second-order Derivative of Vector Potential Over Tangential Coordinates 651\u003c\/p\u003e \u003cp\u003eD.6 Mixed Second-order Derivatives Over X and Z 652\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix E Basis Definitions of Dyadic, Tensor, and Operations with Them 655\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix F Equivalence Principle for the External Electric Field in Free Space 659\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix G Physically Consistent Model for the Extraction of Conductance in Lossy Dielectrics 665\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix H Alternative Expression of Equivalence Principle for the External Magnetic Field 669\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix I Definition of Inductance and Resistance in Frequency Domain 673\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix J Integral Equations of Electrostatics in Multi-Region Scenarios with Free-Space Green’s Functions 677\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eJ.1 Equivalence Principle for the External Electrostatic Field in Layered Media 677\u003c\/p\u003e \u003cp\u003eJ.2 Integral Equation of Electrostatics for Metal Object in Homogeneous Space 679\u003c\/p\u003e \u003cp\u003eJ.3 Integral Equation of Quasi-Electrostatics for Disjoint Metal and Dielectric Objects 679\u003c\/p\u003e \u003cp\u003eJ.4 Integral Equation of Quasi-Electrostatics for Metal and Dielectric Objects Sharing a Common Boundary and Situated in Homogeneous Media 682\u003c\/p\u003e \u003cp\u003eJ.5 Integral Equation of Quasi-Electrostatics for Dielectric Objects Sharing a Common Boundary and Situated in Free Space 683\u003c\/p\u003e \u003cp\u003eJ.6 Method of Moments Solution of Electrostatic Integral Equations 687\u003c\/p\u003e \u003cp\u003eReferences 691\u003c\/p\u003e \u003cp\u003eIndex 701\u003c\/p\u003e   \u003cp\u003e\u003cb\u003eVLADIMIR OKHMATOVSKI, PHD, \u003c\/b\u003eis a Professor in the Department of Electrical and Computer Engineering at the University of Manitoba in Canada. His research is focused on fast algorithms of electromagnetics, high-performance computing, modeling of interconnects, and inverse problems. \u003c\/p\u003e\u003cp\u003e\u003cb\u003eSHUCHENG ZHENG\u003c\/b\u003e is a Postdoctoral Fellow in the Department of Electrical and Computer Engineering at the University of Manitoba. His current research interests include computational electromagnetics, multi-layered media Green’s functions, high-performance computing, the modeling of high-speed interconnects, and transient analysis of power systems.   \u003c\/p\u003e\u003cp\u003e\u003cb\u003eExplore the theory and numerical methods used to compute electromagnetic fields in multi-layered media\u003c\/b\u003e \u003c\/p\u003e\u003cp\u003eIn \u003ci\u003eTheory and Computation of Electromagnetic Fields in Layered Media\u003c\/i\u003e, two distinguished electrical engineering researchers deliver a detailed and up-to-date overview of the theory and numerical methods used to determine electromagnetic fields in layered media with embedded 3D metal\/dielectric objects. The book begins with an introduction to Maxwell’s equations, the fundamentals of electromagnetic theory, and concepts relating to Green’s functions of the layered media. It then moves on to solve canonical problems of vertical and horizontal dipole radiation, describe Method of Moments schemes, discuss integral equations governing electromagnetic fields, and explains the Michalski–Zheng theory of mixed-potential Green’s function representation in multi-layered media. \u003c\/p\u003e\u003cp\u003eChapters on the evaluation of Sommerfeld integrals, procedures for incident field evaluation in layers, and the theory of image extraction are also included, along with: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003e A thorough description to the methods of Weighted Averages, Discrete Complex Images, and Rational Function Fitting\u003c\/li\u003e \u003cli\u003e Comprehensive explorations of the traditional and mixed-potential forms of layered medium Green’s function in three dimensions\u003c\/li\u003e \u003cli\u003e Integral equations for full-wave, electro-quasi-static, and magneto-quasi-static fields in two and three dimensions\u003c\/li\u003e \u003cli\u003e In-depth examinations of the Riemann surfaces, branch cuts, multi-valued functions, and integration techniques on the complex plane\u003c\/li\u003e\n\u003c\/ul\u003e \u003cp\u003ePerfect for scholars and students of electromagnetic analysis in layered media, \u003ci\u003eTheory and Computation of Electromagnetic Fields in Layered Media\u003c\/i\u003e will also earn a place in the libraries of CAD industry engineers and software developers working in the area of computational electromagnetics.\u003c\/p\u003e","brand":"Wiley-IEEE Press","offers":[{"title":"Default Title","offer_id":47990380364005,"sku":"NP9781119763192","price":150.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119763192.jpg?v=1761787592","url":"https:\/\/k12savings.com\/products\/theory-and-computation-of-electromagnetic-fields-in-layered-media-isbn-9781119763192","provider":"K12savings","version":"1.0","type":"link"}