Deterministic and Stochastic Modeling in Computational Electromagnetics : Integral and Differential Equation Approaches.

Author
Poljak, Dragan [Browse]
Format
Book
Language
English
Εdition
1st ed.
Published/​Created
  • Newark : John Wiley & Sons, Incorporated, 2023.
  • ©2024.
Description
1 online resource (576 pages)

Details

Subject(s)
Series
IEEE Press Series on Electromagnetic Wave Theory Series [More in this series]
Summary note
This book explores deterministic and stochastic modeling techniques in computational contexts, focusing on integral and differential equation approaches. Authored by Dragan Poljak and Anna Šušnjara, the work delves into the principles of field theory, variational methods, and numerical methods such as the finite element and boundary element methods. It covers topics like wire frequency domain analysis, exposure of humans to GHz frequency range, and multiphysics phenomena, providing theoretical background and practical computational examples. The book is intended for professionals and researchers in engineering and applied mathematics, offering insights into modeling complex systems and electromagnetic interactions.
Source of description
  • Description based on publisher supplied metadata and other sources.
  • Part of the metadata in this record was created by AI, based on the text of the resource.
Contents
  • Cover
  • Title Page
  • Copyright Page
  • Dedication Page
  • Contents
  • About the Authors
  • Preface
  • Part I Some Fundamental Principles in Field Theory
  • Chapter 1 Least Action Principle in Electromagnetics
  • 1.1 Hamilton Principle
  • 1.2 Newton's Equation of Motion from Lagrangian
  • 1.3 Noether's Theorem and Conservation Laws
  • 1.4 Equation of Continuity from Lagrangian
  • 1.5 Lorentz Force from Gauge Invariance
  • References
  • Chapter 2 Fundamental Equations of Engineering Electromagnetics
  • 2.1 Derivation of Two-Canonical. Maxwell's Equation
  • 2.2 Derivation of Two-Dynamical. Maxwell's Equation
  • 2.3 Integral Form of Maxwell's Equations, Continuity Equations, and Lorentz Force
  • 2.4 Phasor Form of Maxwell's Equations
  • 2.5 Continuity (Interface) Conditions
  • 2.6 Poynting Theorem
  • 2.7 Electromagnetic Wave Equations
  • 2.8 Plane Wave Propagation
  • 2.9 Hertz Dipole as a Simple Radiation Source
  • 2.9.1 Determination of the Q-Factor
  • 2.10 Wire Antennas of Finite Length
  • 2.10.1 Dipole Antennas
  • 2.10.2 Pocklington Integro-Differential Equation for Straight Thin Wire
  • Chapter 3 Variational Methods in Electromagnetics
  • 3.1 Analytical Methods
  • 3.1.1 Capacity of Insulated Charged Sphere
  • 3.1.2 Spherical Grounding Resistance
  • 3.2 Variational Basis for Numerical Methods
  • 3.2.1 Poisson's Equation
  • 3.2.2 Scalar Potential Integral Equation (SPIE)
  • 3.2.3 Correlation Between Variational Principle and Weighted Residual (Galerkin) Approach
  • 3.2.4 Ritz Method
  • Chapter 4 Outline of Numerical Methods
  • 4.1 Variational Basis for Numerical Methods
  • 4.2 The Finite Element Method
  • 4.2.1 Basic Concepts of FEM - One-Dimensional FEM
  • 4.2.2 Two-Dimensional FEM
  • 4.2.3 Three-Dimensional FEM
  • 4.3 The Boundary Element Method
  • 4.3.1 Constant Boundary Elements.
  • 4.3.2 Linear and Quadratic Elements
  • 4.3.3 Quadratic Elements
  • 4.3.4 Numerical Solution of Integral Equations Over Unknown Sources
  • Part II Deterministic Modeling
  • Chapter 5 Wire Configurations - Frequency Domain Analysis
  • 5.1 Single Wire in the Presence of a Lossy Half-Space
  • 5.1.1 Horizontal Dipole Above a Homogeneous Lossy Half-Space
  • 5.1.1.1 Integro-differential Equation Formulation
  • 5.1.1.2 Numerical Solution of the Pocklington Equation
  • 5.1.1.3 Computational Example
  • 5.1.2 Horizontal Dipole Buried in a Homogeneous Lossy Half-Space
  • 5.1.2.1 Pocklington Integro-differential Equation Formulation
  • 5.1.2.2 Numerical Solution of the Pocklington Equation
  • 5.1.2.3 Computational Example
  • 5.2 Horizontal Dipole Above a Multi-layered Lossy Half-Space
  • 5.2.1 Integral Equation Formulation
  • 5.2.2 Radiated Field
  • 5.2.3 Numerical Results
  • 5.3 Wire Array Above a Multilayer
  • 5.3.1 Formulation
  • 5.3.2 Numerical Procedures
  • 5.3.3 Computational Examples
  • 5.4 Wires of Arbitrary Shape Radiating Over a Layered Medium
  • 5.4.1 Curved Single Wire in Free Space
  • 5.4.2 Curved Single Wire in the Presence of a Lossy Half-space
  • 5.4.3 Multiple Curved Wires
  • 5.4.3.1 Numerical Solution Procedures
  • 5.4.3.2 Computational Examples
  • 5.4.4 Electromagnetic Field Coupling to Arbitrarily Shaped Aboveground Wires
  • 5.4.4.1 Formulation via a Set of Coupled Integro-differential Equations
  • 5.4.4.2 Numerical Solution of Coupled Pocklington Equations
  • 5.4.4.3 Computational Example
  • 5.4.5 Buried Wires of Arbitrary Shape
  • 5.4.5.1 Formulation
  • 5.4.5.2 Numerical Procedure
  • 5.4.5.3 Computational Examples
  • 5.5 Complex Power of Arbitrarily Shaped Thin Wire Radiating Above a Lossy Half-Space
  • 5.5.1 Theoretical Background
  • 5.5.2 Numerical Results
  • Chapter 6 Wire Configurations - Time Domain Analysis.
  • 6.1 Single Wire Above a Lossy Ground
  • 6.1.1 Case of Perfectly Conducting (PEC) Ground and Dielectric Half-Space
  • 6.1.2 Modified Reflection Coefficient for the Case of an Imperfect Ground
  • 6.2 Numerical Solution of Hallen Equation via the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM)
  • 6.2.1 Computational Examples
  • 6.3 Application to Ground-Penetrating Radar
  • 6.3.1 Transient Field due to Dipole Radiation Reflected from the Air-Earth Interface
  • 6.3.1.1 Numerical Evaluation Procedure
  • 6.3.1.2 Numerical Results
  • 6.3.2 Transient Field Transmitted into a Lossy Ground Due to Dipole Radiation
  • 6.3.2.1 Numerical Evaluation of the Transmitted Field
  • 6.3.2.2 Numerical Results
  • 6.4 Simplified Calculation of Specific Absorption in Human Tissue
  • 6.4.1 Calculation of Specific Absorption
  • 6.4.2 Numerical Results
  • 6.5 Time Domain Energy Measures
  • 6.6 Time Domain Analysis of Multiple Straight Wires above a Half-Space by Means of Various Time Domain Measures
  • 6.6.1 Theoretical Background
  • 6.6.1.1 Time Domain Energy Measures and Power Measure
  • 6.6.1.2 Root Mean Square Value of Current Distribution
  • 6.6.2 Numerical Results
  • 6.6.2.1 Configuration 1
  • 6.6.2.2 Configuration 2
  • 6.6.2.3 Configuration 3
  • 6.6.2.4 Configuration 4
  • 6.6.2.5 Configuration 5
  • 6.6.2.6 Configuration 6
  • Chapter 7 Bioelectromagnetics - Exposure of Humans in GHz Frequency Range
  • 7.1 Assessment of Sab in a Planar Single Layer Tissue
  • 7.1.1 Analysis of Dipole Antenna in Front of Planar Interface
  • 7.1.2 Calculation of Absorbed Power Density
  • 7.1.3 Computational Examples
  • 7.2 Assessment of Transmitted Power Density in a Single Layer Tissue
  • 7.2.1 Formulation
  • 7.2.2 Results for Current Distribution
  • 7.2.2.1 Results for Transmitted Field, VPD, and TPD
  • 7.2.2.2 Different Distance from the Interface.
  • 7.2.2.3 Different Antenna Length
  • 7.2.2.4 Different Frequencies
  • 7.3 Assessment of Sab in a Multilayer Tissue Model
  • 7.3.1 Theoretical Background
  • 7.3.2 Results
  • 7.4 Assessment of Transmitted Power Density in the Planar Multilayer Tissue Model
  • 7.4.1 Formulation
  • 7.4.2 Results
  • 7.4.2.1 Two-Layer Model
  • 7.4.2.2 Three-Layer Model
  • 7.4.2.3 Skin Depth and Saturation Depth
  • Chapter 8 Multiphysics Phenomena
  • 8.1 Electromagnetic-Thermal Modeling of Human Exposure to HF Radiation
  • 8.1.1 Electromagnetic Dosimetry
  • 8.1.2 Thermal Dosimetry
  • 8.1.3 Computational Examples
  • 8.2 Magnetohydrodynamics (MHD) Models for Plasma Confinement
  • 8.2.1 The Grad-Shafranov Equation
  • 8.2.1.1 Analytical Solution
  • 8.2.1.2 Analytical Results
  • 8.2.1.3 Solution by the Finite Difference Method (FDM)
  • 8.2.1.4 Solution by the Finite Element Method (FEM)
  • 8.2.1.5 Computational Examples
  • 8.2.2 Transport Phenomena Modeling
  • 8.2.2.1 Transport Equations
  • 8.2.2.2 Current Diffusion Equation and Equilibrium in Tokamaks
  • 8.2.2.3 FEM Solution of CDE
  • 8.2.2.4 Analytical Solution Procedure
  • 8.2.2.5 Numerical Results
  • 8.3 Modeling of the Schrodinger Equation
  • 8.3.1 Derivation of the Schrodinger Equation
  • 8.3.2 Analytical Solution of the Schrodinger Equation
  • 8.3.3 FDM Solution of the Schrodinger Equation
  • 8.3.4 FEM Solution of the Schrodinger Equation
  • 8.3.5 Neural Network Approach to the Solution of the Schrodinger Equation
  • Part III Stochastic Modeling
  • Chapter 9 Methods for Stochastic Analysis
  • 9.1 Uncertainty Quantification Framework
  • 9.1.1 Uncertainty Quantification (UQ) of Model Input Parameters
  • 9.1.2 Uncertainty Propagation (UP)
  • 9.1.3 Monte Carlo Method
  • 9.2 Stochastic Collocation Method
  • 9.2.1 Computation of Stochastic Moments
  • 9.2.2 Interpolation Approaches.
  • 9.2.3 Collocation Points Selection
  • 9.2.4 Multidimensional Stochastic Problems
  • 9.2.4.1 Tensor Product
  • 9.2.4.2 Sparse Grids
  • 9.2.4.3 Stroud's Cubature Rules
  • 9.3 Sensitivity Analysis
  • 9.3.1 "One-at-a-Time" (OAT) Approach
  • 9.3.2 ANalysis Of VAriance (ANOVA)-Based Method
  • Chapter 10 Stochastic-Deterministic Electromagnetic Dosimetry
  • 10.1 Internal Stochastic Dosimetry for a Simple Body Model Exposed to Low-Frequency Field
  • 10.2 Internal Stochastic Dosimetry for a Simple Body Model Exposed to Electromagnetic Pulse
  • 10.3 Internal Stochastic Dosimetry for a Realistic Three-Compartment Human Head Exposed to High-Frequency Plane Wave
  • 10.4 Incident Field Stochastic Dosimetry for Base Station Antenna Radiation
  • Chapter 11 Stochastic-Deterministic Thermal Dosimetry
  • 11.1 Stochastic Sensitivity Analysis of Bioheat Transfer Equation
  • 11.2 Stochastic Thermal Dosimetry for Homogeneous Human Brain
  • 11.3 Stochastic Thermal Dosimetry for Three-Compartment Human Head
  • 11.4 Stochastic Thermal Dosimetry below 6 GHz for 5G Mobile Communication Systems
  • Chapter 12 Stochastic-Deterministic Modeling in Biomedical Applications of Electromagnetic Fields
  • 12.1 Transcranial Magnetic Stimulation
  • 12.2 Transcranial Electric Stimulation
  • 12.2.1 Cylinder Representation of Human Head
  • 12.2.2 A Three-Compartment Human Head Model
  • 12.2.3 A Nine-Compartment Human Head Model
  • 12.3 Neuron's Action Potential Dynamics
  • 12.4 Radiation Efficiency of Implantable Antennas
  • Chapter 13 Stochastic-Deterministic Modeling of Wire Configurations in Frequency and Time Domain
  • 13.1 Ground-Penetrating Radar
  • 13.1.1 The Transient Current Induced Along the GPR Antenna
  • 13.1.2 The Transient Field Transmitted into a Lossy Soil
  • 13.2 Grounding Systems.
  • 13.2.1 Test Case #1: Soil And Lighting Pulse Parameters are Random Variables.
ISBN
  • 9781119989271
  • 1119989272
  • 9781119989257
  • 1119989256
OCLC
1409686873
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