Deterministic and Stochastic Modeling in Computational Electromagnetics

DRAGAN POLJAK, PH.D., is Professor in the Department of Electronics and Computing Technology, University of Split, Croatia. He is a Senior Member of the IEEE and author of three books and more than 150 articles on subjects related to computational electromagnetics.ANNA ŠUŠNJARA, PH.D., is a Postdoctoral Researcher in the Department of Electronics and Computing Technology, University of Split, Croatia. She is a member of the IEEE and has authored or co-authored more than 40 journal and conference papers on subjects related to computational electromagnetics.

• About the Authors xvPreface xviiPart I Some Fundamental Principles in Field Theory 11 Least Action Principle in Electromagnetics 31.1 Hamilton Principle 41.2 Newton's Equation of Motion from Lagrangian 71.3 Noether's Theorem and Conservation Laws 81.4 Equation of Continuity from Lagrangian 121.5 Lorentz Force from Gauge Invariance 162 Fundamental Equations of Engineering Electromagnetics 212.1 Derivation of Two-Canonical Maxwell's Equation 212.2 Derivation of Two-Dynamical Maxwell's Equation 222.3 Integral Form of Maxwell's Equations, Continuity Equations, and Lorentz Force 252.4 Phasor Form of Maxwell's Equations 272.5 Continuity (Interface) Conditions 292.6 Poynting Theorem 302.7 Electromagnetic Wave Equations 322.8 Plane Wave Propagation 352.9 Hertz Dipole as a Simple Radiation Source 372.10 Wire Antennas of Finite Length 413 Variational Methods in Electromagnetics 473.1 Analytical Methods 473.2 Variational Basis for Numerical Methods 514 Outline of Numerical Methods 574.1 Variational Basis for Numerical Methods 604.2 The Finite Element Method 614.3 The Boundary Element Method 77Part II Deterministic Modeling 875 Wire Configurations – Frequency Domain Analysis 895.1 Single Wire in the Presence of a Lossy Half-Space 895.2 Horizontal Dipole Above a Multi-layered Lossy Half-Space 1005.3 Wire Array Above a Multilayer 1255.4 Wires of Arbitrary Shape Radiating Over a Layered Medium 1505.5 Complex Power of Arbitrarily Shaped Thin Wire Radiating Above a Lossy Half-Space 1866 Wire Configurations – Time Domain Analysis 2076.1 Single Wire Above a Lossy Ground 2086.2 Numerical Solution of Hallen Equation via the Galerkin–Bubnov Indirect Boundary Element Method (GB-IBEM) 2226.3 Application to Ground-Penetrating Radar 2286.4 Simplified Calculation of Specific Absorption in Human Tissue 2466.5 Time Domain Energy Measures 2556.6 Time Domain Analysis of Multiple Straight Wires above a Half-Space by Means of Various Time Domain Measures 2607 Bioelectromagnetics – Exposure of Humans in GHz Frequency Range 2857.1 Assessment of Sab in a Planar Single Layer Tissue 2867.2 Assessment of Transmitted Power Density in a Single Layer Tissue 2957.3 Assessment of Sab in a Multilayer Tissue Model 3187.4 Assessment of Transmitted Power Density in the Planar Multilayer Tissue Model 3258 Multiphysics Phenomena 3398.1 Electromagnetic-Thermal Modeling of Human Exposure to HF Radiation 3408.2 Magnetohydrodynamics (MHD) Models for Plasma Confinement 3488.3 Modeling of the Schrodinger Equation 370Part III Stochastic Modeling 3859 Methods for Stochastic Analysis 3879.1 Uncertainty Quantification Framework 3889.2 Stochastic Collocation Method 3939.3 Sensitivity Analysis 40210 Stochastic–Deterministic Electromagnetic Dosimetry 40710.1 Internal Stochastic Dosimetry for a Simple Body Model Exposed to Low-Frequency Field 40810.2 Internal Stochastic Dosimetry for a Simple Body Model Exposed to Electromagnetic Pulse 41310.3 Internal Stochastic Dosimetry for a Realistic Three-Compartment Human Head Exposed to High-Frequency Plane Wave 41710.4 Incident Field Stochastic Dosimetry for Base Station Antenna Radiation 42311 Stochastic–Deterministic Thermal Dosimetry 43311.1 Stochastic Sensitivity Analysis of Bioheat Transfer Equation 43411.2 Stochastic Thermal Dosimetry for Homogeneous Human Brain 43711.3 Stochastic Thermal Dosimetry for Three-Compartment Human Head 44711.4 Stochastic Thermal Dosimetry below 6 GHz for 5G Mobile Communication Systems 45012 Stochastic–Deterministic Modeling in Biomedical Applications of Electromagnetic Fields 45912.1 Transcranial Magnetic Stimulation 46012.2 Transcranial Electric Stimulation 46612.3 Neuron's Action Potential Dynamics 48112.4 Radiation Efficiency of Implantable Antennas 48813 Stochastic–Deterministic Modeling of Wire Configurations in Frequency and Time Domain 50313.1 Ground-Penetrating Radar 50313.2 Grounding Systems 51513.3 Air Traffic Control Systems 52314 A Note on Stochastic Modeling of Plasma Physics Phenomena 53514.1 Tokamak Current Diffusion Equation 535References 543Index 545