1. Least Action Principle in electromagnetics 2 1.1. Hamilton principle 2 1.2. Newton equation of motion from Lagrangian 5 1.3. Noether''s theorem and conservation laws 7 1.
4. Equation of continuity from Lagrangian 10 1.5. Lorentz force from Gauge Invariance 14 2. Fundamental Equations of Engineering Electromagnetics 17 2.1. Derivation of two canonical Maxwell equation 17 2.2.
Derivation of two dynamical Maxwell equation 18 2.3. Integral form of Maxwell equations, continuity equations and Lorentz force 21 2.4. Phasor form of Maxwell equations 22 2.4. Continuity (interface) conditions 24 2.5.
Poynting theorem 25 3. Variational methods in electromagnetics 40 3.1. Analytical methods 40 3.2. Capacity of insulated charged sphere 40 3.3. Spherical Grounding resistance 42 3.
4. Variational basis for numerical methods 43 4. Outline of numerical methods 47 4.1. Variational basis for numerical methods 50 4.2. The Finite Element Method (FEM) 51 4.2.
1 Basic concepts of FEM - One dimensional FEM 52 4.3.2 Linear and quadratic elements 74 4.3.2 Quadratic elements 75 4.3.4 Numerical solution of integral equations over unknown sources 76 5. Wire Configurations - Frequency Domain Analysis 79 5.
1. Single wire in a presence of a lossy half-space 79 5.1.1 Horizontal dipole above a homogeneous lossy half-space 79 5.1.2 Horizontal dipole buried in a homogeneous lossy half-space 84 5.2 Horizontal dipole above a multi-layered lossy half-space 88 5.2.
1 Integral equation formulation 88 5.2.2 Radiated field 93 5.2.3 Numerical results 95 5.3 Wire Array above a multilayer 114 5.3.1.
Formulation 116 5.3.2 Numerical procedures 118 5.3.3 Computational examples 120 5.4. Wires of arbitrary shape radiating over a layered medium 137 5.4.
1. Curved single wire in free space 139 5.4.2. Curved single wire in a presence of a lossy half-space 140 5.4.3. Multiple curved wires 142 5.
4.5. Electromagnetic field coupling to arbitrarily shaped aboveground wires 151 5.4.5. Buried wires of arbitrary shape 161 5.5. Complex Power of Arbitrarily Shaped Thin Wire Radiating above a Lossy Half-space 168 5.
5.1. Theoretical background 169 5.5.2. Numerical results 172 6. Wire Configurations - Time Domain Analysis 185 6.1 Single Wire above a Lossy Ground 186 6.
1.1. Case of perfectly conducting ground (PEC) gound and dielectric half-space 190 6.1.2 Modified reflection coefficient for the case of an imperfect ground 191 6.2 Numerical solution of Hallen equation via Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM) 199 6.2.1 Computational examples 202 6.
3 Application to Ground penetrating Radar (GPR) 205 6. 3.1 Transient Field due to Dipole Radiation Reflected from the Air-Earth Interface 207 6. 3.2 Transient Field Transmitted into a Lossy Ground due to Dipole Radiation 214 6.4 Simplified Calculation of Specific Absorption (SA) in Human Tissue 221 6.4.1 Calculation of specific absorption (SA) 222 6.
4.2 Numerical results 223 6.5 Time Domain Energy Measures 229 6.6 Time Domain Analysis of Multiple Straight Wires above a Half-space by means of Various Time Domain Measures 234 6.6.1 Theoretical background 235 6.6.2 Numerical results 237 7.
Bioelectromagnetics - Exposure of Humans in GHz Frequency Range 280 7.1 Assessment of Sab in a planar single layer tissue 280 7.1.1 Analysis of Dipole Antenna in Front of Planar Interface 282 7.1.2. Calculation of Absorbed Power Density 285 7.1.
3 Computational Examples 285 7.2. Assessment of Transmitted Power Density in a Single Layer Tissue 289 7.2.1 Formulation 290 7.2.2 Results for current distribution 294 8. Multiphysics Phenomena 330 8.
1. Electromagnetic-Thermal modeling of the Human Exposure to HF Radiation 330 8.1.1. Electromagnetic Dosimetry 330 8.1.2. Thermal Dosimetry 332 8.
1.3. Computational examples 336 8.2. Magnetohydrodynamics (MHD) Models for Plasma Confinement 337 8.2.1. Grad Shafranov Equation 338 8.
2.2. Transport Phenomena Modeling 349 8.3. Schrodinger Equation 358 8.3.1 Derivation of Schrördinger equation 359 8.3.
2 Analytical solution of Schrördinger equation 360 8.3.3 FDM solution of Schrördinger equation 361 8.3.4 FEM solution of Schrördinger equation 362 8.3.5 Neural netwok approach to the solution of Schrördinger equation 364 9. Methods for stochastic analysis 372 9.
1. Uncertainty quantification framework 373 9.1.1. Uncertainty quantification (UQ) of model input parameters 373 9.1.2. Uncertainty propagation (UP) 374 9.
1.3. Monte Carlo method 375 9.2. Stochastic collocation method 376 9.2.1. Computation of stochastic moments 377 9.
2.2. Interpolation approaches 378 9.2.3. Collocation points selection 379 9.2.4.
Multidimensional stochastic problems 379 9.3. Sensitivity analysis 383 9.3.1. "One-at-a-time" (OAT) approach 384 9.3.2.
ANalysis Of VAriance (ANOVA) based method 384 10. Stochastic-deterministic electromagnetic dosimetry 389 10.1. Internal stochastic dosimetry for a simple body model exposed to low frequency field &nb.