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Deterministic computational models are those for which all inputs are precisely known, whereas stochastic modeling reflects uncertainty or randomness in one or more of the data inputs. Many problems in computational engineering therefore require both deterministic and stochastic modeling to be used in parallel, allowing for different degrees of confidence and incorporating datasets of different kinds. In particular, non-intrusive stochastic methods can be easily combined with widely used deterministic approaches, enabling this more robust form of data analysis to be applied to a range of computational challenges.
Deterministic and Stochastic Modeling in Computational Electromagnetics provides a rare treatment of parallel deterministic-stochastic computational modeling and its beneficial applications. Unlike other works of its kind, which generally treat deterministic and stochastic modeling in isolation from one another, it aims to demonstrate the usefulness of a combined approach and present particular use-cases in which such an approach is clearly required. It offers a non-intrusive stochastic approach which can be incorporated with minimal effort into virtually all existing computational models.
Readers will also find: - A range of specific examples demonstrating the efficiency of deterministic-stochastic modeling - Computational examples of successful applications including ground penetrating radars (GPR), radiation from 5G systems, transcranial magnetic and electric stimulation (TMS and TES), and more - Introduction to fundamental principles in field theory to ground the discussion of computational modeling
Deterministic and Stochastic Modeling in Computational Electromagnetics is a valuable reference for researchers, including graduate and undergraduate students, in computational electromagnetics, as well as to multidisciplinary researchers, engineers, physicists, and mathematicians.
Table of Contents
About the Authors xv
Preface xvii
Part I Some Fundamental Principles in Field Theory 1
1 Least Action Principle in Electromagnetics 3
1.1 Hamilton Principle 4
1.2 Newton's Equation of Motion from Lagrangian 7
1.3 Noether's Theorem and Conservation Laws 8
1.4 Equation of Continuity from Lagrangian 12
1.5 Lorentz Force from Gauge Invariance 16
2 Fundamental Equations of Engineering Electromagnetics 21
2.1 Derivation of Two-Canonical Maxwell's Equation 21
2.2 Derivation of Two-Dynamical Maxwell's Equation 22
2.3 Integral Form of Maxwell's Equations, Continuity Equations, and Lorentz Force 25
2.4 Phasor Form of Maxwell's Equations 27
2.5 Continuity (Interface) Conditions 29
2.6 Poynting Theorem 30
2.7 Electromagnetic Wave Equations 32
2.8 Plane Wave Propagation 35
2.9 Hertz Dipole as a Simple Radiation Source 37
2.10 Wire Antennas of Finite Length 41
3 Variational Methods in Electromagnetics 47
3.1 Analytical Methods 47
3.2 Variational Basis for Numerical Methods 51
4 Outline of Numerical Methods 57
4.1 Variational Basis for Numerical Methods 60
4.2 The Finite Element Method 61
4.3 The Boundary Element Method 77
Part II Deterministic Modeling 87
5 Wire Configurations - Frequency Domain Analysis 89
5.1 Single Wire in the Presence of a Lossy Half-Space 89
5.2 Horizontal Dipole Above a Multi-layered Lossy Half-Space 100
5.3 Wire Array Above a Multilayer 125
5.4 Wires of Arbitrary Shape Radiating Over a Layered Medium 150
5.5 Complex Power of Arbitrarily Shaped Thin Wire Radiating Above a Lossy Half-Space 186
6 Wire Configurations - Time Domain Analysis 207
6.1 Single Wire Above a Lossy Ground 208
6.2 Numerical Solution of Hallen Equation via the Galerkin-Bubnov Indirect Boundary Element Method (GB-IBEM) 222
6.3 Application to Ground-Penetrating Radar 228
6.4 Simplified Calculation of Specific Absorption in Human Tissue 246
6.5 Time Domain Energy Measures 255
6.6 Time Domain Analysis of Multiple Straight Wires above a Half-Space by Means of Various Time Domain Measures 260
7 Bioelectromagnetics - Exposure of Humans in GHz Frequency Range 285
7.1 Assessment of Sab in a Planar Single Layer Tissue 286
7.2 Assessment of Transmitted Power Density in a Single Layer Tissue 295
7.3 Assessment of Sab in a Multilayer Tissue Model 318
7.4 Assessment of Transmitted Power Density in the Planar Multilayer Tissue Model 325
8 Multiphysics Phenomena 339
8.1 Electromagnetic-Thermal Modeling of Human Exposure to HF Radiation 340
8.2 Magnetohydrodynamics (MHD) Models for Plasma Confinement 348
8.3 Modeling of the Schrodinger Equation 370
Part III Stochastic Modeling 385
9 Methods for Stochastic Analysis 387
9.1 Uncertainty Quantification Framework 388
9.2 Stochastic Collocation Method 393
9.3 Sensitivity Analysis 402
10 Stochastic-Deterministic Electromagnetic Dosimetry 407
10.1 Internal Stochastic Dosimetry for a Simple Body Model Exposed to Low-Frequency Field 408
10.2 Internal Stochastic Dosimetry for a Simple Body Model Exposed to Electromagnetic Pulse 413
10.3 Internal Stochastic Dosimetry for a Realistic Three-Compartment Human Head Exposed to High-Frequency Plane Wave 417
10.4 Incident Field Stochastic Dosimetry for Base Station Antenna Radiation 423
11 Stochastic-Deterministic Thermal Dosimetry 433
11.1 Stochastic Sensitivity Analysis of Bioheat Transfer Equation 434
11.2 Stochastic Thermal Dosimetry for Homogeneous Human Brain 437
11.3 Stochastic Thermal Dosimetry for Three-Compartment Human Head 447
11.4 Stochastic Thermal Dosimetry below 6 GHz for 5G Mobile Communication Systems 450
12 Stochastic-Deterministic Modeling in Biomedical Applications of Electromagnetic Fields 459
12.1 Transcranial Magnetic Stimulation 460
12.2 Transcranial Electric Stimulation 466
12.3 Neuron's Action Potential Dynamics 481
12.4 Radiation Efficiency of Implantable Antennas 488
13 Stochastic-Deterministic Modeling of Wire Configurations in Frequency and Time Domain 503
13.1 Ground-Penetrating Radar 503
13.2 Grounding Systems 515
13.3 Air Traffic Control Systems 523
14 A Note on Stochastic Modeling of Plasma Physics Phenomena 535
14.1 Tokamak Current Diffusion Equation 535
References 543
Index 545
