Advances in Time-Domain Computational Electromagnetic Methods

Cover
Title Page
Copyright
Contents
About the Editors
List of Contributors
Preface
Part I Time‐Domain Methods for Analyzing Nonlinear Phenomena
Chapter 1 Integration of Nonlinear Circuit Elements into FDTD Method Formulation
1.1 Introduction
1.2 FDTD Updating Equations for Nonlinear Elements
1.2.1 Junction Diode
1.2.2 Bipolar Junction Transistors: Small‐Signal Model
1.2.3 Bipolar Junction Transistors: Ebers–Moll Model
1.2.4 Bipolar Junction Transistors: Gummel–Poon Model
1.2.5 Field‐Effect Transistors: Small‐Signal Modeling
1.2.6 Field‐Effect Transistors: Large‐Signal Modeling
1.3 FDTD–SPICE
1.4 Data‐Based Models
1.4.1 Linear Lumped Elements: S‐Parameter Approaches
1.4.2 Nonlinear Lumped Elements: X‐Parameters
1.5 Conclusions
References
Chapter 2 FDTD Method for Nonlinear Metasurface Analysis
2.1 Introduction to Nonlinear Metasurface
2.1.1 What is Nonlinear Metasurface?
2.1.2 Material Modeling
2.1.2.1 Classical Approach
2.1.2.2 Semi‐Classical (Semi‐Quantum) Approach
2.1.2.3 Full‐Quantum Approach
2.1.3 Computational Methods for NMS Analysis
2.2 Fundamentals of Classical Models
2.2.1 Carrier Transport Equations
2.2.2 Momentum Equations
2.2.3 Maxwell‐Hydrodynamic Model
2.2.4 Simplified Models at Low Frequencies
2.2.5 Review and Restrictions
2.3 FDTD Analysis
2.3.1 Time‐Domain Perturbation Method (TDPM)
2.3.2 Numerical Algorithm: FDTD‐TDPM
2.3.2.1 Computational Grids
2.3.2.2 Linear FDTD Solver
2.3.2.3 Extra Nonlinear Current Source
2.3.3 Stability Issues
2.3.4 Numerical Results and Validations
2.3.4.1 Linear Responses
2.3.4.2 Nonlinear Responses
2.4 Applications
2.4.1 Nonlinear Surface Susceptibility Extraction
2.4.2 All‐Optical Switch (AOS)
2.4.3 Harmonic‐Modulated NMS (HM‐NMS)
2.5 Summary
References
Chapter 3 The Finite‐Element Time‐Domain Method for Dispersive and Nonlinear Media
3.1 Background and Motivation
3.2 Dispersive and Nonlinear Media
3.2.1 Dispersive Material Models
3.2.2 Dispersive Media Modeling Techniques
3.2.3 Nonlinear Dielectric Models
3.3 Finite‐Element Time‐Domain Formulations
3.3.1 Vector Wave Equation Formulation
3.3.2 Mixed Formulation
3.3.3 Remarks on FETD Formulations
3.4 FETD for Dispersive and Nonlinear Media
3.4.1 Vector Wave Equation (VWE) Formulation
3.4.1.1 Linear Dispersive Media
3.4.1.2 Instantaneous Nonlinearity
3.4.1.3 Dispersive Nonlinearity
3.4.1.4 Numerical Studies
3.4.2 Mixed Formulation
3.4.2.1 Linear Dispersive Media
3.4.2.2 Instantaneous Nonlinearity
3.4.2.3 Dispersive Nonlinearity
3.4.2.4 Numerical Studies
3.4.3 Implementation Issues
3.4.3.1 Newton–Raphson Iteration
3.4.3.2 Evaluation of Elemental Matrices
3.4.3.3 Nonlinear Auxiliary Variable Updating
3.5 Stability Analysis
3.5.1 Numerical Stability
3.5.2 Linear Dispersive Media
3.5.3 Nonlinear Media
3.6 Conclusion
References
Part II Time‐Domain Methods for Multiphysics and Multiscale Modeling
Chapter 4 Discontinuous Galerkin Time‐Domain Method in Electromagnetics: From Nanostructure Simulations to Multiphysics Implementations
4.1 Introduction to the Discontinuous Galerkin Time‐Domain Method
4.1.1 The DGTD Formulation for Maxwell's Equations
4.1.2 Boundary Conditions
4.1.2.1 Absorbing Boundary Conditions (ABCs)
4.1.2.2 Boundary Condition on Perfect Electrically Conducting (PEC) Surfaces
4.1.2.3 Boundary Condition on Perfect Magnetically Conducting (PMC) Surfaces
4.1.3 Hybridization with Time‐Domain Boundary Integral (TDBI) Method
4.1.4 Multi‐time Stepping Scheme of the DGTDBI
4.1.5 Numerical Examples for the DGTDBI
4.1.6 The DGTD Scheme with Nodal Basis Functions
4.2 Application of the DGTD Method to Real Problems
4.2.1 Graphene‐Based Devices
4.2.1.1 A Resistive Boundary Condition to Represent Graphene Within the DGTD Method
4.2.1.2 A Resistive Boundary Condition and an Auxiliary Equation Method to Represent Magnetized Graphene Within the DGTD Method
4.2.2 Multiphysics Simulation of Optoelectronic Devices
References
Chapter 5 Adaptive Discontinuous Galerkin Time‐Domain Method for the Modeling and Simulation of Electromagnetic and Multiphysics Problems
5.1 Introduction
5.2 Nodal Discontinuous Galerkin Time‐Domain Method
5.2.1 High‐Order Spatial Discretization
5.2.1.1 Definition of Basis Functions: Modal Basis and Nodal Basis
5.2.1.2 Choice of Interpolating Nodes
5.2.1.3 Elemental Matrices in the DG Method
5.2.2 High‐Order Temporal Discretization
5.3 Modeling and Simulation of Electromagnetic–Plasma Interaction
5.3.1 Physical Models of EM–Plasma Interactions
5.3.2 Numerical Modeling of EM–Plasma Interactions
5.4 Dynamic Adaptation Algorithm
5.4.1 Dynamic h‐Adaptation
5.4.2 Dynamic p‐Adaptation
5.5 Multirate Time Integration Technique
5.6 Numerical Examples
5.6.1 Scattering from a Cone Sphere with a Slot
5.6.2 Wave Scattering from an Aircraft
5.6.3 Plasma Formation and EM Shielding
5.6.4 HPM Air Discharge and Formation of Plasma Filamentary Array
5.7 Conclusion
References
Chapter 6 DGTD Method for Periodic and Quasi‐Periodic Structures
6.1 Introduction
6.1.1 Background
6.1.2 Overview of the Sections
6.2 The Subdomain‐Level DGTD Method
6.2.1 Discretized System
6.2.2 Time Stepping Schemes
6.3 Memory‐Efficient DGTD Method for Periodic Structures
6.3.1 Discretized System
6.3.1.1 Discretized System of Periodic Structures
6.3.1.2 Discretized System of Embedded Periodic Structures
6.3.2 Time Stepping Schemes
6.3.3 Numerical Results
6.3.3.1 PEC Cavity with Periodic Structures
6.3.3.2 Periodic Patch Antenna Arrays
6.4 Memory‐Efficient DGTD Method for Quasi‐Periodic Structures
6.4.1 Discretized System
6.4.1.1 Discretized System of Quasi‐Periodic Structures
6.4.1.2 Discretized System of Embedded Structures
6.4.2 Time Stepping Schemes
6.4.3 Numerical Results
6.4.3.1 PEC Cavity Filled with Quasi‐Periodic Structures
6.4.3.2 Patch Antenna Array with Quasi‐Periodic Structures
6.5 Conclusions
References
Part III Time‐Domain Integral Equation Methods for Scattering Analysis
Chapter 7 Explicit Marching‐on‐in‐time Solvers for Second‐kind Time Domain Integral Equations
7.1 Introduction
7.2 TD‐MFIE and Its Discretization
7.2.1 Discretization Using RWG Basis Functions
7.2.2 Discretization Using the Nyström Method
7.3 TD‐MFVIE and Its Discretization Using FLC Basis Functions
7.4 Predictor–Corrector Scheme
7.5 Implicit MOT Scheme
7.6 Comparison of Implicit and Explicit Solutions
7.7 Computational Complexity Analysis
7.8 Remarks
7.9 Numerical Results
7.9.1 TD‐MFIE Discretized Using RWG Basis Functions
7.9.2 TD‐MFIE Discretized Using the Nyström Method
7.9.3 TD‐MFVIE Discretized Using FLC Basis Functions
7.10 Conclusion
References
Chapter 8 Convolution Quadrature Time Domain Integral Equation Methods for Electromagnetic Scattering
8.1 Introduction
8.2 Background and Notations
8.2.1 Time Domain Integral Equations
8.3 Solution Using Convolution Quadrature
8.3.1 Laplace Transform
8.3.2 Laplace Domain Integral Equations
8.3.3 Z‐Transform
8.3.4 Runge–Kutta Methods
8.3.5 Solution of a Differential Equation Using Runge–Kutta Methods
8.3.6 Convolution Quadrature Using Runge–Kutta Methods
8.3.7 Discretization of Boundary Integral Equations
8.3.7.1 Space Discretization
8.3.7.2 Time Discretization
8.3.8 Computation of the Interaction Matrices
8.3.9 Marching‐on‐in‐Time (MOT)
8.3.10 Examples
8.3.10.1 Differentiated EFIE
8.3.10.2 MFIE
8.3.10.3 Differentiated MFIE
8.3.10.4 Differentiated CFIE
8.4 Implementation Details
8.4.1 Building a Time Domain Solver from a Frequency Domain Code: Baseline Implementation of the MOT
8.4.2 Choice of the Simulation Parameters
8.4.2.1 Choice of the RK Method
8.4.2.2 Choice of the Time Step and the Discretization Density
8.4.2.3 Choice of the Inverse Z‐Transform Parameters
8.5 Acceleration, Preconditioning, and Stabilizations
8.5.1 Computational Complexity and Fast Solver Acceleration
8.5.1.1 Complexity Analysis of a Naive Implementation
8.5.1.2 Acceleration with Fast Solvers
8.5.2 Ill‐Conditioning and Instabilities
8.5.2.1 Interior Resonances and CFIE
8.5.2.2 DC Instability
8.5.2.3 Large Time Step Breakdown
8.5.2.4 Treatment of the LF Breakdown and DC Instability
8.6 Details of the Numerical Examples Used in the Chapter
8.7 Conclusions
References
Chapter 9 Solving Electromagnetic Scattering Problems Using Impulse Responses
9.1 Introduction
9.2 Impulse Responses
9.3 Behavior at the Interior Resonance Frequencies
9.4 Impact on MOT Late Time Instability
9.5 Analytical Expressions for the Retarded‐Time Potentials
9.6 Numerical Verification of Stability Properties
9.7 Effect of Impulse Response Truncation
9.8 Domain Decomposition Method Based on Impulse Responses
9.8.1 TD‐GTM Model
9.8.2 TD‐GSIE
9.8.3 Numerical Results
9.9 Conclusions
References
Part IV Applications of Deep Learning in Time‐Domain Methods
Chapter 10 Time‐Domain Electromagnetic Forward and Inverse Modeling Using a Differentiable Programming Platform
10.1 Introduction
10.2 RNN‐Based Formulation of Wave Propagation
10.2.1 FDTD Method for Solving Maxwell's Equations
10.2.2 RNN‐Based Implementation
10.2.3 Experiments
10.2.3.1 Accuracy Comparison
10.2.3.2 Efficiency Comparison
10.3 Gradient Sensitivity Analysis
10.4 Electromagnetic Data Inversion Fulfilled by Network Training
10.4.1 RNN Training and Inversion
10.4.2 RNN Training with Different Optimization Algorithms
10.4.2.1 Gradient Descent
10.4.2.2 Momentum
10.4.2.3 RMSprop
10.4.2.4 Adam
10.5 Conclusion
References
Chapter 11 Machine Learning Application for Modeling and Design Optimization of High Frequency Structures
11.1 Introduction
11.2 Background
11.2.1 Feedforward ANN
11.2.2 Deep Neural Networks
11.2.3 Training of Deep Neural Networks
11.2.4 Supervised Deep Learning Steps
11.3 Applications of Machine Learning to Electromagnetics
11.3.1 ANN‐Based Design Optimization
11.3.1.1 Forward ANN Modeling
11.3.1.2 Inverse ANN Modeling
11.3.1.3 Neuro‐Space Mapping
11.3.1.4 Image‐Based ANN
11.3.2 ANN‐Assisted Electromagnetic Modeling
11.3.2.1 ANN‐Based Method of Moments
11.3.2.2 Machine Learning‐Assisted FDTD
11.3.2.3 ANN‐Assisted Variational Methods
11.3.2.4 Physics‐Based Unsupervised Learning of Maxwell's Equations
11.4 Discussion
References
Part V Parallel Computation Schemes for Time‐Domain Methods
Chapter 12 Acceleration of FDTD Code Using MATLAB's Parallel Computing Toolbox
12.1 Introduction
12.2 Parallelization with MATLAB
12.2.1 Explicit Parallelization
12.2.2 Multi‐GPU Processing in MATLAB
12.3 Multi‐CPU and Multi‐GPU for FDTD Simulation
12.3.1 Distribution of the FDTD Domain
12.3.2 Overlapping FDTD Data
12.3.2.1 Initializing the Parallel Pool and Distributed Calculations
12.3.2.2 Distributing the Required Information
12.3.3 The Time Marching Loop
12.3.3.1 Conversion of Time Marching Steps to Functional Programming for SPMD
12.3.3.2 Transferring of Overlapping Data
12.3.3.3 Final Time Marching Loop Code
12.3.4 Gathering the Results
12.4 Sample Results
12.5 Conclusions
References
Chapter 13 Parallel Subdomain‐Level Discontinuous Galerkin Time Domain Method
13.1 Introduction
13.2 Comparison of Parallel Element‐ and Subdomain‐Level DGTD Methods
13.2.1 Subdomain‐Level DGTD
13.2.2 Discretized System
13.2.3 Non‐conformal Mesh
13.2.4 Time Stepping
13.2.5 Element‐Level DGTD
13.2.6 Challenges of Subdomain‐Level DGTD Parallelization
13.3 Parallelization Scheme for Subdomain‐Level DGTD Methods
13.3.1 Automatic Load Balancing
13.3.1.1 Preprocessing
13.3.1.2 Repartition of Subdomains
13.3.1.3 Communication Time Reduction
13.3.2 Numerical Result
13.3.2.1 Metallic Sphere
13.3.2.2 Low‐Pass Filter
13.3.2.3 Shielding of a Desktop Case
13.4 Application of the Parallel Subdomain‐Level DGTD Method for Large‐Scale Cases
13.4.1 Patch Antenna Array
13.4.2 RCS of Boeing 737
13.5 Conclusion
References
Chapter 14 Alternate Parallelization Strategies for FETD Formulations
14.1 Background and Motivation
14.2 Challenges in FETD Parallelization
14.3 Gaussian Belief Propagation for Solving Linear Systems
14.4 Finite Element Formulation of Gaussian Belief Propagation
14.5 Parallelization of Nonlinear Problems
14.5.1 Newton's Method
14.5.2 Nonlinear Dielectric Media
14.5.2.1 Elemental Matrix Evaluation
14.5.2.2 Matrix Assembly and Solving
14.5.3 Multi‐Physics Problems
14.6 Implementation on Parallel Hardware
14.6.1 Graphics Processing Units (GPU)
14.6.1.1 GPU Optimization Strategies
14.6.1.2 GPU Results
14.6.2 Shared Memory Implementations
14.7 Conclusion
References
Part VI Multidisciplinary Explorations of Time‐Domain Methods
Chapter 15 The Symplectic FDTD Method for Maxwell and Schrödinger Equations
15.1 Introduction
15.2 Basic Theory for the Symplectic FDTD Method
15.2.1 The Basic Update Equations of the SFDTD Method
15.2.2 Numerical Results
15.3 The Coupled Maxwell–Schrödinger Equations
15.3.1 The Coupled System Based on Maxwell's and Schrödinger Equations
15.3.2 The FDTD Method Simulation for the Coupled System
15.3.3 The SFDTD Simulation for the Coupled System
15.3.4 The Coupled System Based on EM Potential and Schrödinger Equations
15.3.5 Numerical Simulation for the Coupled M–S System
15.4 A Unified Symplectic Framework for Maxwell–Schrödinger Equations
15.4.1 Symplectic Structure of the M–S System
15.4.2 Symplectic Structure Analysis of Subsystems
15.4.2.1 The Symplectic Structure of the QM System
15.4.2.2 The Symplectic Structure of the EM System
15.4.3 The SFDTD Simulation for the Coupled M–S System
15.4.3.1 The SFDTD Discretized Scheme of M–S Equations
15.4.3.2 The Boundary Condition for the M–S System
15.5 Numerical Simulation
15.5.1 Effect of the EM Field Strength
15.5.2 Effect of Detuning
15.5.3 Application of the Coupled M–S System in a Complex Environment
15.5.3.1 Lossy Medium Environment
15.5.3.2 Inhomogeneous Media Environment
15.5.3.3 Free Space Environment
15.6 Conclusion
Acknowledgments
Author Biography
References
Chapter 16 Cylindrical FDTD Formulation for Low Frequency Applications
16.1 Cylindrical Finite‐Difference Time‐Domain Method
16.2 Convolutional PML in Cylindrical Coordinates
16.2.1 Coordinate Stretching Approach
16.2.2 CPML Update Equations
16.2.3 Numerical Examples
16.3 Cylindrical FDTD Formulation for Circuit Elements
16.3.1 Voltage Source with Internal Impedance
16.3.2 Cylindrical FDTD Updating Equation for a Load Impedance
16.3.2.1 Resistor
16.3.2.2 Capacitor
16.3.2.3 Inductor
16.3.3 Simulation Examples
16.4 Concluding Remarks
References
Index
EULA