Some recent advances in numerical solutions of electromagnetic problems.

Zhang Kai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 99-102).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.6Chapter 1.1 --- The Generalized PML Theory --- p.6Chapter 1.1.1 --- Background --- p.6Chapter 1.1.2 --- Derivation --- p.8Chapter 1.1.3 --- Reflection Properties --- p.11Chapter 1.2 --- Unified Formulation --- p.12Chapter 1.2.1 --- "Face-, Edge- and Corner-PMLs" --- p.12Chapter 1.2.2 --- Unified PML Equations in 3D --- p.15Chapter 1.2.3 --- Unified PML Equations in 2D --- p.16Chapter 1.2.4 --- Examples of PML Formulations --- p.16Chapter 1.3 --- Inhomogeneous Initial Conditions --- p.23Chapter 2 --- Numerical Analysis of PMLs --- p.25Chapter 2.1 --- Continuous PMLs --- p.26Chapter 2.1.1 --- PMLs for Wave Equations --- p.27Chapter 2.1.2 --- Finite PMLs for Wave Equations --- p.31Chapter 2.1.3 --- Berenger's PMLs for Maxwell Equations --- p.33Chapter 2.1.4 --- Finite Berenger's PMLs for Maxwell Equations --- p.35Chapter 2.1.5 --- PMLs for Acoustic Equations --- p.38Chapter 2.1.6 --- Berenger's PMLs for Acoustic Equations --- p.39Chapter 2.1.7 --- PMLs for 1-D Hyperbolic Systems --- p.42Chapter 2.2 --- Discrete PMLs --- p.44Chapter 2.2.1 --- Discrete PMLs for Wave Equations --- p.44Chapter 2.2.2 --- Finite Discrete PMLs for Wave Equations --- p.51Chapter 2.2.3 --- Discrete Berenger's PMLs for Wave Equations --- p.53Chapter 2.2.4 --- Finite Discrete Berenger's PMLs for Wave Equations --- p.56Chapter 2.2.5 --- Discrete PMLs for 1-D Hyperbolic Systems --- p.58Chapter 2.3 --- Modified Yee schemes for PMLs --- p.59Chapter 2.3.1 --- Stability of the Yee Scheme for Wave Equation --- p.61Chapter 2.3.2 --- Decay of the Yee Scheme Solution to the Berenger's PMLs --- p.62Chapter 2.3.3 --- Stability and Convergence of the Yee Scheme for the Berenger's PMLs --- p.67Chapter 2.3.4 --- Decay of the Yee Scheme Solution to the Hagstrom's PMLs --- p.70Chapter 2.3.5 --- Stability and Convergence of the Yee Scheme for the Hagstrom's PMLs --- p.75Chapter 2.4 --- Modified Lax-Wendroff Scheme for PMLs --- p.80Chapter 2.4.1 --- Exponential Decays in Parabolic Equations --- p.80Chapter 2.4.2 --- Exponential Decays in Hyperbolic Equations --- p.82Chapter 2.4.3 --- Exponential Decays of Modified Lax-Wendroff Solutions --- p.86Chapter 3 --- Numerical Simulation --- p.93Bibliography --- p.9

Efficient automotive electromagnetic modelling

The Transmission Line Modelling (TLM) method is applied to the electromagnetic modelling of vehicles. Implications of increasing frequencies in computer models of electromagnetic compatibility (EMC) studies are discussed. Efficient algorithms and resource management strategies are developed With a view to producing accurate results m a realistic computational run time. Theoretical aspects covered are: (1) the development and accuracy of the TLM method; (2) an improved Partial Huygens' surface for plane wave excitation; (3) an evaluation of high-performance local and global absorbing boundary conditions. Implementation aspects of TLM addressed include: (1) the effects of arithmetic precision on link line voltage and stub impedance calculations; (2) the development of an object-oriented computer code using the Object Modelling Technique; (3) methods for estimating and managing the memory requirement and run lime of simulations. It is shown that by optimizing algorithms and carefully managing resources, sufficient improvement can be made to allow relatively sophisticated models to be run on a modest desktop computer

Implementation of the Finite Difference Time Domain algorithm for the analysis of terahertz waves

The aim of this report is to present results related to the application of the Finite Difference Time Domain (FDTD) method for the study of various devices at terahertz frequencies. The FDTD method has emerged as one of the most widely used numerical analysis methods used for electromagnetic simulations. The FDTD method can be used to solve numerous types of problems ranging from modelling the behaviour of microwave circuits, waveguides, and photonics to simulating terahertz devices and plasmas. In this study the FDTD approach is derived from first principles (finite differences) and explicit equations are shown based on Maxwell's equations. Furthermore, absorbing boundary conditions (ABCs) are discussed for the FDTD method. The algorithm is tested against a range of problems to ensure its validity and accuracy. The FDTD method is then applied for the numerical analysis of a range of devices at terahertz frequencies. The numerical results obtained from the application of the FDTD method to examine a microstrip circuit with filter loading and a Multi-mode Interference (MMI) coupler at terahertz frequencies are discussed in detail. Moreover, the results of the application of the FDTD method for the calculation of the dispersion characteristics of plasmonic waveguides are also presented. Finally, a summary of the work carried out is presented and an outline is given for future research which can be carried out by using the FDTD method for the study of terahertz frequency devices

Advances in beam propagation method for facet reflectivity analysis

Waveguide discontinuities are frequently encountered in modern photonic structures. It is important to characterize the reflection and transmission that occurs at the discontinuous during the design and analysis process of these structures. Significant effort has been focused upon the development of accurate modelling tools, and a variety of modelling techniques have been applied to solve this kind of problem. Throughout this work, a Transmission matrix based Bidirectional Beam Propagation Method (T-Bi-BPM) is proposed and applied on the uncoated facet and the single coating layer reflection problems, including both normal and angled incident situations. The T-Bi-BPM method is developed on the basis of an overview of Finite Difference Beam Propagation Method (FD-BPM) schemes frequently used in photonic modelling including paraxial FD-BPM, Imaginary Distance (ID) BPM, Wide Angle (WA) BPM and existing Bidirectional (Bi) BPM methods. The T-Bi-BPM establishes the connection between the total fields on either side of the coating layer and the incident field at the input of a single layer coated structure by a matrix system on the basis of a transmission matrix equation used in a transmission line approach. The matrix system can be algebraically preconditioned and then solved by sparse matrix multiplications. The attraction of the T-Bi-BPM method is the potential for more rapid evaluation without iterative approach. The accuracy of the T-Bi-BPM is verified by simulations and the factors that affect the accuracy are investigated

Numerical methods for electromagnetic wave propagation and scattering in complex media

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Vita.Includes bibliographical references (p. 227-242).Numerical methods are developed to study various applications in electromagnetic wave propagation and scattering. Analytical methods are used where possible to enhance the efficiency, accuracy, and applicability of the numerical methods. Electromagnetic induction (EMI) sensing is a popular technique to detect and discriminate buried unexploded ordnance (UXO). Time domain EMI sensing uses a transient primary magnetic field to induce currents within the UXO. These currents induce a secondary field that is measured and used to determine characteristics of the UXO. It is shown that the EMI response is difficult to calculate in early time when the skin depth is small. A new numerical method is developed to obtain an accurate and fast solution of the early time EMI response. The method is combined with the finite element method to provide the entire time domain response. The results are compared with analytical solutions and experimental data, and excellent agreement is obtained. A fast Method of Moments is presented to calculate electromagnetic wave scattering from layered one dimensional rough surfaces. To facilitate the solution, the Forward Backward method with Spectral Acceleration is applied. As an example, a dielectric layer on a perfect electric conductor surface is studied. First, the numerical results are compared with the analytical solution for layered flat surfaces to partly validate the formulation. Second, the accuracy, efficiency, and convergence of the method are studied for various rough surfaces and layer permittivities. The Finite Difference Time Domain (FDTD) method is used to study metamaterials exhibiting both negative permittivity and permeability in certain frequency bands.(cont.) The structure under study is the well-known periodic arrangement of rods and split-ring resonators, previously used in experimental setups. For the first time, the numerical results of this work show that fields propagating inside the metamaterial with a forward power direction exhibit a backward phase velocity and negative index of refraction. A new metamaterial design is presented that is less lossy than previous designs. The effects of numerical dispersion in the FDTD method are investigated for layered, anisotropic media. The numerical dispersion relation is derived for diagonally anisotropic media. The analysis is applied to minimize the numerical dispersion error of Huygens' plane wave sources in layered, uniaxial media. For usual discretization sizes, a typical reduction of the scattered field error on the order of 30 dB is demonstrated. The new FDTD method is then used to study the Angular Correlation Function (ACF) of the scattered fields from continuous random media with and without a target object present. The ACF is shown to be as much as 10 dB greater when a target object is present for situations where the target is undetectable by examination of the radar cross section only.by Christopher D. Moss.Ph.D

박막형 태양전지 수치해석을 위한 효율적 알고리즘에 관한 연구

학위논문 (박사)-- 서울대학교 대학원 : 협동과정 계산과학 전공, 2013. 8. 신동우.본 논문에서는 무작위의 복잡한 3차원 표면 형상을 가진 물체를 평균적으로 O(logN) 시간 복잡도를 가지고 교차검사를 수행할 수 있는 새로운 알고리즘을 기반으로 박막형 태양전지 (Thin Film Solar Cell)의 흡수 효율을 효과적으로 시뮬레이션 하기 위한 방법을 논하였다. 3차원 피라미드 형상을 박막형 태양전지 표면에 양각한 경우, 3차원 표면 형상의 크기와 밀도가 흡수 효율에 영향을 미치게 되므로 이들에 대한 최적 설계 값들을 찾고자 시뮬레이션 방법을 이용한다. 본 연구에서는 무수히 많은 3차원 표면 형상들에 대한 최적의 교차검사 알고리즘을 kd-tree 가속화 구조를 변형하여 개발하였고, 이를 광선 추적 법 (Ray tracing)에 적용하여 평균 교차검사 시간을 O((log N)으로 하는 새로운 광선 추적에 의한 시뮬레이션 방법을 고안하였다. 이 방법은 기존 연구들에서 한번도 연구되지 않은 새로운 방법으로, 표면 형상들을 실제 객체로 인지하여 교차검사를 수행하면서도 종래의 O(N)~O(N2) 교차검사 시간을 O(log N)으로 단축시키는 결과를 얻었다. 또한 이전 연구들에서 반사율 시뮬레이션에 의존하여 간접적으로 계산하던 에너지 흡수 효율을 직접적으로 시뮬레이션 함은 물론이고 각 층별 에너지 흡수율을 간섭현상을 반영하여 직접적으로 시뮬레이션 할 수 있는 방법을 고안하였다. 이 알고리즘의 효율성 및 정확성은 다른 알고리즘과의 수행 시간 비교 및 실측 자료와 시뮬레이션 결과와의 오차 분석을 통해 검증 하였다. 박막형 태양전지의 크기가 나노미터 단위로 작아진 경우, 유한차분 시간영역 (FDTD)법을 이용하게 되는데, 현재까지 연구된 방법들로는 적은 전산 자원을 사용하여 빠른 시간 내에 정확한 흡수 에너지를 계산하는데 한계가 있었다. 본 연구에서는 이 문제를 해결하기 위하여 자유로운 형태의 시스템에 대해서 각 물질들의 연속된 경계 면을 효율적으로 추출하여 Poynting 이론의 발산 (Divergence) 부분의 식을 적용하는 방법으로 적은 전산 자원으로 빠른 시간 내에 상당한 정확도를 가지고 흡수 에너지를 계산할 수 있는 방법을 고안하였다. 이 방법의 정확성은 해석 가능한 모델의 Mie 확산 모델의 계산 결과와 시뮬레이션 결과를 비교함으로써 검증하였으며, 곡면 모델에 대해서는 곡률 반경을 변화시켜가며 시뮬레이션 한 결과가 물리적 유의성을 나타냄을 보임으로써 검증 하였다.In this thesis, I proposed a novel intersection algorithm based absorption en-ergy simulation methods for thin film solar cells which use a 3-D randomly textured geometry or plasma effects. For the case of pyramidal textured thin film solar cells, Optimizing the de-sign of the surface texture is an essential aspect of the thin film Si solar cells technology as it can maximize the light trapping efficiency of the cells. Thus, the appropriate simulation tools can provide efficient means of designing and analyzing the effects of the texture patterns on light confinement in an active medium. A ray tracing method is a powerful numerical simulation methodol-ogy for this. However, in past researches, a real object intersection method take an O(N2) time complexity and some height map method take an O(N) time complexity. These are time consuming process and inaccurate process, so I developed a novel intersection algorithm with an O(logN) time com-plexity and with keeping the accuracy. Also, an absorption energy calculation algorithm for each layer with a direct method did not exist in the past. To solve the intersection finding problem, I proposed a novel and an efficient 3-D texture intersection algorithm using a modified kd-tree traversal method in Chapter 2. Also, to solve the absorption efficiency calculation problem with ray tracing method, I proposed a new method in Chapter 3. The correctness and efficiency of the algorithms was validated by a measured data and numer-ical simulations. The thickness of the thin film solar cells reach to the nanometer size. The ray tracing method is useless for the nanometer size systems except for a flat surface type. In this case, the FDTD method can be used to solve this nanome-ter scale problems. However, by the past researches, an auto-discretization problem and an absorption efficiency calculation problem were not solved efficiently. In this research, I proposed a robust and an efficient auto-discretization algorithm and an efficient absorption energy calculation algo-rithm with a continuous boundary extraction algorithm in Chapter 4. The correctness and efficiency of the algorithms was validated by an exact solu-tion and numerical simulations. Through this thesis, I proposed an efficient absorption efficiency calcula-tion algorithms for all system ranges of the thin film solar cells.Abstract Publications Table of Contents List of Figures List of Tables List of Algorithms Symbols Abbreviations 1. Introduction 1.1 Motivation 1.2 Thin Film Solar cells 1.2.1 Reduction of Front Surface Reflectance 1.2.2 Enhancement of Back Surface Reflectance 1.2.3 Efficient Light Trapping 1.3 Ray Tracing 1.3.1 Finding Intersection 1.3.1.1 Primitive Object Case 1.3.1.2 CSG Object Case 1.3.2 Acceleration Scheme 1.4 Finite Difference Time Domain (FDTD) 1.4.1 Discretization of the System Domain 1.4.2 Dispersive Materials 1.4.2.1 Lorentz Model 1.4.2.2 Drude Model 1.4.2.3 Drude-Lorentz Model 1.4.3 Boundary Condition 1.4.3.1 Absorbing Boundary Condition (ABC) 1.4.3.2 Periodic Boundary Condition (PBC) 1.5 Scope and Objectives 1.6 Achievements 2. Slab-Outline Algorithm for Fast Intersection Finding 2.1 Overview 2.2 Algorithm 2.2.1 Non-overlapped texture case 2.2.2 Overlapped pyramidal texture case 2.3 Numerical Results : Validation 2.3.1 Examine of Backward Ray Tracing Results 2.3.2 Comparison of Experimental Results 2.3.3 Error Analysis 2.3.4 Time Complexity 2.4 Numerical Analysis : Applications 2.4.1 Simulation 2.4.2 Results and discussion 2.5 Conclusion 3. Simulation with Ray Tracing Method 3.1 Overview 3.2 Algorithm 3.3 Validation 3.3.1 Case I - coherent system 3.3.2 Case II - incoherent system 3.3.3 Case III - coherent + incoherent complex system 3.4 Numerical Analysis : Applications 3.4.1 High-efficiency Grid-type Si Solar Cell Structure 3.4.1.1 Overview 3.4.1.2 Simulation model 3.4.1.3 Results and Discussion 3.4.2 Effect of oxide thin films in back contact on the optical absorption efficiency of thin crystalline Si solar cells 3.4.2.1 Overview 3.4.2.2 Simulation model 3.4.2.3 Results and Discussion 3.5 Conclusion 4. Simulation with FDTD Method 4.1 Overview 4.2 Auto-Discretization of the System Domain 4.2.1 Algorithm 4.2.2 Results of Auto-Discretization 4.3 Implementation of Lorentz Model with ADE 4.4 EffectiveMaterial Function 4.4.1 Round-Off Algorithm 4.4.2 Dispersive Conformal FDTD (D-CFDTD) Algorithm 4.4.3 Validation 4.4.4 Numerical Analysis 4.5 Simulation of Absorption Energy 4.5.1 Algorithm 4.5.1.1 Extract Object's Continuous Boundary 4.5.1.2 Memory allocation and index mapping for the boundary cells 4.5.1.3 Calculation of the absorption energy 4.5.2 Numerical Analysis 4.5.2.1 Flat system 4.5.2.2 Non-Flat system 4.6 Conclusion 5. Conclusion 5.1 Summary 5.2 Evaluation 5.3 Future Work References Appendix I 국문초록 감사의 글Docto