Fast Finite Difference Time Domain Algorithms for Solving Antenna Application Problem

This thesis describes the implementations of new parallel and sequential algorithms for electromagnetic wave propagation from a monopole antenna. Existing method, known as FDTD needs a very long processing time to solve this problem. The objective of the thesis is to develop new sequential and parallel algorithms that are faster than the standard Finite Difference Time Domain method. In this thesis, a SMP machine, the Sun Fire V1280 using six existing processors is used to solve 1D and 2D free space Maxwell equations with perfectly conducting boundary and absorbing boundary conditions. Complexity reduction approach concept is used to develop these algorithms. This approach split the solution domain into 1 3 and 2 3 compartments in 1D case and 1 9 and 8 9 compartments in 2D cases. Only 1 3 and 1 9 parts of the solution domain are solved in the main looping construct for problem in 1D and 2D, while the remaining points are solved outside the loop. The solutions to both parts are discussed in details in this thesis. These new parallel and sequential finite difference time domain (FDTD) algorithms yield from O(h2), ordinary O(h4) and weighted average O(h4) centered difference discretization using direct-domain and temporary-domain are used to solve problems mentioned above. In parallel implementation, techniques such as static scheduling, data decomposition and load balancing is used. Based on experimental results and complexity analysis, these new sequential and parallel algorithms are compared with the standard sequential and parallel FDTD algorithms, respectively. Results show that these new sequential and parallel algorithms run faster than the standard sequential and parallel FDTD algorithms. Beside that, formulation of a new higher accuracy second order method, which is called improved high speed low order finite difference time domain (IHSLO-FDTD) with direct-domain and temporary-domain are also proposed to solve the same problem are also described. Results show that, the IHSLO-FDTD with direct-domain and temporary-domain approaches are more efficient and economical. In general, almost all new proposed methods are more economical and run faster (except the Weighted Average High Speed High Order Finite Difference Time Domain (WAHSHO-FDTD) in directdomain and temporary-domain for 1D case) compared to the standard FDTD method for 1D and 2D case especially for IHSLO-FDTD

Modeling of the excited modes in inverted embedded microstrip lines using the finite-difference time-domain (FDTD) technique

This thesis investigates the presence of multiple (quasi-TEM) modes in inverted embedded microstrip lines. It has already been shown that parasitic modes do exist in inverted embedded microstrips due to field leakage inside the dielectric substrate, especially for high dielectric constants (like Silicon). This thesis expands upon that work and characterizes those modes for a variety of geometrical dimensions. Chapter 1 focuses on the theory behind the different transmission line modes, which may be present in inverted embedded microstrips. Based on the structure of the inverted embedded microstrip, the conventional microstrip mode, the quasi-conventional microstrip mode, and the stripline mode are expected. Chapter 2 discusses in detail the techniques used to decompose the total probed field into the various modes present in the inverted embedded microstrip lines. Firstly, a short explanation of the finite-difference time-domain method, that is used for the simulation and modeling of inverted microstrips up to 50 GHz is provided. Next, a flowchart of the process involved in decomposing the modes is laid out. Lastly, the challenges of this approach are also highlighted to give an appreciation of the difficulty in obtaining accurate results. Chapter 3 shows the results (dispersion diagrams, values/percentage of the individual mode energies ) obtained after running time-domain simulations for a variety of geometrical dimensions. Chapter 4 concludes the thesis by explaining the results in terms of the transmission line theory presented in Chapter 1. Next, possible future work is mentioned.M.S.Committee Chair: Tentzeris, Emmanouil; Committee Member: Andrew Peterson; Committee Member: Laskar, Joy; Committee Member: Papapolymerou, Ioanni

Benchmark of FEM, Waveguide and FDTD Algorithms for Rigorous Mask Simulation

An extremely fast time-harmonic finite element solver developed for the transmission analysis of photonic crystals was applied to mask simulation problems. The applicability was proven by examining a set of typical problems and by a benchmarking against two established methods (FDTD and a differential method) and an analytical example. The new finite element approach was up to 100 times faster than the competing approaches for moderate target accuracies, and it was the only method which allowed to reach high target accuracies.Comment: 12 pages, 8 figures (see original publication for images with a better resolution

Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.Comment: 31 pages, 20 figure

Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices

Terahertz sensing Photoresist Dependent Thickness and Length by Using Two-channel parallel-plate Waveguides

본 논문에서 Chapter 1 테라헤르츠(Terahertz : 0.1 ~ 10THz)란 무엇인지에 대하여, 다른 종류의 전파 특성과 비교하여 테라파를 서술하였다. 또한 본 논문에서 지금까지 사용되어진 대표적인 테라파 발생과 측정 방식과 원리를 설명하였다. 본 논문에서는 광전도 안테나 PCA (Photoconductive antenna) 방식을 사용하였으며, 테라파 시스템에 대한 설명을 하였다. 평행 도파로를 진행하는 전자기파에 대한 이론을 Chapter 2에 서술하였다. 특히, TE (transverse electric) mode 와 TM (transverse magnetic) mode에 대한 이론적인 분석을 통하여 평행도파로 내에서 전파하는 각각의 모드에서의 군속도 분산과 차단 주파수에 대해 서술하였다. FDTD 시뮬레이션에 대해 Chapter 3에 서술하였다. 전기장과 자기장 사이의 맥스웰 방정식을 가상의 공간에서 컴퓨터 계산에 적용하기 위하여, FDTD 시뮬레이션 조건에 대해 설명과, 알고리즘을 적용하여 1차, 2차원의 공간에서의 맥스웰 방정식을 계산 하기위한 방식에 대해 이야기 하고 2차원 공간에서는 전자기파의 대표적인 TE 모드 TM 모드로 나누어 서술하였다. Chapter 4에서는 평행 도파로를 이용한 박막 측정하였다. 처음으로, Chapter 4.1 to 4.3에서는 평행 도파로를 이용한 박막 측정 방식과 지금까지 사용되어진 테라파를 이용한 다양한 측정 방식에 대해 서술하였다. 두 번째로, Chapter 4.4.2 에서는 Chapter 3에서 공부한 FDTD 시뮬레이션을 이용하여 박막의 길이와 두께에 따른 TTS (time turning sensitivity) 와 FTS (frequency turning sensitivity)를 예측하였다. 마지막으로, Chapter 4.4.5 실험을 통하여 박막의 두께와 길이를 변화시켜 측정하고 앞의 시뮬레이션과 비교 분석하여 resonance 이동의 원인에 대한 분석을 하였다.CONTENTS Chapter 1 Introduction .............................................................. 1.1 What is Terahertz? 1.2 THz Pulse Generation and Detection 1.2.1 THz pulse Genneration 1.2.1 THz pulse Detection 1.3 Experiment result 1.4 Overview of Thesis Chapter 2 Theory ........................................... 2.1 Waveguide Theory : PPWG 2.1.1 Mode Classification 2.1.2 TE and TM Mode Chapter 3 Finite-Difference Time-Domain 3.1 what is FDTD (Finite-Difference Time-Domain)? 3.2 1D FDTD 3.3 2D FDTD 3.3.1 TE Simulation 3.3.2 TM Simulation Chapter 4 Application 1 : Thin Film sensing ...... 4.1 Wave guide : PPWG 4.1.1 many kind of Waveguide 4.1.2 History of PPWG 4.2 What is hin film 4.3 Method of thin film sensing 4.4 PPWG : Parallel-plate waveguide sensing 4.4.1 Simulation condition 4.4.2 Simulation : Thin film sensing 4.4.3 Experiment Set up & Thin film 4.4.4 Experiment : Thin film sensing 4.4.5 Analysis Chapter 5 Conclusion ...................................... 5.1 waveguide sensin

A convergent Born series for solving the inhomogeneous Helmholtz equation in arbitrarily large media

We present a fast method for numerically solving the inhomogeneous Helmholtz equation. Our iterative method is based on the Born series, which we modified to achieve convergence for scattering media of arbitrary size and scattering strength. Compared to pseudospectral time-domain simulations, our modified Born approach is two orders of magnitude faster and nine orders of magnitude more accurate in benchmark tests in 1-dimensional and 2-dimensional systems