The Finite-Difference Time-Domain (FDTD) method has been used extensively in electromagnetic field modeling because of its ability to robustly handle interactions of fields with complex heterogeneous structures. In particular, the total/scattered field formulation has allowed for efficient implementation of arbitrarily directed uniform plane waves, consequently facilitating efficient modeling of far-field scattering problems. The total/scattered approach is not restricted to plane waves and can be expanded to any waveforms that can be described in analytical or semi-analytical form. While existing formulations of FDTD have been immensely successful, they are not well suited to problems that involve near field scattering/interaction problems, where both the source and object are in the same domain but at a substantial distance from each other. This is due to the exceedingly high demands for computational resources that may result from the domain size, and/or dramatically different requirements for the mesh density in the source and object areas. One solution to this problem is to separate the domain into source and scatterer regions coupled by surface boundary radiation conditions. However, this method can incur large storage requirements for calculation of the radiation conditions. A specific near-field situation of interest to the utility industry is the case of workers near high voltage powerlines. In this instance, the field pattern takes on a cylindrical, transverse electromagnetic character. More general radiating sources can be accurately represented in the near-field by using spherical wave expansions, which are often used to represent antennas measured on test ranges. Successful implementation of these analytic solutions is feasible within the FDTD framework, and would allow for the illumination of the scatterer modeled at a considerably lower cost than in the standard approach. This thesis presents a method where these non-uniform, near-field, sources can be implemented implicitly as source conditions in an existing FDTD method. The specific case of powerline fields is described first, followed by the more general case of spherical waves. The analytic solution for powerline fields is implemented to show that near-field source configuration can be successfully modeled implicitly with accurate and efficient results. The method is validated by comparing with known analytic solutions, with very good accuracy being achieved. Then, a specific example of a human under a powerline close by is modeled to examine predictions made earlier under the assumption of a plane wave source condition. For a similar powerline source configuration, results of organ dosimetry predict that induced fields are from ten to sixty percent greater than predicted with the plane wave source. This same approach is applied to model a more general and difficult problem, namely spherical waves as sources in the total/scattered FDTD, called the SW-FDTD. Since transverse properties of spherical modes are known, the behavior of a mode can be represented on a one-dimensional radial grid. Thus, much like the plane wave sources in the FDTD method, the spherical wave modes are time-stepped on one-dimensional staggered electric/magnetic field source grids in the radial direction, representing mode propagation in free space. Spherical wave modes can then be interpolated and summed on the Huygens’ surface to represent the total field of the source, thus providing the coupling between the complex source and a scatterer using one-dimensional grids. It is assumed that the object of interest is beyond the reactive near-field of the source, and therefore there is no significant coupling between source and object. The SW-FDTD method is validated by comparing simulations with several analytic solutions that increase in complexity, demonstrating very good accuracy. Issues relating to the numerical implementation are discussed, including the effects of numerical dispersion, stability, and simple Mur first order boundary conditions. Incorporation of the method as a source condition in an existing FDTD program, and validation of this synthesis, show that the SW-FDTD method can implictly model sources as accurately as explicit models do. The efficiency, and the reduction of errors remain issues for further research to improve the overall utility of the SW-FDTD method. / Graduate

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Recent progress in laser and semiconductor technology has allowed for far easier generation and measuring of coherent terahertz radiation, a previously difficult region in the radiation spectrum to coherently generate. Time based terahertz spectroscopy is a rather unique form of spectroscopy. Not only is it time based, but the electric field is measured instead of the intensity. This allows for the measurement of the complex refractive index. From this one can obtain certain details of the structure and environment of the sample being studied. A terahertz time-domain spectroscopy setup was constructed during this project. This setup used low temperature grown GaAs photoconductive antennae, with multiple antenna size options available for both the receiving and transmitting antennae. After the construction and alignment of this setup, the antennae were characterized. Lastly measurements were performed on the background, sugar and silicon to demonstrate the capabilities of the system. It was found that the measured terahertz electric field amplitude increased with the intensity of the pump pulse and that the amplitude of the measured terahertz electric field was dependent on the polarization of the pump pulse. As the size of the antenna was increased so too did the amplitude of the measured electric field and conversely the bandwidth of the measured terahertz electric field decreased with the increase of antenna size. This held true for both the transmitting and receiving antennae. / AFRIKAANSE OPSOMMING: Danksê onlangse tegnologiese onwikkelings in lasers en halfgeleier het dit veel makliker geraak om terahertz straling te genereer wat fase samehangendheid toon. Voor hierdie ontwikkelings was straling in hierdie spektrale gebied moeilik om te genereer op ’n wyse wat fase samehangendheid toon. Tyd verwante terahertz spektroskopie is taamlik uniek, aangesien die metings in tyd geneem word en die elektriese veld amplitude word pleks van die intensiteit gemeet. Een van die voordele van hierdie metode is dat dit toelaat vir die meeting van die komplekse brekingsindeks van monsters. Dit is moontlik om van die komplekse brekingsindeks strukturele en omgewings eienskappe van die monster af te lei. Gedurende die projek was ’n tyd verwante terahertz spektroskopie sisteem gebou wat gebaseer was op lae temperatuur gegroeide GaAs foto-geleidende antennas. Die sisteem bevat vier antennas van verskillende groottes aan beide die sender en ontvanger kant. Die antennas was gekarakteriseer na die bou en belyning van die terahertz sisteem en meetings was gedoen op die agtergrond, suiker en silikon om die sisteem se vermoë te demonstreer. Dit was gevind dat die amplitude van die gemete terahertz elektriese veld groter geraak het soos die intensiteit van die pomp puls verhoog was en dat die die amplitude van die gemete terahertz electriese veld afhanklik was van die polarisasie van die pomp puls. Die amplitude van van die gemete terahertz elektriese veld het gegroei met die grootte van die antenna, maar hoe groter die antenna geraak het, hoe kleiner was die bandwydte van die gemete terahertz elektriese veld. Hierdie was die geval vir beide die sender en ontvanger antennas.

The present paper introduces one very efficient and flexible time-domain analysis technique to predict the kinds of reflections and crosstalk. Numerical results show that this technique is indeed efficient and accurate in the transient analysis of a general multiple line system. Furthermore, this algorithm can be eventually coded in a form of a subroutine compatible with any standard CAD program, such as SPICE.

by Ronald Siu-kwong, Ip. / "June 1999." / Thesis (Ph.D.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (p. 89-94). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

在本文中，我們為了三維空間的馬克士威方程組(Maxwell’s equation)制定和分析了一套新種類的交錯間斷伽遼金(discontinuous Galerkin)方法，同時考慮了時間依賴性和時間諧波的馬克士威方程組。我們用了空間離散上交錯笛卡兒網格，這種方法具有許多良好的性質。首先，我們的方法所得出的數值解保留了電磁能量，並自動符合了高斯定律的離散版本。第二，質量矩陣是對角矩陣，從而時間推進是顯式和非常有效的。第三，我們的方法是高階準確，最佳收斂性在這裏會被嚴格地證明。第四，基於笛卡兒網格，它也很容易被執行，並可視為是典型的Yee’s Scheme的以及四邊形的邊有限元的推廣。最後，超收斂結果也會在這裏被證明。 / 在本文中，我們還提供了幾個數值結果驗證了理論的陳述。我們計算了時間依賴性和時間諧波的馬克士威方程組數值收斂結果。此外，我們計算時間諧波馬克士威方程組特徵值問題的數值特徵值，並與理論特徵值比較結果。最後，完美匹配層(Perfect Matching Layer)吸收邊界的問題也有實行其數值結果。 / We develop and analyze a new type of staggered discontinuous Galerkin methods for the three dimensional Maxwell’s equations in this paper. Both time-dependent and time-harmonic Maxwell’s equations are considered. The spatial discretization is based on staggered Cartesian grids which possess many good properties. First of all, our method has the advantages that the numerical solution preserves the electromagnetic energy and automatically fulfills a discrete version of the Gauss law. Second, the mass matrices are diagonal, thus time marching is explicit and is very efficient. Third, our method is high order accurate and the optimal order of convergence is rigorously proved. Fourth, it is also very easy to implement due to its Cartesian structure and can be regarded as a generalization of the classical Yee’s scheme as well as the quadrilateral edge finite elements. Lastly, a superconvergence result, that is the convergence rate is one order higher at interpolation nodes, is proved. / In this paper, we also provide several numerical results to verify the theoretical statements. We compute the numerical convergence order using L2-norm and discrete-norm respectively for both the time-dependent and time-harmonic Maxwell’s equations. Also, we compute the numerical eigenvalues for the time-harmonic eigenvalue problem and compare the result with the theoretical eigenvalues. Lastly, applications to problems in unbounded domains with the use of PML are also presented. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Yu, Tang Fei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 46-49). / Abstracts also in Chinese. / Chapter 1 --- Introduction and Model Problems --- p.1 / Chapter 2 --- Staggered DG Spaces --- p.4 / Chapter 2.1 --- Review on Gauss-Radau and Gaussisan points --- p.5 / Chapter 2.2 --- Basis functions --- p.6 / Chapter 2.3 --- Finite Elements space --- p.7 / Chapter 3 --- Method derivation --- p.14 / Chapter 3.1 --- Method --- p.14 / Chapter 3.2 --- Time discretization --- p.17 / Chapter 4 --- Energy conservation and Discrete Gauss law --- p.19 / Chapter 4.1 --- Energy conservation --- p.19 / Chapter 4.2 --- Discrete Gauss law --- p.22 / Chapter 5 --- Error analysis --- p.24 / Chapter 6 --- Numerical examples --- p.29 / Chapter 6.1 --- Convergence tests --- p.30 / Chapter 6.2 --- Diffraction by a perfectly conducting object --- p.30 / Chapter 6.3 --- Perfectly matched layers --- p.37 / Chapter 7 --- Time Harmonic Maxwell’s equations --- p.40 / Chapter 7.1 --- Model Problems --- p.40 / Chapter 7.2 --- Numerical examples --- p.40 / Chapter 7.2.1 --- Convergence tests --- p.41 / Chapter 7.2.2 --- Eigenvalues tests --- p.41 / Chapter 8 --- Conclusion --- p.45 / Bibliography --- p.46

Thesis (M.S.)--Brigham Young University. Dept. of Mechanical Engineering, 2005. / Includes bibliographical references (p. 85-88).

A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the electric and magnetic field components on these hypersurfaces. A discretization scheme is developed to solve for the unknown field components at each time step. The method retains many of the good features of the original method of characteristics for hyperbolic systems in two independent variables, such as optimal time step, good behavior near data discontinuities and the ability to treat general boundary conditions. The method is exemplified by calculating the time domain response of a few typical planar interconnect structures to Gaussian and unit step excitations. Although the general emphasis is on interconnect problems, the method is applicable to a number of other transient electromagnetic field problems governed by Maxwell's equations. In addition to the method of characteristics a finite difference scheme, known in mathematic circles as the modified Richtmyer scheme, is applied to the time domain solution of Maxwell's equations. Both methods should be useful for efficient full wave analysis of three dimensional electromagnetic field problems. / Graduation date: 1994

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