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

The application of the finite-difference time-domain (FDTD) method for the numerical analysis of complex electromagnetic problems related to wireless communications is considered. Since exact solutions to many complex electromagnetic problems are difficult, if not impossible, the FDTD method is well suited to modelling a wide range of electromagnetic problems. Structures considered include single and twin-slot antennas for millimetre-wave applications, monopole antennas on mobile handsets and chokes for the suppression of currents on coaxial cables. Memory efficient techniques were implemented for the split-field perfectly matched layer (PML) absorbing boundary condition. The frequency-domain far-field transformations were used for the calculation of far-field radiation patterns. Dipole, slot and mobile handset antenna benchmark problems verified the accuracy of the FDTD implementation. The application of slot antennas for millimetre-wave imaging arrays was investigated. An optimal feed network for an offset-fed single-slot antenna was designed for the X band with numerical and experimental results in excellent agreement. A twin-slot antenna structure reduced surface wave coupling by 7.6 dB in the substrate between coplanar waveguide-fed slot antenna elements in a planar array. The reduction of substrate surface waves for the twin-slot antenna allows for closer element spacings with less radiation pattern degradation in array applications. Suppression techniques for currents flowing on the exterior surface of coaxial cables were investigated. These include the use of ferrite beads and a quarter-wave sleeve balun. The frequency dependent behaviour of ferrite based chokes showed highly resonant effects which resulted in less than 5 dB of isolation at the resonant frequencies of the bead. An analysis of air-gaps between the ferrite bead and cable are shown to be extremely detrimental in the isolation characteristics of ferrite bead chokes. An air-gap of 0.5 mm can reduce the isolation effectiveness of a bead by 20 dB. The first rigorous analysis of a quarter-wave sleeve balun is presented, enabling an optimal choke design for maximum isolation. A standard 0.25[symbols] sleeve balun achieved 10.9 dB isolation with [symbols]=4, whereas a choke of optimal length 0.232[symbols] had an isolation of better than -20 dB. Several techniques for the measurement of antenna characteristics of battery powered handsets were compared and perturbation effects associated with the direct connection of a coaxial cable to a mobile handset was quantified. Significant perturbation in both return loss and radiation pattern can occur depending on cable location on the handset chassis. The effectiveness of ferrite chokes in any location was marginal. However, the application of an optimal quarter-wave sleeve balun in the centre of the largest plane of the handset, orthogonal to the primary polarisation resulted in minimal perturbation of both radiation patterns and return loss.

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

A numerical scheme to simulate time-domain motion responses of multibody floating systems has been successfully proposed. This scheme is integrated into a time-domain simulation tool, with fully coupled hydrodynamic coefficients obtained from the hydrodynamic software - WAMIT which solves the Boundary Value Problem (BVP). The equations of motion are transformed into standard state-space format, using the constant coefficient approximation and the impulse response function method. Thus the Ordinary Differential Equation (ODE) solvers in MATLAB can be directly employed. The time-domain responses of a single spar at sea are initially obtained. The optimal Linear Quadratic Regulator (LQR) controller is further applied to this single spar, by assuming that the Dynamic Positioning (DP) system can provide the optimized thruster forces. Various factors that affect the controlling efficiency, e.g., the time steps ∆τ and ∆t, the weighting factors(Q,R), are further investigated in detail. Next, a two-body floating system is studied. The response amplitude operators (RAOs) of each body are calculated and compared with the single body case. Then the effects of the body-to-body interaction coefficients on the time-domain responses are further investigated. Moreover, the mean drift force is incorporated in the DP system to further mitigate the motion responses of each body. Finally, this tool is extended to a three-body floating system, with the relative motions between them derived.

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

We introduce supplemental methods for the finite-difference time-domain (FDTD) analysis of planar multilayered media. The invariance is allowed to be disturbed by any imperfection, provided that these imperfections are local and therefore can be contained within an FDTD simulation grid. We specifically investigate two FDTD methods that were not previously developed for general multilayered media: the near-field-to-far-field transform (NFFFT) and the total-field/scattered-field (TF/SF) boundary (or the plane-wave injector). The NFFFT uses the FDTD output on a virtual surface surrounding the local imperfections and calculates the radiated field. The plane wave injector builds an incident plane wave inside a certain boundary (TF/SF boundary) while allowing any scattered fields created by the imperfections inside the boundary to exit the boundary with complete transparency. The NFFFT is applicable for any lossless multilayered medium, while the plane-wave injector is applicable for any lossy multilayered medium. After developing the respective theories and giving simple examples, we apply the NFFFT and the plane-wave injector to a series of problems. These problems are divided into two main groups. In the first group, we consider plane-wave scattering problems involving perfectly-conducting objects buried in multilayered media. In the second group, we consider problems that involve radiating structures in multilayered media. Specifically, we investigate the reciprocity of antennas radiating in the presence of an ungrounded dielectric slab using the methods developed in this study. Finally, we present our previous work on an entirely different subject, namely, the theoretical analysis of the input admittance of a prolate-spheroidal monopole fed by a coaxial line through a ground plane.

Dielectric resonator antennas(DRAs) offer some attractive characteristics over conventional microstrip antennas, such as small size, low profile, light weight, ease of excitation, and high radiation efficiency at higher frequency bands. Since DRAs attract more and more attention, theoretical analysis have been insufficient to simulate various configurations of dielectric resonator antennas. Therefore some researchers introduce numerical methods to analyze DRAs, such as Finite Difference Time Domain (FDTD) method, Method of Moment (MoM), Finite Element Method (FEM). In this author, we apply two kinds of methods, including FDTD and MoM, to analysis DRA and compare the results applied these two methods. Then we simulate various configurations of dielectric resonator antennas using FDTD method. About designing the DRA construction, in this author we applied an equivalent approach to solve approximate dimensions of DRAs, and then we obtain accurate dimensions using FDTD method. In this author¡Aa DRA work at 5.8GHz have been proposed, then we using a L-shaped patch to increase impedance bandwidth. Above all, we hope to built a fast and accurate procedure to solve the resonant frequency, bandwidth, and far field pattern of DRAs. And to supply the engineer to reduce time consume in design DRAs.

In recent years, the rapid development of wireless communications has resulted in much better quality of life due to easiness and multitudes in communications. The most representative products are the mobile phones. The product is so popular that in developed countries nearly everyone owns a mobile phone; that applies not only to adults, but also young students. In view of this wide spreading phenomenon, the mobile phone industry has inescapable health related responsibilities for its users, especially for the younger ones. While enjoying the great convenience of the product, the users are advised to understand the possible health related effects caused by electromagnetic radiation. One of the very important considerations is Specific Absorption Rate (SAR), in which absorption of electromagnetic energy by a medium (for example, a human head) is measured. Before a mobile phone is brought into the market, it is important to understand how the SAR values can be affected by the metallic accessories around the human head. This thesis uses software package, SEMCAD, to analyze the metallic accessories on the human head which might influence the SAR value. We would discuss in this thesis three object, eyeglasses, earrings and rings which could affect the maximum SAR value in the human head. For eyeglasses and earring, we would suggest why these metallic accessories at different position could cause different SAR value to suggest people which gesture should be avoided while using the cell phone. For ring, this thesis would use the shape of the ring and place it at special position to decrease the maximum SAR value in the human head to reduce the possible harm from the electromagnetic radiation of mobile phone and ensure the safety while using a cell phone.

Genetic algorithms (GAs) are global optimization methods that can be applied to almost all problems, requiring only proper fitness function to evaluate. However, one problem of general GA is slow convergence. An improved GA is presented to speed up the efficiency of searching for global optimum in this author. The concept of this proposed method uses a few cost to obtain better individuals in initial population, and the evolution of GA is divided into two-stage with the concept of the genetic evolution process, which uses to improve efficiency. An improved GA with finite-difference time-domain (FDTD) will be applied to optimize mushroom-type EBG structures, which can obtain a wide range stop-band by adjusting the position of via with different patch size cascaded without changing via size, then the simulation and measurement results are also compared. In addition, the novel steps will be presented to design broadband mushroom-type EBG structures with smaller size systematically.

The Finite-Difference Time-Domain method ( FDTD ) is a numerical method introduced by K. S. Yee in 1966. However , it needs so much time to simulate circuits by applying the FDTD method and some extensional methods for simulating circuits are still incomplete . Therefore, the author combine the FDTD method with the data extrapolation method to improve the simulation effect. When applying the FDTD method to simulate circuits, it needs a large number of time steps; furthermore, if the structure we simulated is complicated, the simulation time will be so much longer that the efficiency of simulation will be bad as well. The author decrease the number of time steps of the FDTD method, and then extrapolate the time-domain data to reconstruct the complete frequency response, therefore, we can save the simulation time as well because the number of the time steps of the FDTD method decreased. Furthermore, in the thesis, we also introduce a new FDTD method combined with the S-parameter Matrix, called ¡§S-parameter Matrix method¡¨. People can simulate circuits without deriving the equivalent circuit by applying the S-parameter Matrix method. One only have to obtain the S-parameter Matrix by measurement, data sheet, calculation, etc, and then we translate it to time domain data by the IFT technique to apply the FDTD calculation , this way, we avoid the difficulty of deriving the equivalent circuit of general microwave circuits. However, the S-parameter data we can obtain are often limited in a finite bandwidth, we make it to be extrapolated to obtain the complete time-domain response, and this way, the S-parameter Matrix method can by apply to simulate circuits.