When we want to solve electromagnetic problems, the Finite Difference Time Domain (FDTD) method is a very useful numerical simulation technique to solve these problems. However, the traditional FDTD method is an explicit finite-difference scheme, so the method is limited by the Courant-Friedrich-Levy (CFL) stability condition. In other words, the minimum cell size will limit the maximum time-step size in a computational domain. Therefore, while simulating structures of fine scale dimensions, it will relatively result in a prohibitively high computation time generated by the maximum time-step size. The WLP-FDTD is based on the Weighted Laguerre Polynomials technique and the traditional FDTD algorithm. It is an implicit finite-difference equations. Therefore, it can completely avoid the stability constraint, and then improve calculation time by choosing relatively large time-step. In this thesis, we incorporate non-uniform grid method into the WLP-FDTD. By using them to simulate the structures of fine scale dimensions can reduce the computation time and memory usage. Further, we extend this method from two-dimensional to three-dimensional and add loss media into original formulations that will make the application of this method more widely.

In the thesis, we propose a newly-developed method called the method of Connected Local Fields (CLF) to analyze opto-electromagnetic passive devices. The method of CLF somewhat resembles a hybrid between the finite difference and pseudo-spectral methods. For opto-electromagnetic passive devices, our primary concern is their steady state behavior, or narrow-band characteristics, so we use a frequency-domain method, in which the system is governed by the Helmholtz equation. The essence of CLF is to use the intrinsic general solution of the Helmholtz equation to expand the local fields on the compact stencil. The original equation can then be transformed into the discretized form called LFE-9 (in 2-D case), and the intrinsic reconstruction formulae describing each overlapping local region can be obtained. Further, we present rigorous analysis of the numerical dispersion equation of LFE-9, by means of first-order approximation, and acquire the closed-form formula of the relative numerical dispersion error. We are thereby able to grasp the tangible influences brought both by the sampling density as well as the propagation direction of plane wave on dispersion error. In our dispersion analysis, we find that the LFE-9 formulation achieves the sixth-order accuracy: the theoretical highest order for discretizing elliptic partial differential equations on a compact nine-point stencil. Additionally, the relative dispersion error of LFE-9 is less than 1%, given that sampling density greater than 2.1 points per wavelength. At this point, the sampling density is nearing that of the Nyquist-Shannon sampling limit, and therefore computational efforts can be significantly reduced.

Soil properties (shear modulus and damping) are normally determined from laboratory tests. These tests provide both values of the shear modulus in the linear elastic range for very small levels of strain, and its variation with the level of strain. It has become more common to measure the maximum shear modulus at low levels of strain directly in the field, using geophysical techniques. The values obtained in situ can differ significantly in some cases from those determined in the laboratory, and a number of reasons and correction factors have been proposed in the literature to account for this variation. As a result, when in situ properties are available, it is normal to use these values for very low levels of strain, but still assume that the variation of the ratio G/Gmax (normalized shear modulus) with shear strain is the same as determined in the laboratory. Recently, tests have been performed using large vibrators (the Thumper and Tyrannosaurus Rex of the University of Texas at Austin) to determine soil properties in situ for larger strains, and the variation of G/Gmax obtained from these tests has been compared to that reported in the literature from lab tests. Observation indicates some generally good agreement, but also some minor variations. One must take into account, however, that in the determination of the shear modulus versus strain in the field from vibration records, a number of approximations are introduced. The objective of this work is to evaluate the accuracy of some the procedures used and to assess the validity of the simplifying assumptions which are made. For this purpose, a shear cone that would reproduce correctly the horizontal stiffness of a circular mat foundation on the surface of an elastic, homogeneous half space, was considered. The cone was discretized using both a system of lumped masses and springs and a finite difference, using second-order central difference formulation, verifying that in the linear elastic range the results were accurate. A number of studies were conducted next, increasing the level of the applied force and using nonlinear springs that would reproduce a specified G/Gmax vs. γ curve. Using a similar procedure to that used in the field tests, the shear wave velocity between hypothetical receivers and the levels of strain were determined. The resulting values of G/Gmax vs. γ were then compared with the assumed curve to assess the accuracy of the estimated values.

The Finite-Difference Time Domain (FDTD) method is a very useful numerical simulation technique for solving problems related to electromagnetism. However, as the traditional FDTD method is based on an explicit finite-difference algorithm, the Courant-Friedrich-Levy(CFL) stability condition must be satisfied when this method is used. Therefore, a maximum time-step size is limited by minimum cell size in a computational domain, which means that if an object of analysis has fine scale dimensions, a small time-step size creates a significant increase in calculation time. Alternating-Direction Implicit (ADI) method is based on an implicit finite-difference algorithm. Since this method is unconditionally stable, it can improve calculation time by choosing time-step arbitrarily. The ADI-FDTD is based on an Alternating direction implicit technique and the traditional FDTD algorithm. The new method can circumvent the stability constraint. In this thesis, we incorporate Lumped Element and Equivalent Current Source method into the ADI-FDTD. By using them to simulate active or passive device, the application of method will be more widely.

The Finite-Difference Time-Domain Method (FDTD) is a very powerful numerical method for the full wave analysis electromagnetic phenomena. Due to its flexibility, it can be used to solve numerous electromagnetic scattering problems on microwave circuits, dielectrics, and electromagnetic absorption in biological tissue at microwave frequencies. However, it needs so much computation time to simulate microwave integral circuits by applying the FDTD method. If the structure we simulated is complicated and we want to obtain accurate frequency domain scattering parameters, the simulation time will be so much longer that the efficiency of simulation will be bad as well. Therefore, in the thesis, we introduce an artificial neural networks (ANN) method called ¡§Finite Impulse Response Neural Networks (FIRNN)¡¨ can speed up the FDTD simulation time. In order to boost the efficiency of the FDTD simulation time by stopping the simulation after a sufficient number of time steps and using FIRNN as a predictor to predict time series signal.

In recent years, the wireless communication operators use more and more systems based on the transmission and reception of EM waves. As a result, more and more base stations are being installed on the rooftop of existing buildings in densely populated areas. The prevailing of wireless communications has prompted the public¡¦s concern of the health issue. To date, the most prominent and scientifically verifiable biological effect of EM waves is the heating effect. In order to maintain the users¡¦ health from the over-heating due to excessive use, analysis of the temperature distribution inside the human body is also very critical as well as the SAR guidelines. The purpose of this thesis is to investigate the SAR values and temperature distribution inside the human head, under the EM exposure of mobile communication base station and handset based on the use of finite-difference time-domain (FDTD) method. In general, we assumed that the far-field exposure of base station are uniform plane-wave exposures. The total-field / scattered-field (TF/SF) formulation implements a compact uniform plane-wave source permitting FDTD simulations to accurately predict the SAR distribution in the human head due to uniform plane-wave exposures. Furthermore, this thesis investigates the effects of the rectangular frames of the metallic spectacles at 900MHz and 1.8 GHz for the uniform plane wave.

With the enormously developing of the wireless communication technology, the electromagnetic environment exposing to the electrical devices is becoming more and more complex. Besides, the trends of designing high-speed digital computer systems are toward fast edge rates, high clock frequencies, and low voltage levels. The electromagnetic susceptibility (EMS) or immunity of the high-speed circuit has become an important issue today apparently. In this thesis, we will firstly establish the measurement environment and calibration technology for numerical validation. Then we employ the three-dimension finite-differential time-domain (3D-FDTD) numerical method compared to the finite element method (FEM) to simulate the EMS behavior of the power delivery network (PDN) and traces of the printed circuit boards (PCB). In addition to several types of layout of the traces studied in this thesis, we also explain the mechanism and phenomenon of the EMS of the power/ground planes of the PCB. Besides the EMS behavior research of the traditional solutions to suppress the power noise, we propose an electromagnetic bandgap structure (EBG) which has the broadband suppression of the power noise and is validated to be effective to improve the EMS problems. Finally, we also propose a novel concept to increase the signal integrity (SI) by shielding design.

Photonic crystal fibers (PCFs) are divided into two different kinds of fibers. The first one, index-guiding PCF, guides light by total internal reflection between a solid core and a cladding region with multiple air-holes. On the other hand, the second one uses a perfectly periodic structure exhibiting a photonic band-gap (PBG) effect at the operating wavelength to guide light in a low index core-region. A compact 2D-FDTD method based on finite-difference time-domain method is formulated and is effectively applied to analysis PCFs and PBGFs. We study the propagation features of fundamental mode and the fundamental characteristics such as effective index, modal-field diameter and chromatic dispersion in index-guiding PCFs. By optimizing the air-hole diameters and the hole-to-hole spacing of index-guiding PCFs, both the dispersion and the dispersion slope can be controlled in a wide wavelength range. We also investigate the propagation features of fundamental mode and band-gap effect of PBGFs.

The Finite-Difference Time-Domain Method (FDTD) is a very powerful numerical method for the full wave analysis electromagnetic phenomena. Due to its flexibility, it can be used to solve numerous electromagnetic scattering problems on microwave circuits, dielectrics, and electromagnetic absorption in biological tissue at microwave frequencies. However, it needs so much computation time to simulate microwave integral circuits by applying the FDTD method. If the structure we simulated is complicated and we want to obtain accurate frequency domain scattering parameters, the simulation time will be so much longer that the efficiency of simulation will be bad as well. Therefore, in the thesis, we introduce an artificial neural networks (ANN) method called ¡§Infinite Impulse Response Neural Networks (IIRNN)¡¨ can speed up the FDTD simulation time. In order to boost the efficiency of the FDTD simulation time by stopping the simulation after a sufficient number of time steps and using FIRNN as a predictor to predict time series signal.

This article emphasizes on fitting GARCH option pricing model with Taiwan stock market. Duan¡¦s(1995) NGARCH option pricing model is adopted. Duan solved the European option by simulation, this article follow the method and extents to pricing American option. In general, simulation approach is not convenient to solve American options as well as European options. However, the least-squares method proposed by Longstaff and Schwartz is a simple and powerful tool, so this article tests the method. The NGARCH model has parameters, and base on loglikelihood function, we fit the model with empirical observations to obtain parameters. Then we can simulate the stock prices, once stock prices are simulated, the option value can be priced. Since the article simulates the option, there should be the antithetic approaches instead of simulation. In practice, the Black-Schoels model is the benchmark for pricing European option, so this article compares the simulated European options with Black-Scholes. For American option, this article compares the simulated American options which are priced by least-squares method with trinomial tree (finite difference method).