Orientador: Paulo Fernando de Arruda Mancera / Banca: Helenice de Oliveira Florentino Silva / Banca: Valdemir Garcia Ferreira / Resumo: Considera-se a construção de métodos compacto e não compacto de quarta ordem para resolver numericamente as equações de Navier-Stokes na formulação função corrente em uma malha uniforme. Aplica-se esses métodos de alta ordem em um canal-tipo estenose e o conjunto das equações não lineares resultantes da discretização é resolvido pelo método de Newton. Erros RMS e máximo, bem como linhas de corrente são apresentados / Abstract: This work considers the development of compact and wide fourth-order schemes for solving the Navier-Stokes equations in the streamfunction formulation on a uniform grid. These high order schemes are applied in a stenosis channel-type and the set of nonlinear equations resulting from the discretization is solved by Newton's method. The RMS and maximum errors, and also the streamlines are shown / Mestre

Em muitas simulações eletromagnéticas utilizando o método FDTD, é desejado que os campos radiados pelas estruturas em análise sejam transmitidos para fora do domínio computacional. Infelizmente isto não é possível de ser realizado através do método FDTD em sua forma original. Para resolver este problema, deve-se implementar, nas superfícies limítrofes dos domínios computacionais, condições especiais denominadas na literatura técnica de Condições de Fronteiras de Absorção, ou, em inglês, \"Absorbing Boundary Conditions\" (ABC´s). Essas Condições de Fronteiras de Absorção impedem que os campos radiados sejam refletidos nas superfícies limítrofes dos domínios computacionais, retornando para o interior do domínio e interferindo no resultado final das simulações. Não existe uma técnica de absorção ideal, ou seja, que elimine totalmente a reflexão. As técnicas atualmente existentes possuem vantagens e desvantagens, podendo ser mais ou menos eficientes, o que faz com que esse tema ainda seja motivo de extensivos estudos. O objetivo deste trabalho consiste no estudo, implementação e comparação de Condições de Fronteiras de Absorção e na indicação de uma possível melhoria nessa área. São realizadas simulações em domínios bidimensionais e tridimensionais para se determinar vantagens e desvantagens de cada técnica de absorção. A análise dos resultados das simulações está focalizada no grau de atenuação que as ABCs possuem e na carga computacional despendidas por elas. Este trabalho é concluído com simulações empregando as condições de fronteiras analisadas para três estruturas clássicas. As vantagens e desvantagens de cada ABC são apresentadas e uma melhoria proposta na técnica de Auto Teleportação de Campos, ou, em inglês, \"Self Teleportation of Fields\" é validada. As estruturas analisadas são uma microlinha de transmissão, um filtro planar e um cilindro metálico iluminado por uma onda plana uniforme. / In many electromagnetic computational simulations using the FDTD method, it is desired that the electromagnetic fields radiated by the structures under analysis can be transmitted outwards the computational domain. Unfortunately, this is impossible to be done by the FDTD method in its original form. To mitigate this problem, one must apply special conditions to the computational domain boundaries, known in the technical literature as Absorbing Boundary Conditions (ABCs) These Absorbing Boundaries Conditions prevent the radiated fields to be reflected by boundaries back into the computational domain. Without them, these fields would interfere with the final simulation results. However, there is no ideal technique that completely eliminates the reflections. The existing techniques have advantages and disadvantages, which make them more or less efficient, still making this subject a theme of extensive studies. This work is aimed at studying, implementing and comparing these Absorbing Boundary Conditions and at indicating a possible improvement in this field. Simulations in bi-dimensional and three-dimensional domains were made to evaluate advantages and disadvantages of each absorption technique. The analysis of the simulation results was focused in the attenuation degree of the ABCs and their computational burden. The work is concluded with simulations using the analyzed ABCs for three classic structures. The advantages and disadvantages of each ABC are presented and a proposed improvement on the \"Self Teleportation of Fields\" technique is validated. The analyzed structures are a microstrip line, a planar filter and a metallic cylinder illuminated by a uniform plane wave.

An alternative pressure-sensor based method for estimating the acoustic intensity, the phase and amplitude gradient estimation (PAGE) method, is presented. This method is similar to the finite-difference p-p (FD) method, in which the intensity is estimated from pressure measurements made using an array of closely spaced microphones. The PAGE method uses the same hardware as the FD method, but does not suffer from the frequency-dependent bias inherent to the FD method. Detailed derivations of the new method and the traditional FD method are presented. Both methods are then compared using two acoustic fields: a plane wave and a three monopole system. The ability to unwrap the phase component of the PAGE method is discussed, which leads to accurate intensity estimates above previous frequency limits. The uncertainties associated with both methods of estimation are presented. It is shown that the PAGE method provides more accurate intensity estimates over a larger frequency bandwidth. The possibility of using a higher-order least-squares estimation with both methods is briefly demonstrated. A laboratory experiment designed to validate the PAGE method was conducted. The preliminary results from this experiment are presented and compared to analytical predictions. Finally, the application of the PAGE method to a static rocket test firing is presented. The PAGE method is shown to provide accurate intensity estimates at frequencies that are higher than possible with just the FD method.

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.

<p>In this thesis we consider two models for the computation of option prices. The first one is a generalization of the Black-Scholes model. In this generalization the volatility Sigma is not a constant. In the simplest case it changes at once at a certain time moment Tau. In some sense this is the conditionally Levy model. For this generalized Black-Scholes model have been theoretically obtained formulas for vanilla Call/Put option prices. Under the assumption of a good prediction of the parameter Sigma the obtained numerical results fit the real dara better than standard Black-Scholes model.</p><p>Second model is an exponential Levy model, where a Levy process is the CGMY process. We use the finite-difference scheme for computations of option prices. As example we consider vanilla Call/Put, Double-Barrier and Up-and-out options. After the estimation of the parameters of the CGMY process by the method of moments we obtain options prices and calculate fitting error. This fitting error for the CGMY model is smaller than for the Black-Scholes model.</p>

In this thesis we consider two models for the computation of option prices. The first one is a generalization of the Black-Scholes model. In this generalization the volatility Sigma is not a constant. In the simplest case it changes at once at a certain time moment Tau. In some sense this is the conditionally Levy model. For this generalized Black-Scholes model have been theoretically obtained formulas for vanilla Call/Put option prices. Under the assumption of a good prediction of the parameter Sigma the obtained numerical results fit the real dara better than standard Black-Scholes model. Second model is an exponential Levy model, where a Levy process is the CGMY process. We use the finite-difference scheme for computations of option prices. As example we consider vanilla Call/Put, Double-Barrier and Up-and-out options. After the estimation of the parameters of the CGMY process by the method of moments we obtain options prices and calculate fitting error. This fitting error for the CGMY model is smaller than for the Black-Scholes model.

<p>We prove maximum norm regularity properties of L-stable finite difference</p><p>methods for linear-second order parabolic equations with coefficients</p><p>independent of time, valid for large time steps. These results are almost</p><p>sharp; the regularity property for first differences of the numerical solution</p><p>is of the same form as that of the continuous problem, and the regularity</p><p>property for second differences is the same as the continuous problem except for</p><p>logarithmic factors. </p><p>This generalizes a result proved by Beale valid for the constant-coefficient</p><p>diffusion equation, and is in the spirit of work by Aronson, Widlund and</p><p>Thome&eacute.</p><p>To prove maximum norm regularity properties for the homogeneous problem, </p><p> we introduce a semi-discrete problem (discrete in space, continuous in time).</p><p>We estimate the semi-discrete evolution operator and its spatial differences on</p><p>a sector of the complex plan by constructing a fundamental solution.</p><p>The semi-discrete fundamental solution is obtained from the fundamental solution to the frozen coefficient problem by adding a correction term found through an iterative process.</p><p>From the bounds obtained on the evolution operator and its spatial differences,</p><p>we find bounds</p><p>on the resolvent of the discrete elliptic operator and its differences through</p><p>the Laplace transform</p><p>representation of the resolvent. Using the resolvent estimates and the</p><p>assumed stability properties of the time-stepping method in the Cauchy integral</p><p>representation of the fully discrete solution operator</p><p>yields the homogeneous regularity result.</p><p>Maximum norm regularity results for the inhomogeneous</p><p>problem follow from the homogeneous results using Duhamel's principle. The results for the inhomogeneous</p><p>problem</p><p>imply that when the time step is taken proportional to the grid width, the rate of convergence of the numerical solution and its first</p><p>differences is second-order in space, and the rate of convergence for second</p><p>differences</p><p>is second-order except for logarithmic factors .</p><p>As an application of the theory, we prove almost sharp maximum norm resolvent estimates for divergence</p><p>form elliptic operators on spatially periodic grid functions. Such operators are invertible, with inverses and their first differences bounded in maximum norm, uniformly in the grid width. Second differences of the inverse operator are bounded except for logarithmic factors.</p> / Dissertation

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.