Submitted by Alex Sandro R?go (alex@ifpb.edu.br) on 2016-11-23T14:14:27Z No. of bitstreams: 1 An?lise_e_Simula??o_de_Antenas_de_Microfita_Atrav?s_do_M?todo_FDTD.pdf: 6733290 bytes, checksum: d36f54b35c59746e26d58dc9e823c7d6 (MD5) / Approved for entry into archive by Alex Sandro R?go (alex@ifpb.edu.br) on 2016-11-23T14:15:20Z (GMT) No. of bitstreams: 1 An?lise_e_Simula??o_de_Antenas_de_Microfita_Atrav?s_do_M?todo_FDTD.pdf: 6733290 bytes, checksum: d36f54b35c59746e26d58dc9e823c7d6 (MD5) / Made available in DSpace on 2016-11-23T14:15:20Z (GMT). No. of bitstreams: 1 An?lise_e_Simula??o_de_Antenas_de_Microfita_Atrav?s_do_M?todo_FDTD.pdf: 6733290 bytes, checksum: d36f54b35c59746e26d58dc9e823c7d6 (MD5) Previous issue date: 2016-11-23 / Este trabalho tem como finalidade a aplica??o do m?todo das Diferen?as Finitas no Dom?nio do Tempo - Finite Difference Time Domain ? FDTD para an?lise num?rica de antenas de microfita, atrav?s de um programa escrito em linguagem C++. A condi??o de contorno absorvedora necess?ria adotada, para converg?ncia dos resultados, foi a camada perfeitamente casada - Perfect Matched Layer ? PML, posicionada em volta do dom?nio computacional. Para os quatro modelos de antenas propostos, os resultados do par?metro S11 foram encontrados por um programa desenvolvido em linguagem Matlab e os resultados obtidos para os modelos de antenas propostos, foram validados experimentalmente pela constru??o f?sica e medi??o com o analisador de redes vetorial Agilent N5230A e com o software comercial Ansys Design.

A hp-finite element method is implemented to numerically study the modes of waveguides with two dimensional cross-section and to compute electromagnetic scattering from three dimensional objects. A method to control the chromatic dispersion properties of photonic crystal fibers using the selective hole filling technique is proposed. The method is based on a single hole-size fiber geometry, and uses an appropriate index-matching liquid to modify the effective size of the filled holes. The dependence of dispersion properties of the fiber on the design parameters such as the refractive index of the liquid, lattice constant and hole diameter are studied numerically. It is shown that very small dispersion values between 0±0.5ps/nm-km can be achieved over a bandwidth of 430-510nm in the communication wavelength region of 1300-1900nm. Three such designs are proposed with air hole diameters in the range 1.5-2.0μm. A novel multi-core fiber design strategy for obtaining a at in-phase supermode that optimizes utilization of the active medium inversion in the multiple cores is proposed. The spatially at supermode is achieved by engineering the fiber so that the total mutual coupling between neighboring active cores is equal. Different designs suitable for different fabrication processes such as stack-and-draw and drilling are proposed. An important improvement over previous methods is the design simplicity and better tolerance to perturbations. The optimal implementation of perfectly matched layer (PML) in terms of minimizing the computational overhead it introduces is studied. In one dimension it is shown that PML implementation with a single cell and a high order finite element produces minimal overhead. Estimates of optimal cell size and optimal finite element degree are given. Based on the single cell implementation of PML in three dimensions, field enhancement in metallic bowties is computed.

The presence of wave motion is the defining feature in many fields of application,such as electro-magnetics, seismics, acoustics, aerodynamics,oceanography and optics. In these fields, accurate numerical simulation of wave phenomena is important for the enhanced understanding of basic phenomenon, but also in design and development of various engineering applications. In general, numerical simulations must be confined to truncated domains, much smaller than the physical space were the wave phenomena takes place. To truncate the physical space, artificial boundaries, and corresponding boundary conditions, are introduced. There are four main classes of methods that can be used to truncate problems on unbounded or large domains: boundary integral methods, infinite element methods, non-reflecting boundary condition methods and absorbing layer methods. In this thesis, we consider different aspects of non-reflecting boundary conditions and absorbing layers. In paper I, we construct discretely non-reflecting boundary conditions for a high order centered finite difference scheme. This is done by separating the numerical solution into spurious and physical waves, using the discrete dispersion relation. In paper II-IV, we focus on the perfectly matched layer method, which is a particular absorbing layer method. An open issue is whether stable perfectly matched layers can be constructed for a general hyperbolic system. In paper II, we present a stable perfectly matched layer formulation for 2 x 2 symmetric hyperbolic systems in (2 + 1) dimensions. We also show how to choose the layer parameters as functions of the coefficient matrices to guarantee stability. In paper III, we construct a new perfectly matched layer for the simulation of elastic waves in an anisotropic media. We present theoretical and numerical results, showing that the stability properties of the present layer are better than previously suggested layers. In paper IV, we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters which is applicable to all hyperbolic systems, and which we prove is well-posed and perfectly matched. We also use an automatic method, derived in paper V, for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell s equations, the linearized Euler equations, as well as arbitrary 2 x 2 systems in (2 + 1) dimensions. In paper V, we use the method of Sturm sequences for bounding the real parts of roots of polynomials, to construct an automatic method for checking Petrowsky well-posedness of a general Cauchy problem. We prove that this method can be adapted to automatically symmetrize any well-posed problem, producing an energy estimate involving only local quantities. / QC 20100830

The finite-difference time-domain (FDTD) method has been widely and effectively used for analysis in many kinds of electromagnetic problems. Generally, the computational space can be divided into many lattices with rectangular; and the length on each of these meshs is equivalent in unitary aspect. In some of those problems, a greatly improved accuracy of the solution can be obtained if a finer discretization is used in specific regions of the computational space. There are limitations of the present form of uniform FDTD. It must increase the computational cost (memory and CPU time). Concerning the impression, we are trying to find more efficient ways of utilizing nonuniform grids. Coarser mesh for uncomplicated structure and finer mesh for complicated structure in nonuniform grids. However, this way can use in part of cutting area only. There are two edges connects the truncation of computational space. A similar scheme has been used with nonuniform FDTD method by a modification to the mesh scheme. The subcell method is a very general approach, capable of analyzing arbitrarily-shaped structures. In local area the mesh change from rectangular to irregular. Subgridding method is dissimilar to the both methods. Furthermore, the anisotropic PML to decrease the electromagnetic wave from nonuniform mesh of the computational space. It have replaced Mur¡¦s first-order absorbing boundary conditions and Berenger¡¦s PML for improving computationally efficient. Finally, compare them with the anisotropic PML in the essay.

Integrated optics present a potentially low cost and higher performance alternative to electronics in optical communication systems. Surface plasmon waveguides (SPWGs) offer a new approach for manipulating light in integrated optical chips. SPWGs provide several advantages over dielectric waveguides. In this study, a fabrication process for SPWGs is developed. SPWGs are fabricated with various lengths and bend radii to allow for study of absorption and bending losses in the waveguides at telecommunications wavelengths (~1550nm). Finite-element method models of straight, bent, and optically coupled waveguides are developed and analyzed.

Dans ce travail, une méthode basée sur les éléments finis ondulatoires - Wave Finite Elements (WFE) - est proposée en vue de prédire le rayonnement acoustique de conduites axisyrnétriques de longueur finie, comportant un fluide interne, et immergées dans un fluide acoustique de dimensions infinies. La condition de rayonnement de Sommerfeld est prise en compte en entourant le fluide extérieur d'un perfectly matched layer (PML), c'est-à-dire une couche d'éléments absorbants dans laquelle les ondes acoustiques incidentes sont progressivement amorties. Dans le cadre de l'approche WFE, la conduite, le fluide qu'elle contient, le fluide extérieur et le PML constituent un guide d'ondes multiphysique qui est discrétisé par un maillage éléments finis périodique, et peut être ainsi modélisé comme un assemblage de sous-systèmes identiques de faible longueur. Une base d'ondes se propageant le long de la conduite, calculée à partir du modèle éléments finis d'un sous-système, est utilisée afin de prédire le comportement vibroacoustique de guides d'ondes de longueur finie à moindre coût. Des simulations numériques sont réalisées pour des cas de conduites de structure homogène ou multi-couches. La précision et l'efficacité de la méthode WFE sont clairement établies en comparaison avec la méthode des éléments finis conventionnelle. / In this work, a wave finite element (WFE) method is proposed to predict the sound radiation of finite axisymmetric fluid-filled pipes immersed in an external acoustic fluid of infinite extent, The Sommerfeld radiation condition is taken into account by means of a perfectly matched layer (PML) around the external fluid. Within the WFE framework, the fluid-filled pipe, the surrounding fluid and the PML constitute a multiphysics waveguide that is discretized by means of a periodic finite element mesh, and is treated as an assembly of identical subsystems of small length. Wave modes are computed from the FE model of a multi-physics subsystem and used as a representation basis to assess the vibroacoustic behavior of the finite waveguide at a low computational cost. Numerical experiments are carried out in the cases of axisymmetric pipes of either homogeneous or multi-layered crosssections, The accuracy and efficiency of the proposed approach are dearly highlighted in comparison with the conventional FE method.

We are concerned with forward wave motion simulations in two-dimensional elastic, heterogeneous, semi-infinite media. We use Perfectly Matched Layers (PMLs) to truncate the semi-infinite extent of the physical domain to arrive at a finite computational domain. We use a recently developed hybrid formulation, where the Navier equations for the interior domain are coupled with a mixed formulation for an unsplit-field PML. Here, we implement the hybrid formulation using spectral elements, and report on its performance. The motivation stems from the following considerations: Of concern is the long-time instability that has been reported even in homogeneous and isotropic cases, when the standard complex-stretching function is used in the PML. The onset of the instability is always within the PML zone, and it manifests as error growth in time. It has been suggested that the instability arises when waves impinge at grazing angle on the PML-interior domain interface. Yet, the instability does not always appear. Furthermore, different values of the various PML parameters (mesh density, attenuation strength, order of attenuation function, etc) can either hinder or delay the onset of the instability. It is thus conjectured that the instability is associated with the spectral properties of the discrete operators. In this thesis, we report numerical results based on both Lagrange interpolants, and results based on spectral elements. Spectral elements are explored since they lead to diagonal mass matrices, have improved dispersion error, and, more importantly, have different spectral properties than Lagrangian-based finite elements. Spectral elements are thus used in an attempt to explore whether the reported instability issues could be alleviated. We design numerical experiments involving explosive sources situated at varying depths from the surface, capable of inducing grazing-angle waves. We use the energy decay as the primary metric for reporting the results of comparisons between various spectral element orders and classical Lagrange interpolants. We also report the results of parametric studies. Overall, it is shown that the spectral elements alone are not capable of removing the instability, though, on occasion, they can. Careful parameterization of the PML could also either remove it or alleviate it. The issue remains open. / text

Bending loss in silicon-on-insulator rib waveguides was calculated using conformal mapping of the curved waveguide to an equivalent straight waveguide. Finite-element analysis with perfectly matched layer boundaries was used to solve the vector wave equation. Transmission loss was experimentally measured as a function of bend radius for several SOI waveguides. Good agreement was found between simulated and measured losses, and this technique was confirmed as a good predictor for loss and for minimum bend radius for efficient design.

The investigation of the dynamics of chemical reactions, both from the theoretical and experimental side, has drawn an increasing interest since Ahmed H. Zewail was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry. On the experimental side, new techniques such as femtosecond lasers and attosecond lasers enable laser control of chemical reactions. Numerical simulations serve as a valuable complement to experimental techniques, not only for validation of experimental results, but also for simulation of processes that cannot be investigated through experiments. With increasing computer capacity, more and more physical phenomena fall within the range of what is possible to simulate. Also, the development of new, efficient numerical methods further increases the possibilities. The focus of this thesis is twofold; numerical methods for chemical reactions including dissociative states and methods that can deal with coexistence of spatial regions with very different physical properties. Dissociative chemical reactions are reactions where molecules break up into smaller components. The dissociation can occur spontaneously, e.g. by radioactive decay, or be induced by adding energy to the system, e.g. in terms of a laser field. Quantities of interest can for instance be the reaction probabilities of possible chemical reactions. This thesis discusses a boundary treatment model based on the perfectly matched layer (PML) approach to accurately describe dynamics of chemical reactions including dissociative states. The limitations of the method are investigated and errors introduced by the PML are quantified. The ability of a numerical method to adapt to different scales is important in the study of more complex chemical systems. One application of interest is long-range molecules, where the atoms are affected by chemical attractive forces that lead to fast movement in the region where they are close to each other and exhibits a relative motion of the atoms that is very slow in the long-range region. A numerical method that allows for spatial adaptivity is presented, based on the summation-by-parts-simultaneous approximation term (SBP-SAT) methodology. The accuracy and the robustness of the numerical method are investigated. / eSSENCE

The Finite Element Method (FEM) is a powerful numerical method to solve wave propagation problems for open-region electromagnetic radiation/scattering problems involving objects with arbitrary geometry and constitutive parameters. In high-frequency applications, the FEM requires an electrically large computational domain, implying a large number of unknowns, such that the numerical solution of the problem is not feasible even on state-of-the-art computers. An appealing way to solve a large FEM problem is to employ a Domain Decomposition Method (DDM) that allows the decomposition of a large problem into several coupled subproblems which can be solved independently, thus reducing considerably the memory storage requirements. In this thesis, two new domain decomposition algorithms (FB-DDM and ILF-DDM) are implemented for the finite element solution of electromagnetic radiation/scattering problems. For this purpose, a nodal FEM code (FEMS2D) employing triangular elements and a vector FEM code (FEMS3D) employing tetrahedral edge elements have been developed for 2D and 3D problems, respectively. The unbounded domain of the radiation/scattering problem, as well as the boundaries of the subdomains in the DDMs, are truncated by the Perfectly Matched Layer (PML) absorber. The PML is implemented using two new approaches: Locally-conformal PML and Multi-center PML. These approaches are based on a locally-defined complex coordinate transformation which makes possible to handle challenging PML geometries, especially with curvature discontinuities. In order to implement these PML methods, we also introduce the concept of complex space FEM using elements with complex nodal coordinates. The performances of the DDMs and the PML methods are investigated numerically in several applications.