This thesis centers on modified stencils for the Finite-Difference Time-Domain method (FDTD), or Yee scheme, when modelling curved boundaries, obstacles and holes smaller than the discretization length.  The goal is to increase the accuracy while keeping the structure of the standard method, enabling improvements to existing implementations with minimal effort. We present an extension of a previously developed technique for consistent boundary approximation in the Yee scheme.  We consider both Maxwell's equations and the acoustic equations in three dimensions, which require separate treatment, unlike in two dimensions. The stability properties of coefficient modifications are essential for practical usability.  We present an analysis of the requirements for time-stable modifications, which we use to construct a simple and effective method for boundary approximations. The method starts from a predetermined staircase discretization of the boundary, requiring no further data on the underlying geometry that is being approximated. Not only is the standard staircasing of curved boundaries a poor approximation, it is inconsistent, giving rise to errors that do not disappear in the limit of small grid lengths. We analyze the standard staircase approximation by deriving exact solutions of the difference equations, including the staircase boundary. This facilitates a detailed error analysis, showing how staircasing affects amplitude, phase, frequency and attenuation of waves. To model obstacles and holes of smaller size than the grid length, we develop a numerical subgrid method based on locally modified stencils, where a highly resolved micro problem is used to generate effective coefficients for the Yee scheme at the macro scale. The implementations and analysis of the developed methods are validated through systematic numerical tests. / <p>QC 20120530</p>

Thesis (M. Soc. Sc.)--University of Hong Kong, 1986.

Thesis (M.Soc.Sc.)--University of Hong Kong, 1986. / Also available in print.

Thesis (M. Hous. M.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 106-109).

Thesis (M.Hous.M.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 106-109). Also available in print.

Dans cette thèse, nous nous intéressons à l’amélioration du schéma de Yee pour traiter demanière plus efficace et pertinente les problèmes industriels auxquels nous sommes confrontés à l’heureactuelle. Pour cela, nous cherchons avant tout à diminuer les erreurs numériques de dispersion et àaméliorer les modélisations des géométries courbes ainsi que des réseaux de câbles. Pour répondre àces besoins, une solution basée sur un schéma Galerkin discontinu pourrait être envisagée. Toutefois,l’utilisation d’une telle technique sur la totalité du volume de calcul est relativement coûteuse. De plus,la prise en compte de structures filaires sur un tel schéma n’est pas encore opérationnelle. C’est pourquoi,dans l’optique d’avoir un outil industriel, et après une étude bibliographique, nous nous sommes plutôtorientés sur l’étude d’un schéma éléments finis (FEM) sur maillage cartésien qui possède toutes lesbonnes propriétés du schéma de Yee. Notamment, à l’ordre d’approximation spatiale égal à 0 ce schémaFEM est exactement le schéma de Yee, et, pour des ordres supérieurs, il permet de réduire fortementl’erreur de dispersion numérique de ce dernier. Dans le travail de cette thèse, pour ce schéma, nous avons notamment donné un critère de stabilité théorique, étudié sa convergence théorique et fait une analyse de l’erreur de dispersion. Pour tenircompte des possibilités d’ordre d’approximation spatiale variable par direction, nous avons mis en placeune stratégie d’affectation des ordres suivant le maillage donné. Ceci nous a permis d’obtenir un pas detemps optimal pour une précision souhaitée tout en réduisant les coûts de calcul. Après avoir porté ceschéma sur des machines de production, différents problèmes de CEM, antennes, IEM ou foudre ont ététraités afin de montrer les avantages et le potentiel de celui-ci. En conclusion de ces expérimentationsnumériques, il s’avère que la méthode est limitée par le manque de précision pour prendre en comptedes géométries courbes. Afin d’améliorer cela, nous avons proposé une hybridation entre ce schéma et leschéma GD que l’on peut étendre aux autres schémas comme les méthodes différences finies (FDTD) etvolumes finis (FVTD). Nous avons montré que la technique d’hybridation proposée conserve l’énergie etest stable sous une condition que nous avons évaluée de manière théorique. Des exemples de validationont ensuite été montrés. Enfin, pour tenir compte des réseaux de câbles, un modèle de fils minces d’ordred’approximation spatiale élevé a été proposé. Malheureusement, celui-ci ne peut pas couvrir l’ensembledes cas industriels et pour remédier à cela, nous avons proposé une hybridation de notre approche avecune équation de ligne de transmission. L’intérêt de cette hybridation a été montré sur un certain nombred’exemples, que nous n’aurions pas pu traiter par un modèle de structure filaire simple. / In this thesis, we study the improvement of the Yee’s scheme to treat efficiently and in arelevant way the industrial issues we are facing nowadays. For that, we first of all try to reduce thenumerical errors of dispersion and then to improve the modeling of the curved surfaces and of theharness networks. To answer these needs, a solution based on a Galerkin Discontinuous (GD) methodhas been first considered. However, the use of such method on the entire modeling volume is quite costly ;moreover the wires are not taken into account in this method. That is the reason why, with the objectiveof an industrial tool and after a large bibliographic research, we headed for the study of finite elementsscheme (FEM) on a Cartesian mesh which has all the good properties of the Yee’s scheme. Especially,this scheme is exactly the Yee’s scheme when the spatial order of approximation is set to zero. Forthe higher orders, this new scheme allows to greatly reduce the numerical error of dispersion. In theframe of this thesis and for this scheme, we give a theoretical criterion of stability, study its theoreticalconvergence and we perform an analysis of the error of dispersion. To take into account the possibilityof the variable spatial orders of approximation in each direction, we put in place a strategy of orderaffectation according to the given mesh. This strategy allows to obtain an optimal time step for a givenselected precision while reducing the cost of the calculations. Once this new scheme has been adaptedto large industrial computing means, different EMC, antennas, NEMP or lightning problems are treatedto demonstrate the advantages and the potential of this scheme. As a conclusion of these numericalsimulations we demonstrate that this method is limited by a lack of precision when taking into accountcurved geometries. To improve the treatment of the curved surfaces, we propose an hybridization between this scheme andthe GD scheme. This hybridization can also be applied to other methods such as Finite Differences(FDTD) or Finite Volumes (FVTD). We demonstrate that the technique of hybridization proposed,allows to conserve the energy and is stable under a condition that we study theoretically. Some examplesare presented for validation. Finally and to take into account the cables, a thin wire model with a highorder of spatial approximation is proposed. Unfortunately, this model does not allow to cover all theindustrial cases. To solve this issue we propose an hybridization with a transmission line method. Theadvantage of this hybridization is demonstrated thanks to different cases which would not have beenfeasible with a more simple thin wire method.

Defining rarity as a relative quality in matter roughly opposite to density, this dissertation focusses on the way material qualities of molecular gases, such as semi-opacity, permeation, and blending, inform modernist representations of embodied spatial experience. In modernist writing, rare matter—including air, fog, smoke, and haze—functions as an active component of the sensory environment, filling up the negative space that sets off subjects from objects, and characters from settings. Representing matter across the full range of the rarity-density spectrum allows modernist writers to challenge the ontological status of such boundaries, and to develop dynamic spatial models of the self-world threshold. The Introduction defines rare matter and examines its function as a sensory medium that can alternately define and blur subject/object boundaries. Interpreting dynamic thresholds as products of authorial activism, I argue that modernist narratives disrupt the normative constructions of the self-world boundary that prevailed in biomedical discourse around the turn of the century. Chapter 1, seeking to expand the scope of modernist object studies to include rare matter, analyzes illustrated books about London to demonstrate the increased cultural visibility of the atmosphere in the modernist period. Visual and verbal gestalt effects, modelled on the hermeneutic oscillation between looking at and looking through the fog, foreground the materiality of the atmosphere that fills up three-dimensional space, pressing up against the thresholds of the body and disrupting fixed distinctions between subjects and their surroundings. Chapter 2 shows how D. H. Lawrence harnesses the properties of rare matter to construct dynamic representations of the self-world boundary. In his early novels and his criticism, the oscillation between self-diffusion and self-differentiation expresses characters’ psychological responsiveness to changing interpersonal and ontological pressures. Chapter 3 demonstrates how Virginia Woolf takes advantage of rare attributes like permeation, fluid motion, and variable particle spacing to model process-oriented communities that incorporate dynamic shifts between social autonomy and collective identity. The Conclusion examines rare imagery in modernist scenes of narration, arguing that dynamic self-world thresholds help to articulate a responsive form of reader-text interaction that allows for the alternation of independent and collaborative reading practices.

Defining rarity as a relative quality in matter roughly opposite to density, this dissertation focusses on the way material qualities of molecular gases, such as semi-opacity, permeation, and blending, inform modernist representations of embodied spatial experience. In modernist writing, rare matter—including air, fog, smoke, and haze—functions as an active component of the sensory environment, filling up the negative space that sets off subjects from objects, and characters from settings. Representing matter across the full range of the rarity-density spectrum allows modernist writers to challenge the ontological status of such boundaries, and to develop dynamic spatial models of the self-world threshold. The Introduction defines rare matter and examines its function as a sensory medium that can alternately define and blur subject/object boundaries. Interpreting dynamic thresholds as products of authorial activism, I argue that modernist narratives disrupt the normative constructions of the self-world boundary that prevailed in biomedical discourse around the turn of the century. Chapter 1, seeking to expand the scope of modernist object studies to include rare matter, analyzes illustrated books about London to demonstrate the increased cultural visibility of the atmosphere in the modernist period. Visual and verbal gestalt effects, modelled on the hermeneutic oscillation between looking at and looking through the fog, foreground the materiality of the atmosphere that fills up three-dimensional space, pressing up against the thresholds of the body and disrupting fixed distinctions between subjects and their surroundings. Chapter 2 shows how D. H. Lawrence harnesses the properties of rare matter to construct dynamic representations of the self-world boundary. In his early novels and his criticism, the oscillation between self-diffusion and self-differentiation expresses characters’ psychological responsiveness to changing interpersonal and ontological pressures. Chapter 3 demonstrates how Virginia Woolf takes advantage of rare attributes like permeation, fluid motion, and variable particle spacing to model process-oriented communities that incorporate dynamic shifts between social autonomy and collective identity. The Conclusion examines rare imagery in modernist scenes of narration, arguing that dynamic self-world thresholds help to articulate a responsive form of reader-text interaction that allows for the alternation of independent and collaborative reading practices.

Ce mémoire étudie un échantillon de fictions historiques écrites pour les adultes ou les enfants par les auteurs contemporains chinois canadiens Paul Yee et Sky Lee. Ce mémoire soutient que dans ces œuvres de fiction, les auteurs tentent de réviser et de réécrire l'histoire, longtemps passée sous silence, des canadiens d'origine chinoise. Ces œuvres mêlent des faits historiques avec le récit de fiction dans le but de contester non seulement les nombreuses idées préconçues au sujet des canadiens d'origine chinoise retrouvées dans l'histoire canadienne, dans le folklore et dans la mythologie traditionnelle, mais aussi les nombreuses représentations stéréotypées des canadiens d'origine chinoise dans la littérature et dans l'histoire canadiennes. Ces œuvres contestent ouvertement le fait qu'une version de l'historié puisse détenir la vérité en créant de nouvelles versions de cette histoire qui transforment radicalement certains mythes et motifs concernant la construction de la nation canadienne. Ces travaux sont ainsi destinés à être considérés comme des œuvres de fiction canadiennes et pas multiculturelles. En effet, ces auteurs tentent de redéfinir leur identité culturelle et ethnique au sein du Canada en écrivant leur histoire au sein de notre histoire nationale. Au-delà d'être simplement des œuvres de fiction historique révisionniste, les deux auteurs mettent en avant le fait que l'histoire est une construction en utilisant des techniques de métafiction historiographique post-moderne, tel que l'utilisation de plusieurs narrateurs et l'incorporation de plusieurs sources, à la fois historiques et fictives, dans leur réécriture de l'histoire.