<p> Ten different reduced models, of a particular test system are selected. Two cost functions are selected and the test system minimum cost is found for each. The model optimal controls are found for each cost function and are used to provide sub-optimal control of the system using two different methods. The system cost is calculated for each case and compared to the minimum attainable. The reduction methods are compared with a view to application for the near-optimal control of a linear system.</p> / Thesis / Master of Engineering (MEngr)

<p> The main focus of this paper is to investigate retail found in designated industrial districts within the City of Mississauga. Specifically, it will concentrate on the high order goods retailing or retail warehousing, its location and the planning policies that seek, in theory, to control its development. This is a new trend in retailing that should be investigated in more detail.</p> / Thesis / Candidate in Philosophy

<p> Three existing techniques are selected as the most promising methods of system reduction. These methods are analysed and then applied to a realistic high order system. A second order model of the actual system is derived using each of the reduction techniques. The step response of the actual system and each of the models is obtained for comparison purposes. The reduction methods are compared with a view to application, limitations and accuracy. A new method for system reduction is also proposed which fashions a low order model after the response characteristics of the actual system. </p> / Thesis / Master of Engineering (MEngr)

We study noise from wind turbines while taking irregular terrain and non-constant atmosphere into consideration. We will show that simulating the distribution of 3D acoustic waves can be done by using only low frequencies, thus reducing the computational complexity significantly.

A new high order theory, referred to as the Extended High-Order Sandwich Panel Theory (EHSAPT), was formulated for orthotropic sandwich beams/wide panels with a general layout. This new theory accounts for the axial, transverse normal, and shear rigidity of the core. Validation of the present theory was performed for several structural analysis problems including: static loading, static instability (global buckling and wrinkling), free vibrations (natural frequencies), and dynamic loading (blast and impact). The accuracy of the theory was assessed by comparison with elasticity solutions and with experiment. It is shown that this new theory has superior accuracy over other available computational models, especially for sandwich beams/wide panel configurations with stiffer cores.

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Les axes de recherche et les analyses faites dans cette thèse portent sur les méthodes d'ordre élevé en éléments finis appliquées dans le cadre de la résolution des équations de Navier-Stokes et de modèles de turbulence. Elle se décompose en deux thématiques principales: -La mise en oeuvre de méthodes d'ordre élevé dans un code de calcul industriel -L'élaboration d'une méthodologie de création de maillages courbes sur des géométries 3D Une série de cas tests de difficulté croissante a été menée afin de valider ces méthodes. On présente, notamment, un cas complet d'avion où la démarche complète d'obtention du maillage ainsi que le calcul Navier-Stokes et modèle de turbulence sont détaillés et commentés. La motivation, l'apport et les obstacles techniques sont enfin discutés. / The areas of research and analysis covered ​​in this thesis focus on methods using high order finite elements applied for solving Navier-Stokes equations and turbulence models. It consists of two main parts:-The implementation of high-order methods in an industrial computer code -The development of a methodology for creating curved meshes on 3D geometries A series of test cases of increasing difficulty were conducted to validate these methods. We present, moreover, a case of a full aircraft where the process used to obtain the full mesh and the Navier-Stokes/turbulence model calculation are fully described and discussed. Motivation, contribution and technical barriers are finally discussed.

The transient time-domain simulation, of the circuit response, is a fundamental component in the Computer-Aided Design tools of all integrated circuit and systems. It is typically desirable that a method adopted in the transient circuit simulator be of high- order and numerically stable. The two requirements, however, proved to be in conflict with each other, especially in the larger class of methods that were used in traditional circuit simulators. Recent work based on utilizing the Obreshkov formula has proved that it is possible to combine the high order with the numerical stability. The objective of this thesis is to show how the present implementation of the Obreshkov- based method can be improved and generalized to handle different types of circuits. The first aspect of improvement targets the computation of the high-order derivatives re- quired by the Obreshkov formula. The second aspect of improvement, presented in the thesis, develops a generalized formulation that takes into account the presence of non- linear memory elements, whose nonlinearity is based on a capacitive or inductive-based nonlinear model.

In this thesis we investigate the accuracy of high-order Extended Finite Element Methods (XFEMs) for the solution of discontinuous problems, with a view to computing high-order solutions to a two-phase flow problem. We start by demonstrating optimal exponential rates of convergence for a spectral/hp element method applied to a smooth problem. We then consider an immersed method on a fixed background mesh that uses level sets to capture the location of a discontinuity and the XFEM to characterise this discontinuity on element interiors. We present an improvement to the modified XFEM of [Moes et. al., 2003] and then use it to solve both a Poisson problem and a linear elasticity problem with discontinuities modelled independently of the mesh. Very close to optimal rates of convergence are recovered for the Poisson problem with both straight and quadratically curved interfaces for approximations up to order p=4. These rates are better than those published in the literature for the XFEM with a curved weak discontinuity, and they are also the first optimally convergent results achieved using the modified XFEM for any problem with approximations of order p>1. Almost optimal rates of convergence are then also recovered for an elastic problem with a circular discontinuity for approximations up to order p=4.The use of the XFEM for time-dependent problems is investigated, and a novel level set update method that retains the signed distance property without need for reinitialisation is also presented. Finally we apply these methods to the time-dependent simulation of a two-phase flow problem. We validate the method against both an analytic dispersion relation for relaxation under small interface perturbations and an existing implementation for large interface perturbations. We then present a proof-of-concept implementation of a high-order immersed method for an oscillating tank flow problem and demonstrate the ability of our implementation to simulate problems with large amplitude interface deformations.

A new implicit and compact optimization-based method is presented for high order derivative calculation for finite-volume numerical method on unstructured meshes. Highorder approaches to gradient calculation are often based on variants of the Least-Squares (L-S) method, an explicit method that requires a stencil large enough to accommodate the necessary variable information to calculate the derivatives. The new scheme proposed here is applicable for an arbitrary order of accuracy (demonstrated here up to 3rd order), and uses just the first level of face neighbors to compute all derivatives, thus reducing stencil size and avoiding stiffness in the calculation matrix. Preliminary results for a static variable field example and solution of a simple scalar transport (advection) equation show that the proposed method is able to deliver numerical accuracy equivalent to (or better than) the nominal order of accuracy for both 2nd and 3rd order schemes in the presence of a smoothly distributed variable field (i.e., in the absence of discontinuities). This new Optimization-based Gradient REconstruction (herein denoted OGRE) scheme produces, for the simple scalar transport test case, lower error and demands less computational time (for a given level of required precision) for a 3rd order scheme when compared to an equivalent L-S approach on a two-dimensional framework. For three-dimensional simulations, where the L-S scheme fails to obtain convergence without the help of limiters, the new scheme obtains stable convergence and also produces lower error solution when compared to a third order MUSCL scheme. Furthermore, spectral analysis of results from the advection equation shows that the new scheme is better able to accurately resolve high wave number modes, which demonstrates its potential to better solve problems presenting a wide spectrum of wavelengths, for example unsteady turbulent flow simulations.