Cette thèse se situe dans le domaine de l'électromagnétisme et plus particulièrement, celui de la compatibilité électromagnétique. L'objectif de cette thèse est de proposer une condition d'interface qui évite de mailler les plaques minces conductrices lors d’une modélisation tridimensionnelle. Cette condition permet de prendre en compte de manière précise la réflexion d'une onde ou sa transmission par une plaque conductrice. Elle permet aussi de tenir compte de l'effet de peau de l'effet de peau à l'intérieur de la plaque. Cette condition d'interface est intégrée dans une méthode Galerkin discontinue. La présence des termes de flux dans cette méthode rend facile l'implémentation de cette condition d'interface. Afin de montrer l'intérêt de cette condition dans le cadre de la compatibilité électromagnétique, des configurations d'interaction ondes-Structures sont traitées. Elles ont pour but d'étudier l'efficacité de blindage de diverses cavités bidimensionnelles et tridimensionnelles. / This thesis concerns electromagnetic fields and more particularly electromagnetic compatibility. The aim of this thesis is the modeling an interface condition to avoid the mesh of thin conductive sheets in 3D numerical methods. This interface condition allows to take in account the reflection or the transmission of an incident wave on a conductive sheet. It also takes into account the skin effect in this sheet. This interface condition is integrated in discontinuous Galerkin method. The presence of flux terms is this method makes easy to implement this interface condition. To demonstrate the advantage of this interface condition in electromagnetic compatibility problems, many configurations of interaction wave-Structure are treated. They aim to study the shielding effectiveness of different cavities in two and three dimensions.

S’inscrivant dans le cadre d’une littérature qui proclame le renouveau, l’écriture de Chevillard procède à l’expérimentation et aux jeux entre la norme et la distorsion, entre le retour et le détour, avec et contre le roman. Le discontinu s’avère un pont primordial sur lequel se tracent ces enjeux littéraires. À travers le décryptage de la mise en scène esthétique de la discontinuité, le présent travail vise la sollicitation et l’interprétation des différentes manifestations de la rupture et de la dislocation, génératrices de l’éclatement de la narration, de l’écriture digressive et métaleptique, et de la complexité de la lecture. Renforcés par la portée ludique et comique, ainsi que par l’abolition des frontières entre le fictif et le réel, avec ses clichés et ses stéréotypes, de tels procédés se révèlent au service de la vision ironique et critique qui contre-attaque ce que Chevillard appelle le « bon vieux roman ». De ce fait, la lecture du roman chevillardien ne devrait plus se stagner au niveau de la déconstruction et du discontinu, mais elle présuppose le déchiffrage d’une unité profonde que camouflent l’incohérence et la rupture, signes de provocation et de dérangement d’un lecteur complice de l’acte diégétique et esthétique de l’œuvre. Ce lecteur ne serait pas une instance naïve manipulée, mais une instance critique « compétente » qui, emportée par l’émotionnel, entre en communication avec le texte. De ce fait, les idées et la réflexion de ce lecteur dynamique seraient confrontées à celles de l’écrivain, et son raisonnement aboutirait à une reconstruction de la déconstruction, par la production du sens et la participation performative à la fictionnalisation du récit. La « jouissance du texte » naît d’une telle créativité coopérative et intelligente, qui admet le dérangement, déjoue la complexité et dégage l’essence poétique du roman. / Being part of a literary movement that proclaims renewal, Chevillard's writings proceed in experimentation and games between norm and distortion, the return and the detour, with and against the novel. Discontinuity proves to be a primordial bridge which such literary matters draw on. Through the decoding of the aesthetic staging of discontinuity, the present work aims at the solicitation and interpretation of the different manifestations of rupture and dislocation, generated by the bursting of narration, digressive and metaleptic writing as well as reading complexity. Reinforced by the playful and comical range in addition to the abolition of the borders between the fictitious and the real, its clichés and stereotypes, such processes turn out to be in the service of the ironic and critical vision that counter-attacks what Chevillard calls the "Good old novel." As a result, the reading of the Chevillardian novel should no longer stagnate at the level of deconstruction and discontinuity, but on the contrary it presupposes the deciphering of a deep unity that camouflages incoherence and rupture, the signs of provocation and disturbance of an accomplice reader of the diegetic and aesthetic act of the work. This reader would not be naïve and manipulated, but a critical and "competent" entity, which, carried away by the emotional, enters into communication with the text so that its ideas and reflection are confronted with those of the writer, and his reasoning results in a reconstruction of deconstruction through the production of meaning and the performative participation in the fictionalization of the narrative. The enjoyment of the text is born of such a cooperative and intelligent creativity that plays with the disturbance, thwarts the complexity and releases the poetic essence of the novel.

O desenvolvimento de uma ferramenta de Dinâmica de Fluidos Computacional que utiliza Método de Elementos Finitos baseada na discretização de Galerkin descontínuo é apresentado neste trabalho com objetivo de resolver a equação de Euler linearizada para escoamento compressível em duas dimensões usando malhas estruturadas e não estruturadas. Procuramos utilizar esta ferramenta como um propagador de ondas sonoras para estudar fenômenos aeroacústicos. O problema de Riemann presente no fluxo convectivo da equação de Euler é tratado com um método upwind HLL e para o avanço da solução no tempo é usado o método de Runge-Kutta explícito de 4 estágios com segunda ordem de precisão. A eficiência computacional, a convergência do método e a precisão são testadas através de simulações de escoamentos já apresentadas na literatura. A taxa de convergência para altas ordens de aproximação é assintótica que é um resultado compatível com a formulação Galerkin descontínuo. / The development of a Computation Fluid Dynamic Tool based on the Finite Element Method with discontinuous Galerkin discretization is presented in this work. The aim of this study is to solve the compressible linearized Euler\'s equation in two dimensions on structured and non structured meshes. This tool has been used as a means to study aeroacoustics phenomena. The Riemann\'s problem presented on a convective flow in Euler\'s equation is tackled by a HLL\'s method and the time integration being used is the four-stage Runge-Kutta explicit method with second order of accuracy. The computational efficiency, the convergence of the method and the accuracy are tested by comparing our results for flow simulations with those that are available in the literature. The convergence rate to high approximation order is asymptotic and it shows a result which is compatible with a discontinuous Galerkin formulation.

In this thesis we develop and analyze the performance ofadaptive finite element methods for multiphysics problems. Inparticular, we propose a methodology for deriving computable errorestimates when solving unidirectionally coupled multiphysics problemsusing segregated finite element solvers.  The error estimates are of a posteriori type and are derived using the standard frameworkof dual weighted residual estimates.  A main feature of themethodology is its capability of automatically estimating thepropagation of error between the involved solvers with respect to anoverall computational goal. The a posteriori estimates are used todrive local mesh refinement, which concentrates the computationalpower to where it is most needed.  We have applied and numericallystudied the methodology to several common multiphysics problems usingvarious types of finite elements in both two and three spatialdimensions. Multiphysics problems often involve convection-diffusion equations for whichstandard finite elements can be unstable. For such equations we formulatea robust discontinuous Galerkin method of optimal order with piecewiseconstant approximation. Sharp a priori and a posteriori error estimatesare proved and verified numerically. Fractional step methods are popular for simulating incompressiblefluid flow. However, since they are not genuine Galerkin methods, butrather based on operator splitting, they do not fit into the standardframework for a posteriori error analysis. We formally derive an aposteriori error estimate for a prototype fractional step method byseparating the error in a functional describing the computational goalinto a finite element discretization residual, a time steppingresidual, and an algebraic residual.

We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.

The miscible displacement equations provide the mathematical model for simulating the displacement of a mixture of oil and miscible fluid in underground reservoirs during the Enhance Oil Recovery(EOR) process. In this thesis, I propose a stable numerical scheme combining a mixed finite element method and space-time discontinuous Galerkin method for solving miscible displacement equations under low regularity assumption. Convergence of the discrete solution is investigated using a compactness theorem for functions that are discontinuous in space and time. Numerical experiments illustrate that the rate of convergence is improved by using a high order time stepping method. For petroleum engineers, it is essential to compute finely detailed fluid profiles in order to design efficient recovery procedure thereby increase production in the EOR process. The method I propose takes advantage of both high order time approximation and discontinuous Galerkin method in space and is capable of providing accurate numerical solutions to assist in increasing the production rate of the miscible displacement oil recovery process.

<p>Engineering mechanics problems involving interfaces, whether physical or introduced by numerical methodologies, are commonplace.  Just a few examples include fracture and fault mechanics, classical contact-impact, phase boundary propagation, and fluid-structure interaction.  This dissertation focuses on issues of numerical stability and accuracy that must be addressed when such interfaces are included in a realistic simulation of a physical system. </p><p>We begin by presenting a novel numerical method of fluid/structure interaction that may be applied to the problem of movable devices and ocean waves. The work is done with finite differences, large motion Lagrangian mechanics, and an eye towards creating a model in which complex rigid body dynamics can be incorporated.</p><p>We then review the many advantages of embedded mesh techniques for interface representation, and investigate a completely finite element based strategy for embedding domains. The work is seen as a precursor to robust multi-physics simulation capabilities.  Special attention must be given to these techniques in terms of stable and convergent representation of surface fluxes.  Mesh locking and over-constraint are particularly addressed.   We show that traditional methods for enforcing continuity at embedded interfaces cannot adequately guarantee flux stability, and show a less traditional method, known as Nitsche's method, to be a stable alternative. We address the open problem of applying Nitsche's method to non-linear analysis by drawing parallels between the embedded mesh and discontinuous Galerkin (DG) methods, and propose a DG style approach to Nitsche's method. We conclude with stable interfacial fluxes for a continuity constraint for a case of embedded finite element meshes in large deformation elasticity. The general conclusion is drawn that stability must be addressed in the choice of interface treatment in computational mechanics.</p> / Dissertation

Renewable energy sources including photovoltaic cells, fuel cells, and wind turbines require converters with high voltage gain in order to interface with power transmission and distribution networks. These conversions are conventionally made using bulky, complex, and costly transformers. Multiple modules of single-switch, single-inductor DC-DC converters can serve these high-gain applications while eliminating the transformer. This work generally classifies multiple modules of single-switch, single-inductor converters as high gain DC-DC converters transformers. The gain and efficiency of both series and cascade configurations are investigated analytically, and a method is introduced to determine the maximum achievable gain at a given efficiency. Simulations are used to verify the modeling approach and predict the performance at different power levels. Experimental prototypes for both low power and high power applications demonstrate the value of multiple module converters in high gain DC-DC converters for renewable energy applications.

Linear discontinuous (LD) spatial discretization of the transport operator can generate negative angular flux solutions. In slab geometry, negativities are limited to optically thick cells. However, in multi-dimension problems, negativities can even occur in voids. Past attempts to eliminate the negativities associated with LD have focused on inherently positive solution shapes and ad-hoc fixups. We present a new, strictly non-negative finite element method that reduces to the LD method whenever the LD solution is everywhere positive. The new method assumes an angular flux distribution, e , that is a linear function in space, but with all negativities set-to- zero. Our new scheme always conserves the zeroth and linear spatial moments of the transport equation. For these reasons, we call our method the consistent set-to-zero (CSZ) scheme. CSZ can be thought of as a nonlinear modification of the LD scheme. When the LD solution is everywhere positive within a cell, psi csz = psi LD. If psi LD < 0 somewhere within a cell, psi csz is a linear function psi csz with all negativities set to zero. Applying CSZ to the transport moment equations creates a nonlinear system of equations which is solved to obtain a non-negative solution that preserves the moments of the transport equation. These properties make CSZ unique; it encompasses the desirable properties of both strictly positive nonlinear solution representations and ad-hoc fixups. Our test problems indicate that CSZ avoids the slow spatial convergence properties of past inherently positive solutions representations, is more accurate than ad-hoc fixups, and does not require significantly more computational work to solve a problem than using an ad-hoc fixup. Overall, CSZ is easy to implement and a valuable addition to existing transport codes, particularly for shielding applications. CSZ is presented here in slab and rect- angular geometries, but is readily extensible to three-dimensional Cartesian (brick) geometries. To be applicable to other simulations, particularly radiative transfer, additional research will need to be conducted, focusing on the diffusion limit in multi-dimension geometries and solution acceleration techniques.