[pt] Esta tese apresenta as formulações dos métodos de elementos de contorno convencional e híbrido simplificado para problemas axissimétricos de elasticidade, empregando-se as soluções fundamentais do espaço completo e do semi-espaço. Para problemas de elasticidade axissimétricos no semi-espaço pelos métodos de elementos de contorno, o uso das soluções fundamentais para espaço completo exige a discretização e o truncamento da superfície livre. No entanto, essa discretização é dispensada se as soluções fundamentais empregadas satisfizerem a condição de forças de superfície nulas. Este trabalho apresenta a implementação dessas soluções fundamentais axissimétricas para o espaço completo e o semi-espaço elástico, em termos de integrais do tipo Lipschitz-Hankel. São apresentadas todas as expressões necessárias para o cálculo de resultados em pontos internos e a correta integração numérica das integrais de contorno. Partindo da formulação do espaço completo, mostra-se que é necessária pouca modificação para a implementação da formulação proposta. Esse trabalho também desenvolve a formulação axissimétrica para o método híbrido simplificado dos elementos de contorno, tanto para o espaço completo como para o semi-espaço. Na sua versão original, o uso de propriedades espectrais para a total formulação do problema não era possível para certas configurações topológicas. No entanto, a aplicação de um princípio de contragradiência híbrida às equações do método levou à obtenção de uma nova relação matricial que tornou possível sua total formulação para qualquer topologia, independentemente de propriedades espectrais. A necessidade de se integrar apenas uma matriz e a facilidade de obtenção de resultados em pontos internos tornam o método híbrido simplificado dos elementos de contorno ainda mais vantajoso para problemas axissimétricos. Alguns exemplos numéricos validam as formulações apresentadas. Essa tese é composta por oito capítulos e dois apêndices, como descritos a seguir. O Capítulo 2 trata das soluções fundamentais axissimétricas para o espaço completo e o semi-espaço elástico. As equações governantes para um meio elástico axissimétrico são apresentadas em coordenadas cilíndricas. As soluções fundamentais correspondentes são deduzidas, em termos de integrais do tipo Lipschitz-Hankel, a partir da solução de Muki das equações de equilíbrio de Navier. O Capítulo 3 apresenta o método dos elementos de contorno para problemas axissimétricos no espaço completo e no semi-espaço. A partir das soluções fundamentais apresentadas no Capítulo 2, as equações integrais no contorno são deduzidas, bem como as equações matriciais governantes. Além disso, discute-se a obtenção de uma matriz de rigidez e o cálculo das inversas generalizadas presentes na formulação. As expressões para o cálculo de deslocamentos e tensões no domínio e ao longo do contorno são fornecidas de maneira explícita. O Capítulo 4 apresenta o método híbrido simplificado dos elementos de contorno para problemas axissimétricos no espaço completo e no semi-espaço. Uma nova versão do método é proposta, em que as equações governantes do problema são obtidas a partir de trabalhos virtuais de deslocamentos, uma equação de compatibilidade de deslocamentos e um teorema híbrido de contragradiência. O esquema para o cálculo dos coeficientes indeterminados de U está descrito detalhadamente para o espaço completo, incluindo as soluções analíticas necessárias. A obtenção de uma matriz de rigidez, bem como de deslocamentos e tensões em pontos internos, também é discutida. Bases ortonormais, projetores e inversas generalizadas presentes na formulação são apresentados ao longo do capítulo. O Capítulo 5 apresenta os esquemas numéricos para o cálculo das integrais presentes nos métodos de elementos de contorno convencional e híbrido simplificado aplicados a problemas axissimétricos no espaço completo e no semi-espaço. / [en] This thesis presents the formulation of the conventional and simplified-hybrid boundary element methods for axisymmetric problems, employng fullspace as well as halfspace fundamental solutions. As it is mostly found in the literature on axisymmetric problems in the elastic halfspace, the boundary element formulations make use of fullspace fundamental solutions and insert a mesh discretization of the free surface, with truncation at a reasonable distance from the axis of axisymmetry. This discretization can be circunvented if one employs the fundamental solutions that satisfy in advance the traction free boundary condition on the free surface. This work presents the implementation of these axisymmetric fundamental solutions for both the fullspace and the halfspace, given in terms of integrals of Lipschitz-Hankel type. Explicit equations for post-processing results at internal points are provided, as well as the adequate numerical schemes to evaluate the boundary integrals that arise in the formulation. It is shown that the boundary element method for the halfspace can be easily implemented from existing computation codes for fullspace problems, requiring only a few modifications. This work also addresses the simplified-hybrid boundary element method for the axisymmetric fullspace and halfspace problems. In its original version, the use of spectral properties to completely formulate the method was possible for only strictly non-convex topological configurations. The key contribution of the present developments consisted in the correct application of a hybrid contragradient theorem to derive a simple means of using analytical solutions of the elastic problem in order to substitute for the spectral properties that have been originally proposed. In the simplified-hybrid boundary element method, only one matrix requires integration and the results at internal points can be evaluated directly, which makes the method extremely advantageous for axisymmetric problems. Some numerical examples validate the proposed formulations.

This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasi-sparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within optimal complexity. By numerical experiments we provide results which corroborate the theory.

[EN] The behavior of the heart is governed by electrical currents generated in the myocardium, and therefore, the study of the cardiac electrical activity is essential for the diagnosis of cardiac diseases. The forward problem of the electrocardiography (FP) entails the calculation of the torso potentials from the electrical activity of the heart and the 3D body model, while the inverse problem (IP) resolution allows the noninvasive reconstruction of the electrical activity of the heart from surface potentials. The IP is of great importance in clinical applications since it allows estimating the electrical activity of the myocardium with only noninvasive recordings. However, IP resolution is still a big challenge in electrocardiography since it is ill-posed, very unstable and has multiple solutions. In this thesis different algorithms and strategies based on the IP resolution were developed and applied in the noninvasive diagnosis of ventricular and atrial arrhythmias and evaluated with mathematical cellular models and clinical data bases. The thesis focuses on the IP resolution for the noninvasive reconstruction of the myocardial electrical activity for different diseases and propagation patterns, implementing a novel system for complex propagation patterns. The obtained results and propagation patterns were evaluated and classified with the corresponding optimal resolution strategy that minimizes the error and increases the stability of the system, proving its advantages and disadvantages depending on the different diseases and their activation pattern. A novel iterative method was implemented for the IP dipolar resolution optimized for representing simple propagation patterns, achieving a high stability and robustness against noise by constraining the solution to a limited number of dipoles. However, propagation patterns not representable by few dipoles need to be computed with the IP in terms of epicardial solutions which provide a more detailed estimation of the myocardial activity. IP resolution in the voltage and phase domains showed a good accuracy for simple and organized propagation patterns. This method allowed the noninvasive diagnosis of the Brugada syndrome or the location of ectopic focus in atrial arrhythmias by performing a parametric analysis of the electrograms morphology or the activation map reconstruction. However, mathematical and patient results presented in this thesis proved that, for complex propagation patterns like atrial fibrillation (AF), inverse solutions in the voltage and phase domains are over-smoothed and over-optimistic, simplifying the complex AF activity, leading to non-physiological results that do not match with the complex intracardiac electrograms recorded in AF patients. In this thesis, we proposed a novel technique for the noninvasive identification and location of high dominant frequency AF sources, based on the assumption that in many cases atrial drivers present the highest activation rate with an intermittent propagation to the rest of the tissue that activates at a slower rate. Although, voltage and phase inverse solutions for AF complex propagation patterns were over smoothed and inaccurate, the noninvasive estimation of frequency maps was significantly more accurate, allowing the identification of the AF frequency gradient and location of high frequency sources. This technique may help in planning ablation procedures, avoiding unnecessary interseptal punctures for right-to-left frequency gradients cases and facilitating the targeting of the AF drivers, reducing risk and time of the clinical procedure. / [ES] El comportamiento del corazón se rige por corrientes eléctricas generadas en el miocardio y, por lo tanto, el estudio de su actividad eléctrica es esencial para el diagnóstico de enfermedades cardíacas. El problema directo (PD) de la electrocardiografía implica el cálculo de los potenciales del torso a partir de la actividad eléctrica del corazón y el modelo 3D del cuerpo, mientras que la resolución del problema inverso (PI) permite la reconstrucción no invasiva de la actividad eléctrica del corazón a partir de los potenciales de superficie, cobrando una gran importancia en la práctica clínica. Sin embargo, sigue siendo un gran desafío para la electrocardiografía ya que está mal planteado, es muy inestable y tiene múltiples soluciones. A lo largo de esta tesis se han desarrollado diferentes estrategias para la resolución del PI, aplicándolas en el diagnóstico no invasivo de arritmias ventriculares y auriculares, verificándolas mediante modelos celulares matemáticos y bases de datos clínicas. La tesis se centra en la resolución del PI para la reconstrucción no invasiva de la actividad eléctrica del miocardio para diferentes enfermedades cardiacas con diferentes patrones de propagación, implementando un novedoso sistema para patrones de propagación complejos. Además, se han validado los resultados obtenidos y se han clasificado los diferentes patrones de propagación con la estrategia de resolución del PI óptima que minimice el error y aumente la estabilidad del sistema. Un nuevo método iterativo fue implementado para la resolución del PI para fuentes dipolares, siendo óptimo para representar patrones de propagación simples, logrando una alta estabilidad e inmunidad al ruido al restringir la solución a un número limitado de dipolos. Sin embargo, los patrones de propagación que no pueden ser representados por un número limitado de dipolos deben calcularse mediante la resolución del PI en términos de potenciales epicárdicos, proporcionando una estimación más detallada de la actividad del miocardio. La resolución del PI en el dominio de la tensión y fase mostró ser muy preciso para patrones de propagación simples y organizados. Este método permite el diagnóstico no invasivo del síndrome de Brugada o la ubicación de focos ectópicos en arritmias auriculares mediante un análisis paramétrico de la morfología de los electrogramas o la reconstrucción de los mapas de activación. Sin embargo, los resultados matemáticos y clínicos presentados en esta tesis demostraron que, para patrones de propagación complejos como la fibrilación auricular (FA), los resultados obtenidos mediante la resolución del PI en el dominio de la tensión y fase son demasiado suaves y optimistas, simplificando enormemente la complejidad de la FA, llevando a resultados no fisiológicos que no coinciden con la actividad compleja de los electrogramas intracardiacos registrados en pacientes con FA. En esta tesis, se ha propuesto una novedosa técnica para la identificación y localización no invasiva de fuentes con una frecuencia dominante alta, basado en la suposición de que en muchos casos las fuentes eléctricas que generan y mantienen la FA presentan una tasa de activación más alta, con una propagación intermitente hacia el resto del tejido auricular cuya frecuencia de activación es más lenta. Aunque las soluciones en el dominio de la tensión y fase para patrones de propagación complejos fueron más suaves y menos precisas, la estimación no invasiva de los mapas de frecuencia fue significativamente más precisa, permitiendo la identificación del gradiente de frecuencia y ubicación de las fuentes de FA de alta frecuencia. Esta técnica puede ser de gran ayuda en la planificación de los procedimientos de ablación, evitando punciones interseptales innecesarias para casos con un gradiente de frecuencia de derecha a izquierda y facilitando la localización de las fuentes de alta frecuencia / [CAT] El comportament del cor es regeix per corrents elèctrics generades en el miocardi i, per tant, l'estudi de la seua activitat elèctrica és essencial per al diagnòstic de malalties cardíaques. El problema directe (PD) de l'electrocardiografia implica el càlcul dels potencials del tors a partir de l'activitat elèctrica del cor i el model 3D del cos, mentre que la resolució del problema invers (PI) permet la reconstrucció no invasiva de l'activitat elèctrica del cor a partir de els potencials de superfície. La resolució del PI de l'electrocardiografia té una gran importància en la pràctica clínica atès que fa possible una estimació de l'activitat elèctrica del miocardi únicament a partir de registres no invasius. No obstant això, la resolució del PI segueix sent un gran desafiament per a la electrocardiografia ja que està mal plantejat, és molt inestable i té múltiples solucions. Al llarg d'aquesta tesi s'han desenvolupat diferents estratègies basades en la resolució PI, aplicant-les en el diagnòstic no invasiu d'arítmies ventriculars i auriculars, verificant mitjançant models cel·lulars matemàtics i bases de dades clíniques. La tesi se centra en la resolució del PI per a la reconstrucció no invasiva de l'activitat elèctrica del miocardi per a diferents malalties cardíaques amb diferents patrons de propagació, implementant un nou sistema per a patrons de propagació complexos. A més se han validat els resultats obtinguts i se han classificat els diferents patrons de propagació amb l'estratègia de resolució del PI òptima que minimitze l'error i augmente l'estabilitat del sistema. Un nou mètode iteratiu va ser implementat per a la resolució del PI per fonts dipolars, sent òptim per representar patrons de propagació simples, aconseguint una alta estabilitat i immunitat al soroll en restringir la solució a un nombre limitat de dipols. No obstant això, els patrons de propagació que no poden ser representats per un nombre limitat de dipols s'han de calcular mitjançant la resolució del PI en termes de potencials epicàrdics, proporcionant una estimació més detallada de l'activitat del miocardi. La resolució del PI en el domini de la tensió i fase va mostrar ser molt precís per a patrons de propagació simples i organitzats. Aquest mètode permet el diagnòstic no invasiu de la síndrome de Brugada o la ubicació de focus ectòpics en arítmies auriculars mitjançant una anàlisi paramètric de la morfologia dels electrogrames o la reconstrucció dels mapes d'activació. No obstant això, els resultats matemàtics i clínics presentats en aquesta tesi van demostrar que, per patrons de propagació complexos com la fibril·lació auricular (FA), els resultats obtinguts mitjançant la resolució del PI en el domini de la tensió i fase són massa suaus i optimistes, simplificant enormement la complexitat de la FA, obtenint resultats no fisiològics que no coincideixen amb l'activitat complexa dels electrogrames intracardiacos registrats en pacients amb FA. En aquesta tesi, s'ha proposat una nova tècnica per a la identificació i localització no invasiva de fonts amb una freqüència dominant alta, basat en la suposició que en molts casos les fonts elèctriques que generen i mantenen la FA presenten una taxa d'activació més alta, amb una propagació intermitent cap a la resta del teixit auricular on la freqüència d'activació és més lenta. Encara que, les solucions en el domini de la tensió i fase per patrons de propagació complexos van ser més suaus i menys precises, l'estimació no invasiva dels mapes de freqüència va ser significativament més precisa, permetent la identificació del gradient de freqüència i ubicació de les fonts de FA d'alta freqüència. Aquesta tècnica pot ser de gran ajuda en la planificació dels procediments d'ablació, evitant puncions interseptales innecessaris per a casos amb un gradient de freqüència de dreta a esquerra i facilitant la / Pedrón Torrecilla, J. (2015). Non-invasive Reconstruction of the Myocardial Electrical Activity from Body Surface Potential Recordings [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/58268 / TESIS

Cette thèse porte sur le problème de la diffration acoustique par un obstacle et sa résolution numérique par la méthode des éléments finis de frontière. Dans les trois premiers chapitres, on s'intéresse au cas où l'obstacle possède des singularités géométriques. Nous traitons le cas particulier des singularités de bord, courbes ouvertes en dimension 2, et surfaces ouvertes en dimension 3. Nous introduisons un formalisme qui permet de retrouver les bonnes propriétés de la méthode pour des objets réguliers. Une fonction de poids est définie sur les objets diffractant, et les opérateurs intégraux usuels (simple-couche et hypersingulier) sont renormalisés de manière adéquate par ce poids. Des préconditioneurs sont proposés sous la forme de racines carrées d'opérateurs locaux. En dimension 2, nous proposons une analyse théorique et numérique complète du problème. Nous montrons en particulier que les opérateurs intégraux renormalisés font partie d'une classe d'opérateurs pseudo-différentiels sur des courbes ouvertes, que nous introduisons et étudions ici. Le calcul pseudo-différentiel ainsi développé nous permet de calculer des paramétrices des les opérateurs intégraux qui correspondent aux versions continues de nos préconditionneurs. En dimension 3, nous montrons comment ces idées se généralisent théoriquement et numériquement dans le cas pour des surfaces ouvertes. Dans le dernier chapitre, nous introduisons une nouvelle méthode de calcul rapide des convolutions par des fonctions radiales en dimension 2, l'une des tâches les plus coûteuses en temps dans la méthode des éléments finis de frontière. Notre algorithme repose sur l'algorithme de transformée de Fourier rapide non uniforme, et est la généralisation un algorithme analogue disponible en dimension 3, la décomposition creuse en sinus cardinal. / In this thesis, we are concerned with the numerical resolution of the problem of acoustic waves scattering by an obstacle in dimensions 2 and 3, with the boundary element method. In the first three chapters, we consider objects with singular geometries. We focus on the case of objects with edge singularities, first open curves in the plane, and then open surfaces in dimension 3. We present a formalism that allows to restore the good properties that held for smooth objects. A weight function is defined on the scattering object, and the usual layer potentials (single-layer and hypersingular) are adequately rescaled by this weight function. Suitable preconditioners are proposed, that take the form of square roots of local operators. In dimension 2, we give a complete theoretical and numerical analysis of the problem. We show in particular that the weighted layer potentials belong to a class of pseudo-differential operators on open curves that we define and analyze here. The pseudo-differential calculus thus developed allows us to compute parametrices for the weighted layer potentials, which correspond to the continuous versions of our preconditioners. In dimension 3, we show how those ideas can be extended theoretically and numerically, for the particular case of the scattering by an infinitely thin disk. In the last chapter, we present a new method for the rapid evaluation of discrete convolutions by radial functions in dimension 2. Such convolutions represent a computational bottleneck in the boundary element methods. Our algorithm relies on the non-uniform fast Fourier transform and generalizes to dimension 2 an analogous algorithm available in dimension 3, namely the sparse cardinal sine decomposition.

There are many shape and other changes in the engineering constructions. These changes cause the concentration of the stress. There is a higher probability of the crack initiation in the vicinity of these stress concentrators. The problems of the crack can be solved nowadays only with help of sufficient numeric tools. The Boundary Element Method is one of the many numerical tools which offer the solution of some problems of the mechanics. The goal of this diploma thesis is to formulate boundary element method for the plane problem of the linear elasticity for izotropic material with different types of the stress concentrators.

This master’s thesis deals with boundary vorticity element method for 2D fluid flow. The aim of this work is to program this method with continuous vorticity lay-out and to validate method with various boundary conditions. The computed results are presented in this work. Advantages and disadvantages of each one boundary condition are pointed out. New one boundary condition for boundary vorticity element method is applied in this thesis.

This paper presents a wavelet Galerkin scheme for the fast solution of boundary integral equations. Wavelet Galerkin schemes employ appropriate wavelet bases for the discretization of boundary integral operators. This yields quasi-sparse system matrices which can be compressed to O(N_J) relevant matrix entries without compromising the accuracy of the underlying Galerkin scheme. Herein, O(N_J) denotes the number of unknowns. The assembly of the compressed system matrix can be performed in O(N_J) operations. Therefore, we arrive at an algorithm which solves boundary integral equations within optimal complexity. By numerical experiments we provide results which corroborate the theory.

No description available.

Thermal systems often feature composite regions that are mechanically mated. In general, there exists a significant temperature drop across the interface between such regions which may be composed of similar or different materials. The parameter characterizing this temperature drop is the thermal contact resistance, which is defined as the ratio of the temperature drop to the heat flux normal to the interface. The thermal contact resistance is due to roughness effects between mating surfaces which cause certain regions of the mating surfaces to loose contact thereby creating gaps. In these gap regions, the principal modes of heat transfer are conduction across the contacting regions of the interface, conduction or natural convection in the fluid filling the gap regions of the interface, and radiation across the gap surfaces. Moreover, the contact resistance is a function of contact pressure as this can significantly alter the topology of the contact region. The thermal contact resistance is a phenomenologically complex function and can significantly alter prediction of thermal models of complex multi-component structures. Accurate estimates of thermal contact resistances are important in engineering calculations and find application in thermal analysis ranging from relatively simple layered and composite materials to more complex biomaterials. There have been many studies devoted to the theoretical predictions of thermal contact resistance and although general theories have been somewhat successful in predicting thermal contact resistances, most reliable results have been obtained experimentally. This is due to the fact that the nature of thermal contact resistance is quite complex and depends on many parameters including types of mating materials, surface characteristics of the interfacial region such as roughness and hardness, and contact pressure distribution. In experiments, temperatures are measured at a certain number of locations, usually close to the contact surface, and these measurements are used as inputs to a parameter estimation procedure to arrive at the sought-after thermal contact resistance. Most studies seek a single value for the contact resistance, while the resistance may in fact also vary spatially. In this thesis, an inverse problem (IP) is formulated to estimate the spatial variation of the thermal contact resistance along an interface in a two-dimensional configuration. Temperatures measured at discrete locations using embedded sensors appropriately placed in proximity to the interface provide the additional information required to solve the inverse problem. A superposition method serves to determine sensitivity coefficients and provides guidance in the location of the measuring points. Temperature measurements are then used to define a regularized quadratic functional that is minimized to yield the contact resistance between the two mating surfaces. A boundary element method analysis (BEM) provides the temperature field under current estimates of the contact resistance in the solution of the inverse problem when the geometry of interest is not regular, while an analytical solution can be used for regular geometries. Minimization of the IP functional is carried out by the Levenberg-Marquadt method or by a Genetic Algorithm depending on the problem under consideration. The L-curve method of Hansen is used to choose the optimal regularization parameter. A series of numerical examples are provided to demonstrate and validate the approach.

No / The paper describes model testing of the acoustic performance of vertically louvred and the corresponding predicted performance using a modified Boundary Element Method (BEM) program. The program was developed in a previous phase of the Transport Research Laboratory's research into the performance of modified barriers. Measurements on 1/20th scale model barriers were carried out in a semi-anechoic chamber designed primarily for scale model experiments to investigate outdoor sound propagation under controlled conditions. It was concluded from measurements in the scale model facility that the modified BEM code provided an adequate description of the leakage of sound through louvred barriers. The program was subsequently used to examine the performance of various designs of barrier in order to identify likely cost effective designs.