Consolidation problems

The analysis of deformation in soils is of paramount importance in geotechnical engineering. For a long time the complex behaviour of natural deposits defied the ingenuity of engineers. The time has come that, with the aid of computers, numerical methods will allow the solution of every problem if the material law can be specified with a certain accuracy. Boundary Techniques (B.E.) have recently exploded in a splendid flowering of methods and applications that compare advantegeously with other well-established procedures like the finite element method (F.E.). Its application to soil mechanics problems (Brebbia 1981) has started and will grow in the future. This paper tries to present a simple formulation to a classical problem. In fact, there is already a large amount of application of B.E. to diffusion problems (Rizzo et al, Shaw, Chang et al, Combescure et al, Wrobel et al, Roures et al, Onishi et al) and very recently the first specific application to consolidation problems has been published by Bnishi et al. Here we develop an alternative formulation to that presented in the last reference. Fundamentally the idea is to introduce a finite difference discretization in the time domain in order to use the fundamental solution of a Helmholtz type equation governing the neutral pressure distribution. Although this procedure seems to have been unappreciated in the previous technical literature it is nevertheless effective and straightforward to implement. Indeed for the special problem in study it is perfectly suited, because a step by step interaction between the elastic and flow problems is needed. It allows also the introduction of non-linear elastic properties and time dependent conditions very easily as will be shown and compares well with performances of other approaches.

Unidad did��ctica sobre el uso del programa Virtual.Lab para simulaciones ac��sticas. Parte I

El presente Proyecto de Fin de Carrera supone el prop��sito conjunto de los alumnos ��lvaro Morillas y Fernando S��ez, y del profesor Vladimir Ulin, de desarrollar una unidad did��ctica sobre el programa de simulaci��n para ingenier��a Virtual.Lab. La versi��n sobre la que se ha trabajado para realizar este texto es la 11, publicada en agosto de 2012. Virtual.Lab, del fabricante belga LMS International, es una plataforma software de ingenier��a asistida por ordenador, que agrupa en una misma aplicaci��n varias herramientas complementarias en el dise��o de un producto, desde su definici��n geom��trica a los an��lisis de durabilidad, ruido u optimizaci��n. No obstante, de entre todas las posibles simulaciones que nos permite el programa, en este proyecto s��lo se tratan las que est��n relacionadas con la ac��stica. Cabe resaltar que gran parte de los conceptos manejados en Virtual.Lab son compatibles con el programa CATIA V5, ya que ambos programas vienen instalados y funcionan conjuntamente. Por eso, el lector de este proyecto podr�� transportar sus conocimientos al que es uno de los programas est��ndar en las industrias aeron��utica, naval y automovil��stica, entre otras. Antes de este proyecto, otros alumnos de la escuela tambi��n realizaron proyectos de fin de carrera en el campo de la simulaci��n computarizada en ac��stica. Una caracter��stica com��n a estos trabajos es que era necesario hacer uso de distintos programas para cada una de las etapas de simulaci��n (como por ejemplo, ANSYS para el modelado y estudio de la vibraci��n y SYSNOISE para las simulaciones ac��sticas, adem��s de otros programas auxiliares para las traducciones de formato). Con Virtual.Lab desaparece esta necesidad y el tiempo empleado se reduce. Debido a que las soluciones por ordenador est��n ganando cada vez m��s importancia en la industria actual, los responsables de este proyecto consideran la necesidad de formaci��n de profesionales en esta rama. Para responder a la demanda empresarial de trabajadores cualificados, se espera que en los pr��ximos a��os los planes de estudio contengan m��s cursos en esta materia. Por tanto la intenci��n de los autores es que este material sea de utilidad para el aprendizaje y docencia de estas asignaturas en cursos sucesivos. Por todo esto, se justifica la relevancia de este PFC como manual para introducir a los alumnos interesados en iniciarse en un sistema actual, de uso extendido en otras universidades tecnol��gicas europeas, y con buenas perspectivas de futuro. En este proyecto se incluyen varios ejemplos ejecutables desde el programa, as�� como v��deos explicativos que ayudan a mostrar gr��ficamente los procesos de simulaci��n. Estos archivos se pueden encontrar en el CD adjunto. Abstract This final thesis is a joint project made by the students ��lvaro Morillas and Fernando S��ez, and the professor Vladimir Ulin. The nature of the joint regards the writing of a didactic unit on Virtual.Lab, the simulation software. The software version used in this text is the number 11, released in August 2012. Virtual.Lab, from the Belgian developer LMS International, is a computer-aided engineering software which is used for several related tasks in this field: product design, durability simulation, optimization, etc. However, this project is focused on the acoustical capabilities. It is worthy to highlight that most procedures explained in this text can be used in the software CATIA V5 as well. Both tools come installed together and may be used at the same time. Therefore, the reader of this project will be able to use the acquired knowledge in one of the most relevant softwares for the aerospace, marine and automotive engineering. Previously to the development of this project, this School has conducted projects on this field. These projects regarded the use of ANSYS for modeling and meshing stages as well as the use of SYSNOISE for the final acoustic analysis. Since both systems use different file formats, a third-party translation software was required. This thesis fulfill this pending necessity with Virtual.Lab; the translation software procedure is not necessary anymore and simulations can be done in a more flexible, fast way. Since companies have an increasing usage of numerical methods in the development of their products and services, the authors think that it is important to develop the appropriate method to instruct new professionals in the field. Thus, the aim of this project is to help teachers and students in their process of learning the use of this leading software in acoustical simulations. For all the reasons mentioned above, we consider that this project is relevant for the School and the educational community. Aiming to achieve this objective the author offers example files and video demonstrations with guidance in the CD that accompanies this material. This facilitates the comprehension of the practical tasks and guides the prospect users of the software.

Contribuci��n al desarrollo de t��cnicas CAD para el dise��o de antenas impresas y dispositivos pasivos de microondas basadas en el m��todo de elementos finitos

El objetivo principal de esta tesis es el desarrollo de herramientas num��ricas basadas en t��cnicas de onda completa para el dise��o asistido por ordenador (Computer-Aided Design,���CAD���) de dispositivos de microondas. En este contexto, se desarrolla una herramienta num��rica basada en el m��todo de los elementos finitos para el dise��o y an��lisis de antenas impresas mediante algoritmos de optimizaci��n. Esta t��cnica consiste en dividir el an��lisis de una antena en dos partes. Una parte de an��lisis 3D que se realiza s��lo una vez en cada punto de frecuencia de la banda de funcionamiento donde se sustituye una superficie que contiene la metalizaci��n del parche por puertas artificiales. En una segunda parte se inserta entre las puertas artificiales en la estructura 3D la superficie soportando una metalizaci��n y se procede un an��lisis 2D para caracterizar el comportamiento de la antena. La t��cnica propuesta en esta tesis se puede implementar en un algoritmo de optimizaci��n para definir el perfil de la antena que permite conseguir los objetivos del dise��o. Se valida experimentalmente dicha t��cnica emple��ndola en el dise��o de antenas impresas de banda ancha para diferentes aplicaciones mediante la optimizaci��n del perfil de los parches. Tambi��n, se desarrolla en esta tesis un procedimiento basado en el m��todo de descomposici��n de dominio y el m��todo de los elementos finitos para el dise��o de dispositivos pasivos de microonda. Se utiliza este procedimiento en particular para el dise��o y sinton��a de filtros de microondas. En la primera etapa de su aplicaci��n se divide la estructura que se quiere analizar en subdominios aplicando el m��todo de descomposici��n de dominio, este proceso permite analizar cada segmento por separado utilizando el m��todo de an��lisis adecuado dado que suele haber subdominios que se pueden analizar mediante m��todos anal��ticos por lo que el tiempo de an��lisis es m��s reducido. Se utilizan m��todos num��ricos para analizar los subdominios que no se pueden analizar mediante m��todos anal��ticos. En esta tesis, se utiliza el m��todo de los elementos finitos para llevar a cabo el an��lisis. Adem��s de la descomposici��n de dominio, se aplica un proceso de barrido en frecuencia para reducir los tiempos del an��lisis. Como m��todo de orden reducido se utiliza la t��cnica de bases reducidas. Se ha utilizado este procedimiento para dise��ar y sintonizar varios ejemplos de filtros con el fin de comprobar la validez de dicho procedimiento. Los resultados obtenidos demuestran la utilidad de este procedimiento y confirman su rigurosidad, precisi��n y eficiencia en el dise��o de filtros de microondas. ABSTRACT The main objective of this thesis is the development of numerical tools based on full-wave techniques for computer-aided design ���CAD��� of microwave devices. In this context, a numerical technique based on the finite element method ���FEM��� for the design and analysis of printed antennas using optimization algorithms has been developed. The proposed technique consists in dividing the analysis of the antenna in two stages. In the first stage, the regions of the antenna which do not need to be modified during the CAD process are initially characterized only once from their corresponding matrix transfer function (Generalized Admittance matrix, ���GAM���). The regions which will be modified are defined as artificial ports, precisely the regions which will contain the conducting surfaces of the printed antenna. In a second stage, the contour shape of the conducting surfaces of the printed antenna is iteratively modified in order to achieve a desired electromagnetic performance of the antenna. In this way, a new GAM of the radiating device which takes into account each printed antenna shape is computed after each iteration. The proposed technique can be implemented with a genetic algorithm to achieve the design objectives. This technique is validated experimentally and applied to the design of wideband printed antennas for different applications by optimizing the shape of the radiating device. In addition, a procedure based on the domain decomposition method and the finite element method has been developed for the design of microwave passive devices. In particular, this procedure can be applied to the design and tune of microwave filters. In the first stage of its implementation, the structure to be analyzed is divided into subdomains using the domain decomposition method; this process allows each subdomains can be analyzed separately using suitable analysis method, since there is usually subdomains that can be analyzed by analytical methods so that the time of analysis is reduced. For analyzing the subdomains that cannot be analyzed by analytical methods, we use the numerical methods. In this thesis, the FEM is used to carry out the analysis. Furthermore the decomposition of the domain, a frequency sweep process is applied to reduce analysis times. The reduced order model as the reduced basis technique is used in this procedure. This procedure is applied to the design and tune of several examples of microwave filters in order to check its validity. The obtained results allow concluding the usefulness of this procedure and confirming their thoroughness, accuracy and efficiency for the design of microwave filters.

Elastostatics

In this chapter, we are going to describe the main features as well as the basic steps of the Boundary Element Method (BEM) as applied to elastostatic problems and to compare them with other numerical procedures. As we shall show, it is easy to appreciate the adventages of the BEM, but it is also advisable to refrain from a possible unrestrained enthusiasm, as there are also limitations to its usefulness in certain types of problems. The number of these problems, nevertheless, is sufficient to justify the interest and activity that the new procedure has aroused among researchers all over the world. Briefly speaking, the most frequently used version of the BEM as applied to elastostatics works with the fundamental solution, i.e. the singular solution of the governing equations, as an influence function and tries to satisfy the boundary conditions of the problem with the aid of a discretization scheme which consists exclusively of boundary elements. As in other numerical methods, the BEM was developed thanks to the computational possibilities offered by modern computers on totally "classical" basis. That is, the theoretical grounds are based on linear elasticity theory, incorporated long ago into the curricula of most engineering schools. Its delay in gaining popularity is probably due to the enormous momentum with which Finite Element Method (FEM) penetrated the professional and academic media. Nevertheless, the fact that these methods were developed before the BEM has been beneficial because de BEM successfully uses those results and techniques studied in past decades. Some authors even consider the BEM as a particular case of the FEM while others view both methods as special cases of the general weighted residual technique. The first paper usually cited in connection with the BEM as applied to elastostatics is that of Rizzo, even though the works of Jaswon et al., Massonet and Oliveira were published at about the same time, the reason probably being the attractiveness of the "direct" approach over the "indirect" one. The work of Tizzo and the subssequent work of Cruse initiated a fruitful period with applicatons of the direct BEM to problems of elastostacs, elastodynamics, fracture, etc. The next key contribution was that of Lachat and Watson incorporating all the FEM discretization philosophy in what is sometimes called the "second BEM generation". This has no doubt, led directly to the current developments. Among the various researchers who worked on elastostatics by employing the direct BEM, one can additionallly mention Rizzo and Shippy, Cruse et al., Lachat and Watson, Alarc��n et al., Brebbia el al, Howell and Doyle, Kuhn and M��hrmann and Patterson and Sheikh, and among those who used the indirect BEM, one can additionally mention Benjumea and Sikarskie, Butterfield, Banerjee et al., Niwa et al., and Altiero and Gavazza. An interesting version of the indirct method, called the Displacement Discontinuity Method (DDM) has been developed by Crounh. A comprehensive study on various special aspects of the elastostatic BEM has been done by Heisse, while review-type articles on the subject have been reported by Watson and Hartmann. At the present time, the method is well established and is being used for the solution of variety of problems in engineering mechanics. Numerous introductory and advanced books have been published as well as research-orientated ones. In this sense, it is worth noting the series of conferences promoted by Brebbia since 1978, wich have provoked a continuous research effort all over the world in relation to the BEM. In the following sections, we shall concentrate on developing the direct BEM as applied to elastostatics.

Statistical mechanics approaches to granular media: between micromechanics and macromechanics

The mechanical behavior of granular materials has been traditionally approached through two theoretical and computational frameworks: macromechanics and micromechanics. Macromechanics focuses on continuum based models. In consequence it is assumed that the matter in the granular material is homogeneous and continuously distributed over its volume so that the smallest element cut from the body possesses the same physical properties as the body. In particular, it has some equivalent mechanical properties, represented by complex and non-linear constitutive relationships. Engineering problems are usually solved using computational methods such as FEM or FDM. On the other hand, micromechanics is the analysis of heterogeneous materials on the level of their individual constituents. In granular materials, if the properties of particles are known, a micromechanical approach can lead to a predictive response of the whole heterogeneous material. Two classes of numerical techniques can be differentiated: computational micromechanics, which consists on applying continuum mechanics on each of the phases of a representative volume element and then solving numerically the equations, and atomistic methods (DEM), which consist on applying rigid body dynamics together with interaction potentials to the particles. Statistical mechanics approaches arise between micro and macromechanics. It tries to state which the expected macroscopic properties of a granular system are, by starting from a micromechanical analysis of the features of the particles and the interactions. The main objective of this paper is to introduce this approach.

Letters to the editor [An implementation of the Boundary Element Method for zoned media with stress discontinuities, T.J. Rudolphi, 1983]

En esta carta al editor, el profesor D. Enrique Alarc��n ��lvarez comenta el art��culo de Thomas J. Rudolphi "An implementation of the Boundary Element Method for zoned media with stress discontinuities" publicado en la revista "International Journal for Numerical Methods in Engineering" Vol. 19, N�� 1, pags. 1���15, enero 1983.

Generaci��n de modelos f��sicos personalizados y segmentaci��n de la pared arterial y el trombo intraluminal en im��genes de aneurismas a��rticos abdominales

Esta tesis doctoral est�� encuadrada dentro del marco general de la ingenier��a biom��dica aplicada al tratamiento de las enfermedades cardiovasculares, enfermedades que provocan alrededor de 1.9 millones (40%) de muertes al a��o en la Uni��n Europea. En este contexto surge el proyecto europeo SCATh-Smart Catheterization, cuyo objetivo principal es mejorar los procedimientos de cateterismo a��rtico introduciendo nuevas tecnolog��as de planificaci��n y navegaci��n quir��rgica y minimizando el uso de fluoroscop��a. En particular, esta tesis aborda el modelado y diagn��stico de aneurismas a��rticos abdominales (AAA) y del trombo intraluminal (TIL), all�� donde est�� presente, as�� como la segmentaci��n de estas estructuras en im��genes preoperatorias de RM. Los modelos f��sicos espec��ficos del paciente, construidos a partir de im��genes m��dicas preoperatorias, tienen m��ltiples usos, que van desde la evaluaci��n preoperatoria de estructuras anat��micas a la planificaci��n quir��rgica para el guiado de cat��teres. En el diagn��stico y tratamiento de AAA, los modelos f��sicos son ��tiles a la hora de evaluar diversas variables biomec��nicas y fisiol��gicas de las estructuras vasculares. Existen m��ltiples t��cnicas que requieren de la generaci��n de modelos f��sicos que representen la anatom��a vascular. Una de las principales aplicaciones de los modelos f��sicos es el an��lisis de elementos finitos (FE). Las simulaciones de FE para AAA pueden ser espec��ficas para el paciente y permiten modelar estados de estr��s complejos, incluyendo los efectos provocados por el TIL. La aplicaci��n de m��todos num��ricos de an��lisis tiene como requisito previo la generaci��n de una malla computacional que representa la geometr��a de inter��s mediante un conjunto de elementos poli��dricos, siendo los hexa��dricos los que presentan mejores resultados. En las estructuras vasculares, generar mallas hexa��dricas es un proceso especialmente exigente debido a la compleja anatom��a 3D ramificada. La mayor��a de los AAA se encuentran situados en la bifurcaci��n de la arteria aorta en las arterias iliacas y es necesario modelar de manera fiel dicha bifurcaci��n. En el caso de que la sangre se estanque en el aneurisma provocando un TIL, ��ste forma una estructura adyacente a la pared a��rtica. De este modo, el contorno externo del TIL es el mismo que el contorno interno de la pared, por lo que las mallas resultantes deben reflejar esta particularidad, lo que se denomina como "mallas conformadas". El fin ��ltimo de este trabajo es modelar las estructuras vasculares de modo que proporcionen nuevas herramientas para un mejor diagn��stico cl��nico, facilitando medidas de riesgo de rotura de la arteria, presi��n sist��lica o diast��lica, etc. Por tanto, el primer objetivo de esta tesis es dise��ar un m��todo novedoso y robusto para generar mallas hexa��dricas tanto de la pared a��rtica como del trombo. Para la identificaci��n de estas estructuras se utilizan im��genes de resonancia magn��tica (RM). Deben mantenerse sus propiedades de adyacencia utilizando elementos de alta calidad, prestando especial atenci��n al modelado de la bifurcaci��n y a que sean adecuadas para el an��lisis de FE. El m��todo tiene en cuenta la evoluci��n de la l��nea central del vaso en el espacio tridimensional y genera la malla directamente a partir de las im��genes segmentadas, sin necesidad de reconstruir superficies triangulares. Con el fin de reducir la intervenci��n del usuario en el proceso de generaci��n de las mallas, es tambi��n objetivo de esta tesis desarrollar un m��todo de segmentaci��n semiautom��tica de las distintas estructuras de inter��s. Las principales contribuciones de esta tesis doctoral son: 1. El dise��o, implementaci��n y evaluaci��n de un algoritmo de generaci��n de mallas hexa��dricas conformadas de la pared y el TIL a partir de los contornos segmentados en im��genes de RM. Se ha llevado a cabo una evaluaci��n de calidad que determine su aplicabilidad a m��todos de FE. Los resultados demuestran que el algoritmo desarrollado genera mallas conformadas de alta calidad incluso en la regi��n de la bifurcaci��n, que son adecuadas para su uso en m��todos de an��lisis de FE. 2. El dise��o, implementaci��n y evaluaci��n de un m��todo de segmentaci��n autom��tico de las estructuras de inter��s. La luz arterial se segmenta de manera semiautom��tica utilizando un software disponible a partir de im��genes de RM con contraste. Los resultados de este proceso sirven de inicializaci��n para la segmentaci��n autom��tica de las caras interna y externa de la pared a��rtica utilizando m��todos basado en modelos de textura y forma a partir de im��genes de RM sin contraste. Los resultados demuestran que el algoritmo desarrollado proporciona segmentaciones fieles de las distintas estructuras de inter��s. En conclusi��n, el trabajo realizado en esta tesis doctoral corrobora las hip��tesis de investigaci��n postuladas, y pretende servir como aportaci��n para futuros avances en la generaci��n de modelos f��sicos de geometr��as biol��gicas. ABSTRACT The frame of this PhD Thesis is the biomedical engineering applied to the treatment of cardiovascular diseases, which cause around 1.9 million deaths per year in the European Union and suppose about 40% of deaths per year. In this context appears the European project SCATh-Smart Catheterization. The main objective of this project is creating a platform which improves the navigation of catheters in aortic catheterization minimizing the use of fluoroscopy. In the framework of this project, the specific field of this PhD Thesis is the diagnosis and modeling of abdominal aortic aneurysm (AAAs) and the intraluminal thrombus (ILT) whenever it is present. Patient-specific physical models built from preoperative imaging are becoming increasingly important in the area of minimally invasive surgery. These models can be employed for different purposes, such as the preoperatory evaluation of anatomic structures or the surgical planning for catheter guidance. In the specific case of AAA diagnosis and treatment, physical models are especially useful for evaluating pressures over vascular structures. There are multiple techniques that require the generation of physical models which represent the target anatomy. Finite element (FE) analysis is one the principal applications for physical models. FE simulations for AAA may be patient-specific and allow modeling biomechanical and physiological variables including those produced by ILT, and also the segmentation of those anatomical structures in preoperative MR images. Applying numeric methods requires the generation of a proper computational mesh. These meshes represent the patient anatomy using a set of polyhedral elements, with hexahedral elements providing better results. In the specific case of vascular structures, generating hexahedral meshes is a challenging task due to the complex 3D branching anatomy. Each patient���s aneurysm is unique, characterized by its location and shape, and must be accurately represented for subsequent analyses to be meaningful. Most AAAs are located in the region where the aorta bifurcates into the iliac arteries and it is necessary to model this bifurcation precisely and reliably. If blood stagnates in the aneurysm and forms an ILT, it exists as a conforming structure with the aortic wall, i.e. the ILT���s outer contour is the same as the wall���s inner contour. Therefore, resulting meshes must also be conforming. The main objective of this PhD Thesis is designing a novel and robust method for generating conforming hexahedral meshes for the aortic wall and the thrombus. These meshes are built using largely high-quality elements, especially at the bifurcation, that are suitable for FE analysis of tissue stresses. The method accounts for the evolution of the vessel���s centerline which may develop outside a single plane, and generates the mesh directly from segmented images without the requirement to reconstruct triangular surfaces. In order to reduce the user intervention in the mesh generation process is also a goal of this PhD. Thesis to develop a semiautomatic segmentation method for the structures of interest. The segmentation is performed from magnetic resonance image (MRI) sequences that have tuned to provide high contrast for the arterial tissue against the surrounding soft tissue, so that we determine the required information reliably. The main contributions of this PhD Thesis are: 1. The design, implementation and evaluation of an algorithm for generating hexahedral conforming meshes of the arterial wall and the ILT from the segmented contours. A quality inspection has been applied to the meshes in order to determine their suitability for FE methods. Results show that the developed algorithm generates high quality conforming hexahedral meshes even at the bifurcation region. Thus, these meshes are suitable for FE analysis. 2. The design, implementation and evaluation of a semiautomatic segmentation method for the structures of interest. The lumen is segmented in a semiautomatic way from contrast filled MRI using an available software. The results obtained from this process are used to initialize the automatic segmentation of the internal and external faces of the aortic wall. These segmentations are performed by methods based on texture and shape models from MRI with no contrast. The results show that the algorithm provides faithful segmentations of the structures of interest requiring minimal user intervention. In conclusion, the work undertaken in this PhD. Thesis verifies the investigation hypotheses. It intends to serve as basis for future physical model generation of proper biological anatomies used by numerical methods.

Simulaci��n num��rica de un problema de contaminaci��n atmosf��rica

La ecuaci��n en derivadas parciales de advecci��n difusi��n con reacci��n qu��mica es la base de los modelos de dispersi��n de contaminantes en la atm��sfera, y los diferentes m��todos num��ricos empleados para su resoluci��n han sido objeto de amplios estudios a lo largo de su desarrollo. En esta Tesis se presenta la implementaci��n de un nuevo m��todo conservativo para la resoluci��n de la parte advectiva de la ecuaci��n en derivadas parciales que modela la dispersi��n de contaminantes dentro del modelo mesoescalar de transporte qu��mico CHIMERE. Este m��todo est�� basado en una t��cnica de vol��menes finitos junto con una interpolaci��n racional. La ventaja de este m��todo es la conservaci��n exacta de la masa transportada debido al empleo de la ley de conservaci��n de masas. Para ello emplea una formulaci��n de flujo basado en el c��lculo de la integral ponderada dentro de cada celda definida para la discretizaci��n del espacio en el m��todo de vol��menes finitos. Los resultados num��ricos obtenidos en las simulaciones realizadas (implementando el modelo conservativo para la advecci��n en el modelo CHIMERE) se han comparado con los datos observados de concentraci��n de contaminantes registrados en la red de estaciones de seguimiento y medici��n distribuidas por la Pen��nsula Ib��rica. Los datos estad��sticos de medici��n del error, la media normalizada y la media absoluta normalizada del error, presentan valores que est��n dentro de los rangos propuestos por la EPA para considerar el modelo preciso. Adem��s, se introduce un nuevo m��todo para resolver la parte advectivadifusiva de la ecuaci��n en derivadas parciales que modeliza la dispersi��n de contaminantes en la atm��sfera. Se ha empleado un m��todo de diferencias finitas de alto orden para resolver la parte difusiva de la ecuaci��n de transporte de contaminantes junto con el m��todo racional conservativo para la parte advectiva en una y dos dimensiones. Los resultados obtenidos de la aplicaci��n del m��todo a diferentes situaciones incluyendo casos acad��micos y reales han sido comparados con la soluci��n anal��tica de la ecuaci��n de advecci��n-difusi��n, demostrando que el nuevo m��todo proporciona un resultado preciso para aproximar la soluci��n. Por ��ltimo, se ha desarrollado un modelo completo que contempla los fen��menos advectivo y difusivo con reacci��n qu��mica, usando los m��todos anteriores junto con una t��cnica de diferenciaci��n regresiva (BDF2). Esta t��cnica consiste en un m��todo impl��cito multipaso de diferenciaci��n regresiva de segundo orden, que nos permite resolver los problemas r��gidos t��picos de la qu��mica atmosf��rica, modelizados a trav��s de sistemas de ecuaciones diferenciales ordinarias. Este m��todo hace uso de la t��cnica iterativa Gauss- Seidel para obtener la soluci��n de la parte impl��cita de la f��rmula BDF2. El empleo de la t��cnica de Gauss-Seidel en lugar de otras t��cnicas com��nmente empleadas, como la iteraci��n por el m��todo de Newton, nos proporciona rapidez de c��lculo y bajo consumo de memoria, ideal para obtener modelos operativos para la resoluci��n de la cin��tica qu��mica atmosf��rica. ABSTRACT Extensive research has been performed to solve the atmospheric chemicaladvection- diffusion equation and different numerical methods have been proposed. This Thesis presents the implementation of an exactly conservative method for the advection equation in the European scale Eulerian chemistry transport model CHIMERE based on a rational interpolation and a finite volume algorithm. The advantage of the method is that the cell-integrated average is predicted via a flux formulation, thus the mass is exactly conserved. Numerical results are compared with a set of observation registered at some monitoring sites in Spain. The mean normalized bias and the mean normalized absolute error present values that are inside the range to consider an accurate model performance. In addition, it has been introduced a new method to solve the advectiondiffusion equation. It is based on a high-order accurate finite difference method to solve de diffusion equation together with a rational interpolation and a finite volume to solve the advection equation in one dimension and two dimensions. Numerical results obtained from solving several problems include academic and real atmospheric problems have been compared with the analytical solution of the advection-diffusion equation, showing that the new method give an efficient algorithm for solving such problems. Finally, a complete model has been developed to solve the atmospheric chemical-advection-diffusion equation, adding the conservative method for the advection equation, the high-order finite difference method for the diffusion equation and a second-order backward differentiation formula (BDF2) to solve the atmospheric chemical kinetics. The BDF2 is an implicit, second order multistep backward differentiation formula used to solve the stiff systems of ordinary differential equations (ODEs) from atmospheric chemistry. The Gauss-Seidel iteration is used for approximately solving the implicitly defined BDF solution, giving a faster tool than the more commonly used iterative modified Newton technique. This method implies low start-up costs and a low memory demand due to the use of Gauss-Seidel iteration.

P-adaptive boundary elements for three-dimensional potential problems

This paper deals with the boundary element method (BEM) p-convergence approach applied to three-dimensional problems governed by Laplace's equation. The advantages derived from the boundary discretization and hierarchical interpolation functions are collated in order to minimize human effort in preparation of input data and improve numerical results.

On the analytical approach for modeling photovoltaic systems behavior

The 1-diode/2-resistors electric circuit equivalent to a photovoltaic system is analyzed. The equations at particular points of the I���V curve are studied considering the maximum number of terms. The maximum power point as a boundary condition is given special attention. A new analytical method is developed based on a reduced amount of information, consisting in the normal manufacturer data. Results indicate that this new method is faster than numerical methods and has similar (or better) accuracy than other existing methods, numerical or analytical.

Bayesian scene analysis for multi-camera 3D tracking and camera positioning

Los sistemas de seguimiento mono-c��mara han demostrado su notable capacidad para el an��lisis de trajectorias de objectos m��viles y para monitorizaci��n de escenas de inter��s; sin embargo, tanto su robustez como sus posibilidades en cuanto a comprensi��n sem��ntica de la escena est��n fuertemente limitadas por su naturaleza local y monocular, lo que los hace insuficientes para aplicaciones realistas de videovigilancia. El objetivo de esta tesis es la extensi��n de las posibilidades de los sistemas de seguimiento de objetos m��viles para lograr un mayor grado de robustez y comprensi��n de la escena. La extensi��n propuesta se divide en dos direcciones separadas. La primera puede considerarse local, ya que est�� orientada a la mejora y enriquecimiento de las posiciones estimadas para los objetos m��viles observados directamente por las c��maras del sistema; dicha extensi��n se logra mediante el desarrollo de un sistema multi-c��mara de seguimiento 3D, capaz de proporcionar consistentemente las posiciones 3D de m��ltiples objetos a partir de las observaciones capturadas por un conjunto de sensores calibrados y con campos de visi��n solapados. La segunda extensi��n puede considerarse global, dado que su objetivo consiste en proporcionar un contexto global para relacionar las observaciones locales realizadas por una c��mara con una escena de mucho mayor tama��o; para ello se propone un sistema autom��tico de localizaci��n de c��maras basado en las trayectorias observadas de varios objetos m��viles y en un mapa esquem��tico de la escena global monitorizada. Ambas l��neas de investigaci��n se tratan utilizando, como marco com��n, t��cnicas de estimaci��n bayesiana: esta elecci��n est�� justificada por la versatilidad y flexibilidad proporcionada por dicho marco estad��stico, que permite la combinaci��n natural de m��ltiples fuentes de informaci��n sobre los par��metros a estimar, as�� como un tratamiento riguroso de la incertidumbre asociada a las mismas mediante la inclusi��n de modelos de observaci��n espec��ficamente dise��ados. Adem��s, el marco seleccionado abre grandes posibilidades operacionales, puesto que permite la creaci��n de diferentes m��todos num��ricos adaptados a las necesidades y caracter��sticas espec��ficas de distintos problemas tratados. El sistema de seguimiento 3D con m��ltiples c��maras propuesto est�� espec��ficamente dise��ado para permitir descripciones esquem��ticas de las medidas realizadas individualmente por cada una de las c��maras del sistema: esta elecci��n de dise��o, por tanto, no asume ning��n algoritmo espec��fico de detecci��n o seguimiento 2D en ninguno de los sensores de la red, y hace que el sistema propuesto sea aplicable a redes reales de vigilancia con capacidades limitadas tanto en t��rminos de procesamiento como de transmision. La combinaci��n robusta de las observaciones capturadas individualmente por las c��maras, ruidosas, incompletas y probablemente contaminadas por falsas detecciones, se basa en un metodo de asociaci��n bayesiana basado en geometr��a y color: los resultados de dicha asociaci��n permiten el seguimiento 3D de los objetos de la escena mediante el uso de un filtro de part��culas. El sistema de fusi��n de observaciones propuesto tiene, como principales caracter��sticas, una gran precisi��n en t��rminos de localizaci��n 3D de objetos, y una destacable capacidad de recuperaci��n tras eventuales errores debidos a un n��mero insuficiente de datos de entrada. El sistema autom��tico de localizaci��n de c��maras se basa en la observaci��n de m��ltiples objetos m��viles y un mapa esquem��tico de las ��reas transitables del entorno monitorizado para inferir la posici��n absoluta de dicho sensor. Para este prop��sito, se propone un novedoso marco bayesiano que combina modelos din��micos inducidos por el mapa en los objetos m��viles presentes en la escena con las trayectorias observadas por la c��mara, lo que representa un enfoque nunca utilizado en la literatura existente. El sistema de localizaci��n se divide en dos sub-tareas diferenciadas, debido a que cada una de estas tareas requiere del dise��o de algoritmos espec��ficos de muestreo para explotar en profundidad las caracter��sticas del marco desarrollado: por un lado, an��lisis de la ambig��edad del caso espec��ficamente tratado y estimaci��n aproximada de la localizaci��n de la c��mara, y por otro, refinado de la localizaci��n de la c��mara. El sistema completo, dise��ado y probado para el caso espec��fico de localizaci��n de c��maras en entornos de tr��fico urbano, podr��a tener aplicaci��n tambi��n en otros entornos y sensores de diferentes modalidades tras ciertas adaptaciones. ABSTRACT Mono-camera tracking systems have proved their capabilities for moving object trajectory analysis and scene monitoring, but their robustness and semantic possibilities are strongly limited by their local and monocular nature and are often insufficient for realistic surveillance applications. This thesis is aimed at extending the possibilities of moving object tracking systems to a higher level of scene understanding. The proposed extension comprises two separate directions. The first one is local, since is aimed at enriching the inferred positions of the moving objects within the area of the monitored scene directly covered by the cameras of the system; this task is achieved through the development of a multi-camera system for robust 3D tracking, able to provide 3D tracking information of multiple simultaneous moving objects from the observations reported by a set of calibrated cameras with semi-overlapping fields of view. The second extension is global, as is aimed at providing local observations performed within the field of view of one camera with a global context relating them to a much larger scene; to this end, an automatic camera positioning system relying only on observed object trajectories and a scene map is designed. The two lines of research in this thesis are addressed using Bayesian estimation as a general unifying framework. Its suitability for these two applications is justified by the flexibility and versatility of that stochastic framework, which allows the combination of multiple sources of information about the parameters to estimate in a natural and elegant way, addressing at the same time the uncertainty associated to those sources through the inclusion of models designed to this end. In addition, it opens multiple possibilities for the creation of different numerical methods for achieving satisfactory and efficient practical solutions to each addressed application. The proposed multi-camera 3D tracking method is specifically designed to work on schematic descriptions of the observations performed by each camera of the system: this choice allows the use of unspecific off-the-shelf 2D detection and/or tracking subsystems running independently at each sensor, and makes the proposal suitable for real surveillance networks with moderate computational and transmission capabilities. The robust combination of such noisy, incomplete and possibly unreliable schematic descriptors relies on a Bayesian association method, based on geometry and color, whose results allow the tracking of the targets in the scene with a particle filter. The main features exhibited by the proposal are, first, a remarkable accuracy in terms of target 3D positioning, and second, a great recovery ability after tracking losses due to insufficient input data. The proposed system for visual-based camera self-positioning uses the observations of moving objects and a schematic map of the passable areas of the environment to infer the absolute sensor position. To this end, a new Bayesian framework combining trajectory observations and map-induced dynamic models for moving objects is designed, which represents an approach to camera positioning never addressed before in the literature. This task is divided into two different sub-tasks, setting ambiguity analysis and approximate position estimation, on the one hand, and position refining, on the other, since they require the design of specific sampling algorithms to correctly exploit the discriminative features of the developed framework. This system, designed for camera positioning and demonstrated in urban traffic environments, can also be applied to different environments and sensors of other modalities after certain required adaptations.

A C1 finite element for Kirchhoff plate bending

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented.. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.

Dise��o de receptor de torre central para generaci��n directa de vapor con perfil de potencia variable longitudinal y transversalmente

En este estudio se ha realizado el dise��o de un receptor de una central de Torre Central de energ��a solar para generaci��n directa de vapor, mediante el uso de m��todos num��ricos, con un perfil de potencia incidente variable longitudinal y transversalmente. Para ello se ha dividido la geometr��a del receptor seg��n el m��todo de diferencias finitas, y se ha procedido a resolver las ecuaciones del balance de energ��a. Una vez resuelto el sistema de ecuaciones se dispone de la distribuci��n de temperaturas en el receptor y se puede proceder a analizar los resultados as�� como a calcular otros datos de inter��s. ABSTRACT In this study it has been made a Central Receiver Solar Thermal Power Plant���s Receiver design for direct steam production, by using numerical methods, with a variable longitudinally and transversely income solar power profile. With this propose, the receiver���s geometry has been divided using the finite difference method, and the energy balance equations have been solved. Once the equations system has been solved, the receiver��s temperature distribution is known, and you can analyze the results as well as calculate other interesting data.

Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given.

Some theoretical aspects in computational analysis of adhesive lap joints

This paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend-adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor of these singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro-crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro-cracks. Some numerical results are presented.