963 resultados para Picard iteration
Resumo:
Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.
Resumo:
Software Product Line Engineering (SPLE) has proved to have significant advantages in family-based software development, but also implies the up¬front design of a product-line architecture (PLA) from which individual product applications can be engineered. The big upfront design associated with PLAs is in conflict with the current need of "being open to change". However, the turbulence of the current business climate makes change inevitable in order to stay competitive, and requires PLAs to be open to change even late in the development. The trend of "being open to change" is manifested in the Agile Software Development (ASD) paradigm, but it is spreading to the domain of SPLE. To reduce the big upfront design of PLAs as currently practiced in SPLE, new paradigms are being created, one being Agile Product Line Engineering (APLE). APLE aims to make the development of product-lines more flexible and adaptable to changes as promoted in ASD. To put APLE into practice it is necessary to make mechanisms available to assist and guide the agile construction and evolution of PLAs while complying with the "be open to change" agile principle. This thesis defines a process for "the agile construction and evolution of product-line architectures", which we refer to as Agile Product-Line Archi-tecting (APLA). The APLA process provides agile architects with a set of models for describing, documenting and tracing PLAs, as well as an algorithm to analyze change impact. Both the models and the change impact analysis offer the following capabilities: Flexibility & adaptability at the time of defining software architectures, enabling change during the incremental and iterative design of PLAs (anticipated or planned changes) and their evolution (unanticipated or unforeseen changes). Assistance in checking architectural integrity through change impact analysis in terms of architectural concerns, such as dependencies on earlier design decisions, rationale, constraints, and risks, etc.Guidance in the change decision-making process through change im¬pact analysis in terms of architectural components and connections. Therefore, APLA provides the mechanisms required to construct and evolve PLAs that can easily be refined iteration after iteration during the APLE development process. These mechanisms are provided in a modeling frame¬work called FPLA. The contributions of this thesis have been validated through the conduction of a project regarding a metering management system in electrical power networks. This case study took place in an i-smart software factory and was in collaboration with the Technical University of Madrid and Indra Software Labs. La Ingeniería de Líneas de Producto Software (Software Product Line Engi¬neering, SPLE) ha demostrado tener ventajas significativas en el desarrollo de software basado en familias de productos. SPLE es un paradigma que se basa en la reutilización sistemática de un conjunto de características comunes que comparten los productos de un mismo dominio o familia, y la personalización masiva a través de una variabilidad bien definida que diferencia unos productos de otros. Este tipo de desarrollo requiere el diseño inicial de una arquitectura de línea de productos (Product-Line Architecture, PLA) a partir de la cual los productos individuales de la familia son diseñados e implementados. La inversión inicial que hay que realizar en el diseño de PLAs entra en conflicto con la necesidad actual de estar continuamente "abierto al cam¬bio", siendo este cambio cada vez más frecuente y radical en la industria software. Para ser competitivos es inevitable adaptarse al cambio, incluso en las últimas etapas del desarrollo de productos software. Esta tendencia se manifiesta de forma especial en el paradigma de Desarrollo Ágil de Software (Agile Software Development, ASD) y se está extendiendo también al ámbito de SPLE. Con el objetivo de reducir la inversión inicial en el diseño de PLAs en la manera en que se plantea en SPLE, en los último años han surgido nuevos enfoques como la Ingeniera de Líneas de Producto Software Ágiles (Agile Product Line Engineering, APLE). APLE propone el desarrollo de líneas de producto de forma más flexible y adaptable a los cambios, iterativa e incremental. Para ello, es necesario disponer de mecanismos que ayuden y guíen a los arquitectos de líneas de producto en el diseño y evolución ágil de PLAs, mientras se cumple con el principio ágil de estar abierto al cambio. Esta tesis define un proceso para la "construcción y evolución ágil de las arquitecturas de lineas de producto software". A este proceso se le ha denominado Agile Product-Line Architecting (APLA). El proceso APLA proporciona a los arquitectos software un conjunto de modelos para de¬scribir, documentar y trazar PLAs, así como un algoritmo para analizar vel impacto del cambio. Los modelos y el análisis del impacto del cambio ofrecen: Flexibilidad y adaptabilidad a la hora de definir las arquitecturas software, facilitando el cambio durante el diseño incremental e iterativo de PLAs (cambios esperados o previstos) y su evolución (cambios no previstos). Asistencia en la verificación de la integridad arquitectónica mediante el análisis de impacto de los cambios en términos de dependencias entre decisiones de diseño, justificación de las decisiones de diseño, limitaciones, riesgos, etc. Orientación en la toma de decisiones derivadas del cambio mediante el análisis de impacto de los cambios en términos de componentes y conexiones. De esta manera, APLA se presenta como una solución para la construcción y evolución de PLAs de forma que puedan ser fácilmente refinadas iteración tras iteración de un ciclo de vida de líneas de producto ágiles. Dicha solución se ha implementado en una herramienta llamada FPLA (Flexible Product-Line Architecture) y ha sido validada mediante su aplicación en un proyecto de desarrollo de un sistema de gestión de medición en redes de energía eléctrica. Dicho proyecto ha sido desarrollado en una fábrica de software global en colaboración con la Universidad Politécnica de Madrid e Indra Software Labs.
Resumo:
Abstraction-Carrying Code (ACC) is a framework for mobile code safety in which the code supplier provides a program together with an abstraction (or abstract model of the program) whose validity entails compliance with a predefined safety policy. The abstraction plays thus the role of safety certificate and its generation is carried out automatically by a fixed-point analyzer. The advantage of providing a (fixed-point) abstraction to the code consumer is that its validity is checked in a single pass (i.e., one iteration) of an abstract interpretation-based checker. A main challenge to make ACC useful in practice is to reduce the size of certificates as much as possible, while at the same time not increasing checking time. Intuitively, we only include in the certificate the information which the checker is unable to reproduce without iterating. We introduce the notion of reduced certifícate which characterizes the subset of the abstraction which a checker needs in order to validate (and re-construct) the full certificate in a single pass. Based on this notion, we show how to instrument a generic analysis algorithm with the necessary extensions in order to identify the information relevant to the checker.
Resumo:
Abstraction-Carrying Code (ACC) has recently been proposed as a framework for mobile code safety in which the code supplier provides a program together with an abstraction (or abstract model of the program) whose validity entails compliance with a predefined safety policy. The abstraction plays thus the role of safety certifícate and its generation is carried out automatically by a fixed-point analyzer. The advantage of providing a (fixed-point) abstraction to the code consumer is that its validity is checked in a single pass (i.e., one iteration) of an abstract interpretation-based checker. A main challenge to make ACC useful in practice is to reduce the size of certificates as much as possible while at the same time not increasing checking time. The intuitive idea is to only include in the certifícate information that the checker is unable to reproduce without iterating. We introduce the notion of reduced certifícate which characterizes the subset of the abstraction which a checker needs in order to validate (and re-construct) the full certifícate in a single pass. Based on this notion, we instrument a generic analysis algorithm with the necessary extensions in order to identify information which can be reconstructed by the single-pass checker. Finally, we study what the effects of reduced certificates are on the correctness and completeness of the checking process. We provide a correct checking algorithm together with sufficient conditions for ensuring its completeness. Our ideas are illustrated through a running example, implemented in the context of constraint logic programs, which shows that our approach improves state-of-the-art techniques for reducing the size of certificates.
Resumo:
Abstraction-Carrying Code (ACC) has recently been proposed as a framework for mobile code safety in which the code supplier provides a program together with an abstraction (or abstract model of the program) whose validity entails compliance with a predefined safety policy. The abstraction plays thus the role of safety certificate and its generation is carried out automatically by a fixpoint analyzer. The advantage of providing a (fixpoint) abstraction to the code consumer is that its validity is checked in a single pass (i.e., one iteration) of an abstract interpretation-based checker. A main challenge to make ACC useful in practice is to reduce the size of certificates as much as possible while at the same time not increasing checking time. The intuitive idea is to only include in the certificate information that the checker is unable to reproduce without iterating. We introduce the notion of reduced certificate which characterizes the subset of the abstraction which a checker needs in order to validate (and re-construct) the fall certificate in a single pass. Based on this notion, we instrument a generic analysis algorithm with the necessary extensions in order to identify the information relevant to the checker. Interestingly, the fact that the reduced certificate omits (parts of) the abstraction has implications in the design of the checker. We provide the sufficient conditions which allow us to ensure that 1) if the checker succeeds in validating the certificate, then the certificate is valid for the program (correctness) and 2) the checker will succeed for any reduced certificate which is valid (completeness). Our approach has been implemented and benchmarked within the CiaoPP system. The experimental results show t h a t our proposal is able to greatly reduce the size of certificates in practice. To appear in Theory and Practice of Logic Programming (TPLP).
Resumo:
RESUMEN Los procesos de diseño de zonas o diseño del territorio implican la partición de un espacio geográfico, organizado en un conjunto de unidades de área, en diferentes regiones o zonas según un conjunto especifico de criterios que varían en función del campo de aplicación. En la mayoría de los casos, el objetivo fundamental consiste en crear zonas de tamaño aproximadamente igual respecto a uno o varios atributos de medida -de carácter cuantitativo- (zonas con igual número de habitantes, igual promedio de ventas...). Sin embargo, están apareciendo nuevas aplicaciones, algunas en el contexto de las políticas de desarrollo sostenible, cuya finalidad es la definición de regiones con un tamaño predeterminado, no necesariamente similar. Además, en estos casos las zonas han de formarse en torno a un conjunto específico de posiciones, semillas o generadores. Este tipo de particiones no han sido lo suficientemente investigadas, de manera que no se conocen modelos de solución para la delimitación automática de las zonas. En esta tesis se ha diseñado un nuevo método basado en una versión discreta del diagrama de Voronoi con peso aditivo adaptativo (DVPAA), que permite la partición de un espacio bidimensional en zonas de un tamaño específico, considerando tanto la posición como el peso de cada uno de los generadores. El método consiste en resolver repetidamente un tradicional diagrama de Voronoi con peso aditivo, de forma que los pesos de cada generador se actualizan en cada iteración. En el proceso de cálculo de distancias se usa una métrica basada en el camino más corto, lo que garantiza que la partición obtenida esté formada por un conjunto de zonas conexas. La heurística diseñada se integra en una aplicación prototipo, desarrollada en un entorno SIG (Sistemas de Información Geográfica), que permite el trazado automático de zonas según los criterios anteriormente expuestos. Para analizar la viabilidad del método se ha utilizado como caso de estudio la gestión de los recursos pastorales para la ganadería extensiva en tres municipios de Castilla-La Mancha. Las pruebas realizadas ponen de manifiesto que la heurística diseñada, adaptada a los criterios que se plantean en el contexto de la gestión de sistemas extensivos agropecuarios, es válida para resolver este tipo de problemas de partición. El método propuesto se caracteriza por su eficacia en el tratamiento de un gran número de unidades superficiales en formato vectorial, generando soluciones que convergen con relativa rapidez y verifican los criterios establecidos. En el caso estudiado, aunque la posición prefijada de los generadores reduce considerablemente la complejidad del problema, existen algunas configuraciones espaciales de estos elementos para las que el algoritmo no encuentra una solución satisfactoria, poniéndose de manifiesto una de las limitaciones de este modelo. Tal y como se ha podido comprobar, la localización de los generadores puede tener un considerable impacto en la zonificación resultante, por lo que, de acuerdo con Kalcsics et al. (2005), una selección "inadecuada" difícilmente puede generar regiones válidas que verifiquen los criterios establecidos. ABSTRACT Tenitory or zone design processes entail partitioning a geographic space, organized as a set of basic areal units, into different regions or zones according to a specific set of entena that are dependent on the application context. In most cases the aim is to create zones that have approximately equal sizes with respect to one or several measure attributes (zones with equal numbers of inhabitants, same average sales, etc). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of positions, seeds or generators. This type of partitioning has not been sufñciently researched; therefore there are no known approaches for automated zone delimitation. This thesis proposes a new method based on a discrete versión of the Adaptive Additively Weighted Voronoi Diagram (AAWVD) that makes it possible to partition a 2D space into zones of specific sizes, taking both the position and the weight of each (seed) generator into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that the weights of each generator are updated at every iteration. The partition s zones are geographically connected nsing a metric based 011 the shortest path. The proposed heuristic lias been included in an application, developed in a GIS environment that allows the automated zone delimitation according to the mentioned criteria. The management of the extensive farming system of three municipalities of Castilla-La Mancha (Spain) has been used as study case to analyze the viability of the method. The tests carried out have established that the proposed method, adapted to the criteria of this application field, is valid for solving this type of partition problem. The applied algorithm is capable of handling a high number of vector areal units, generating solutions that converge in a reasonable CPU time and comply with the imposed constraints. Although the complexity of this problem is greatly reduced when the generator's positions are fixed, in many cases, these positions impose a spatial confignration that the algorithm proposed is unable to solve, thus revealing one of the limitations of this method. It has been shown that the location of the generators has a considerable impact on the final solution, so that, as Kalcsics et al. (2005) observed, an "inadequate" selection can hardly generate valid zones that comply with the established criteria.
Resumo:
This paper proposes the optimization relaxation approach based on the analogue Hopfield Neural Network (HNN) for cluster refinement of pre-classified Polarimetric Synthetic Aperture Radar (PolSAR) image data. We consider the initial classification provided by the maximum-likelihood classifier based on the complex Wishart distribution, which is then supplied to the HNN optimization approach. The goal is to improve the classification results obtained by the Wishart approach. The classification improvement is verified by computing a cluster separability coefficient and a measure of homogeneity within the clusters. During the HNN optimization process, for each iteration and for each pixel, two consistency coefficients are computed, taking into account two types of relations between the pixel under consideration and its corresponding neighbors. Based on these coefficients and on the information coming from the pixel itself, the pixel under study is re-classified. Different experiments are carried out to verify that the proposed approach outperforms other strategies, achieving the best results in terms of separability and a trade-off with the homogeneity preserving relevant structures in the image. The performance is also measured in terms of computational central processing unit (CPU) times.
Resumo:
The arrival of European master masons to Burgos and Toledo during the mid-fifteenth century was essential for the promotion of the late Gothic ribbed vault design techniques in Spain. The Antigua Chapel in Seville Cathedral, designed by the Spanish master mason Simón de Colonia on 1497, provides an outstanding case study on this subject. This vault is characterized by the interlacing of the ribs near the springing, reflecting the influence of German ribbed vault designs. This paper analyses the relationship between German ribbed vaults and their design methods with those of Spanish ribbed vaults; with particular attention to the presence of ribs that cut through one another above the springing, materialized in the work of Simón de Colonia. This characteristic is reflected in some manuscripts in the German area, like the Wiener Sammlungen (15th-16th centuries) and the Codex Miniatus 3 (ca. 1560-1570), but no Spanish documents of the same period make reference to it.
Resumo:
The vault of the sacristy of the Cathedral of Saint-Jean Baptiste in Perpignan (France), constructed by the Majorcan architect Guillem Sagrera between 1433 and 1447, is an outstanding, yet strikingly unknown, example of rib vaulting. This paper analyzes the overall construction of the form of the vault, characterized by its highly irregular perimeter, with particular attention to an isolated decorated corbel which solves the problem of the wall support of a group of six ribs and is in stark contrast with the rest of the supports, which are completely unadorned. Given the extreme rigour of Sagrera in all his works (and this one in particular), this apparent “capriccio” must be justified not only by decorative or formal requirements, but also by the constructive logic of Gothic vaulting system
Resumo:
A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.
Resumo:
Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed?s weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition.
Resumo:
El objetivo principal de esta tesis es el desarrollo de herramientas numéricas basadas en técnicas de onda completa para el diseño asistido por ordenador (Computer-Aided Design,‘CAD’) de dispositivos de microondas. En este contexto, se desarrolla una herramienta numérica basada en el método de los elementos finitos para el diseño y análisis de antenas impresas mediante algoritmos de optimización. Esta técnica consiste en dividir el análisis de una antena en dos partes. Una parte de análisis 3D que se realiza sólo una vez en cada punto de frecuencia de la banda de funcionamiento donde se sustituye una superficie que contiene la metalización del parche por puertas artificiales. En una segunda parte se inserta entre las puertas artificiales en la estructura 3D la superficie soportando una metalización y se procede un análisis 2D para caracterizar el comportamiento de la antena. La técnica propuesta en esta tesis se puede implementar en un algoritmo de optimización para definir el perfil de la antena que permite conseguir los objetivos del diseño. Se valida experimentalmente dicha técnica empleándola en el diseño de antenas impresas de banda ancha para diferentes aplicaciones mediante la optimización del perfil de los parches. También, se desarrolla en esta tesis un procedimiento basado en el método de descomposición de dominio y el método de los elementos finitos para el diseño de dispositivos pasivos de microonda. Se utiliza este procedimiento en particular para el diseño y sintonía de filtros de microondas. En la primera etapa de su aplicación se divide la estructura que se quiere analizar en subdominios aplicando el método de descomposición de dominio, este proceso permite analizar cada segmento por separado utilizando el método de análisis adecuado dado que suele haber subdominios que se pueden analizar mediante métodos analíticos por lo que el tiempo de análisis es más reducido. Se utilizan métodos numéricos para analizar los subdominios que no se pueden analizar mediante métodos analíticos. En esta tesis, se utiliza el método de los elementos finitos para llevar a cabo el análisis. Además de la descomposición de dominio, se aplica un proceso de barrido en frecuencia para reducir los tiempos del análisis. Como método de orden reducido se utiliza la técnica de bases reducidas. Se ha utilizado este procedimiento para diseñar 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, precisión y eficiencia en el diseño 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.
Resumo:
El objetivo de este trabajo es evaluar la influencia de la utilización de una muestra de calentamiento sobre la respuesta emocional del consumidor. Para el estudio de la respuesta emocional del consumidor se ha traducido al español el léxico propuesto por King y Meiselman (2010) y se ha aplicado el método EsSense Profile propuesto por dichos autores, con un total de 38 términos. La prueba ha sido realizada por 69 consumidores sobre dos marcas de chocolate distintas. El orden de presentación se equilibró de forma que cada producto apareciese el mismo número de veces en la primera posición. Después de probar un producto, los consumidores evaluaban primero su aceptación mediante la escala hedónica de 9 puntos. Luego, describían cómo se sentían, puntuando cada uno de los sentimientos de la lista en una escala de 5 puntos desde “nada en absoluto” hasta “muchísimo”. Se observaron diferencias estadísticamente significativas en la respuesta del consumidor en función de la posición del producto. Tanto para la evaluación hedónica como para algunas emociones, la muestra evaluada en primer lugar presenta una puntuación más extrema que la otra, independientemente de cuál de las dos muestras se presente primero. Este estudio demuestra la importancia de usar una muestra de calentamiento en ese tipo de experimento para evitar el sesgo debido al orden de presentación. Además se comprueba que el método EsSense Profile se puede adaptar al español para describir la respuesta emocional de los consumidores.
Resumo:
Software architecture is a key factor to scale up Agile Software Development ASD in large softwareintensive systems. Currently, software architectures are more often approached through mechanisms that enable to incrementally design and evolve software architectures aka. agile architecting. Agile architecting should be a light-weight decision-making process, which could be achieved by providing knowledge to assist agile architects in reasoning about changes. This paper presents the novel solution of using change-impact knowledge as the main driver for agile architecting. The solution consists of a Change Impact Analysis technique and a set of models to assist agile architects in the change -decision-making- process by retrieving the change-impact architectural knowledge resulting from adding or changing features iteration after iteration. To validate our approach, we have put our solution into practice by running a project of a metering management system in electric power networks in an i-smart software factory.
Resumo:
La ecuación en derivadas parciales de advección difusión con reacción química es la base de los modelos de dispersión de contaminantes en la atmósfera, y los diferentes métodos numéricos empleados para su resolución han sido objeto de amplios estudios a lo largo de su desarrollo. En esta Tesis se presenta la implementación de un nuevo método conservativo para la resolución de la parte advectiva de la ecuación en derivadas parciales que modela la dispersión de contaminantes dentro del modelo mesoescalar de transporte químico CHIMERE. Este método está basado en una técnica de volúmenes finitos junto con una interpolación racional. La ventaja de este método es la conservación exacta de la masa transportada debido al empleo de la ley de conservación de masas. Para ello emplea una formulación de flujo basado en el cálculo de la integral ponderada dentro de cada celda definida para la discretización del espacio en el método de volúmenes finitos. Los resultados numéricos obtenidos en las simulaciones realizadas (implementando el modelo conservativo para la advección en el modelo CHIMERE) se han comparado con los datos observados de concentración de contaminantes registrados en la red de estaciones de seguimiento y medición distribuidas por la Península Ibérica. Los datos estadísticos de medición del error, la media normalizada y la media absoluta normalizada del error, presentan valores que están dentro de los rangos propuestos por la EPA para considerar el modelo preciso. Además, se introduce un nuevo método para resolver la parte advectivadifusiva de la ecuación en derivadas parciales que modeliza la dispersión de contaminantes en la atmósfera. Se ha empleado un método de diferencias finitas de alto orden para resolver la parte difusiva de la ecuación de transporte de contaminantes junto con el método racional conservativo para la parte advectiva en una y dos dimensiones. Los resultados obtenidos de la aplicación del método a diferentes situaciones incluyendo casos académicos y reales han sido comparados con la solución analítica de la ecuación de advección-difusión, demostrando que el nuevo método proporciona un resultado preciso para aproximar la solución. Por último, se ha desarrollado un modelo completo que contempla los fenómenos advectivo y difusivo con reacción química, usando los métodos anteriores junto con una técnica de diferenciación regresiva (BDF2). Esta técnica consiste en un método implícito multipaso de diferenciación regresiva de segundo orden, que nos permite resolver los problemas rígidos típicos de la química atmosférica, modelizados a través de sistemas de ecuaciones diferenciales ordinarias. Este método hace uso de la técnica iterativa Gauss- Seidel para obtener la solución de la parte implícita de la fórmula BDF2. El empleo de la técnica de Gauss-Seidel en lugar de otras técnicas comúnmente empleadas, como la iteración por el método de Newton, nos proporciona rapidez de cálculo y bajo consumo de memoria, ideal para obtener modelos operativos para la resolución de la cinética química atmosférica. 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.