ITERATIVE METHODS

Author: Fe Marqués Jaime Miguel.
Year: 2004.
University: A CORUÑA [www.udc.es].
Place of defense: ETS Caminos, Canales y Puertos.
Place of preparation: ETS Caminos, Canales y Puertos.

Summary: The purpose of this work is resolution numerical equations delas shallow waters in two dimensions, taking into account the efforts due to the turbulence. It has developed a model consisting of a module and another hydrodynamic turbulence working together. For discretization has used the finite volume method, derived from a triangular mesh. The turbulence model chosen is the k-épsilon averaged in the vertical. Have been deducted in detail the equations of two-dimensional shallow waters with turbulent term from the Navier-Stokes equations using an average time, the vertical integration and various assumptions simplificativas, with three possible expressions for the turbulent term. It has applied the finite volume method for obtaining a hydrodynamic model: in a first approximation is not taken into account by adding the word turbulent source, which has led to the simplified hydrodynamic model, which has been validated by applying it to uni resolving various problems and two-dimensional, two of whom is a comparison with experimental measures. The derived by adding temporary equations shallow waters has discretizado three ways: by the methods of Euler forward, Adams-Moulton and Runge-Kutta. We have implemented all three at the same problem, comparing results and times of calculation. There were two expressions discretizado the end of the turbulent equations using two different methods for each. It has been obtained and discretizado how conservative the equations of the model of turbulence. Validation of the model has been conducted in three parts: In the first it has been shown to reduce the spread numerical discretization introduced the pair and has proposed the use of a coefficient descentrado within flow, making a comparison formulations and discretizaciones term studying turbulent and accelerating the process achieved with the use of methods of Adams-Moulton and Runge-Kutta. - In the second part, the model results obtained in the turbulence scale fish have been compared with experimental measures. The third has been devoted to presenting the full operation of model cycles, each composed of two gases, hydraulic and k-épsilon.

Author: SANDOVAL SOLIS MARIA LUISA.
Year: 2005.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: ETSECCPB.
Place of preparation: U FACULTAT DE MATEMATIQUES I ESTADISTICA SUD.

Summary: Various natural processes and industrial environmental interest are modeled by the equation convección-difusión-reacción transient. Two technological applications that have led to this thesis are the operation of activated charcoal filters and the dispersion of pollutants in the atmosphere. For the numerical modeling of these problems effectively is a critical need for an efficient solver for solving linear systems of equations obtained discretizar equation in partial derivatives, using finite elements. Therefore, the objective of this thesis is to efficiently solve the major systems of equations, defined symmetric positive (SDP), type sparse associated with the problems of convección-difusión transient. To this end explores preconditioners whether express or implied, as well as methods of decomposition domain (DD). The thesis is divided into three parts. In the first developing a detailed computational analysis of the behavior of two families of factoring incomplete Cholesky (FIC): Memory and prescribed threshold. These techniques are used to precondicionar the iterative method gradients conjugates (GWP). The second part is built around an approximate sparse symmetric (SSPAI) based on minimizing the norm of Frobenius. The precondicionador explicit is designed to solve large parallel systems of equations sparse, SDP, tridiagonales block with multiple sides rights. Finally, we developed the method of multiplicative Schwarz (MSM) in assets domains, ie DD overlapping with innovation to activate and deactivate domains. It examines the behavior of this strategy to solve subproblemas through: (1) the direct method of Cholesky and (2) GWP + FIC threshold. Of the numerical results presented it is concluded that it is preferable to use the direct method of Cholesky for systems with fewer than 30000 variables. For older systems, and even 80000 unknowns suggested using a threshold of FIC. And for even larger systems, the MSM domain assets GWP + + FIC proposed threshold is the most efficient using a single processor. For its part, SSPAI presented to the FIC could exceed threshold when working in parallel.

Author: ROMERO ÁLVAREZ NATALIA.
Year: 2005.
University: LA RIOJA [www.unirioja.es].
Place of defense: UNIVERSIDAD DE LA RIOJA.
Place of preparation: UNIVERSIDAD DE LA RIOJA.

Summary: The resolution of non-linear equations using iterative processes is the objective of this report. We raised families parametric analysis of iterative processes in Newton type Banach spaces, so that we can cover a wide range of problems, such as integral equations, equations in partial derivatives or securities problems at the border. We get in Banach spaces for a family of iterative processes in order convergence at least three, which includes the best-known iterative processes with at least cubic convergence, as the Chebyshev method, the method of Super-Halley, method of Halley or euler's method, as well as other families of iterative processes. Suavizamos gradually assumptions convergence ordinarily employed, obtaining domains of existence and uniqueness of solutions and levels of the a priori and a posteriori error. To address the convergence semilocal of the family in Banach spaces we use two different techniques: the principle of mayorante and based on the construction of a system of relations of recurrence. In the particular case of quadratic equations in Banach spaces, we set a family of iterative processes with preset order of convergence. It is interesting to note that in this case the parameters that appear in the family are defined from the Catalan numbers. For this family establish convergence semilocal in Banach spaces, in the real case if global convergence order is general convergence pair and if the order is odd, and at present a complex study of convergence from a numerical point of view and dynamic . In order to generalize the study to quadratic equations, we analyze the convergence of the family when it is applied in the resolution of a broader set of equations. We get a new family of iterative processes in order for the convergence pre forging results of convergence semilocal and comprehensive.

Author: PEREA DE DIOS CRISTIAN.
Year: 2006.
University: POLITÉCNICA DE VALENCIA [www.upv.es].
Place of defense: Dep. Ing. de la Cons. y Proy. de Ing. Civil.
Place of preparation: Universidad Politécnica de Valencia.

Summary: This paper addresses the design and automatic optimization of economic structures of reinforced concrete using heuristic methods to demonstrate the possibility of applying the optimization to the practice of engineering structures. The structures under investigation have been reinforced concrete frames of employees in the construction of roads and railways primarily as a step lower and also as drainage, as well as in urban areas for the passage of pedestrians and cyclists. The optimization methods have been employed both methods of search methods based on local populations, such as: Random Walk (RW), Descent Local Search (DLS), Simulated Annealing (SA) Threshold Accepting (TA), Genetic Algorithms (GA ) and Memetic Algorithms (MA). The structure is defined by a set of variables and parameters. The number of variables is used to 50, which can be divided into 3 geometric, 3 types of concrete and 44 on the armature. The proposed model has taken into account the practical application of the performance, and thus, all the armor are preparing to work in executable separations. The objective function used includes the cost of concrete and steel, considering the difficulty of placing different bars greater or lesser diameter, as well as the cost of shuttering and cimbra. The results for a concrete step below show that the random selection of variables is not an effective strategy optimization, the better cost per unit length is 5206.107 €. The DLS improves this solution reaching costs 4722.301 €, however this method tends to be a convergence premature because it is not able to escape minimum local low quality. TA and SA find solutions with cost 4592.300 €. GA and MA have been applied in sequential machines in computer systems in parallel with the MA getting the best result of 4579.729 €. The final model is the result of a long and painstaking process that has been critical frameworks obtained during the intermediate stages of the investigation. One example is the need for verification of the fatigue of concrete and steel under the burden of road, and include checking arrows. The slenderness of the optimal structure is within the bounds of normal practice constructive. The distances between bars are selected in a rational way, especially when using relationships diameter bar-cost steel. The metaheurística is capable of taking appropriate size, proper disposal of armor, and succeeds in placing reinforcements and their lengths, and so on. Finally, the proposed model has been used in real practical problems, achieving significant cost savings. We have built a tunnel to the underground of Palma de Mallorca with a total length exceeding 800 m, and a step lower in the city of Valencia over 500 m in length, using the optimal solutions obtained by the methods of optimization heuristics.

Author: REQUENA PÉREZ MARÍA EUGENIA.
Year: 2006.
University: POLITÉCNICA DE CARTAGENA [www.upct.es].
Place of defense: E.T.S. INGENIEROS DE TELECOMUNICACIÓN.
Place of preparation: ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE TELECOMUNICACIÓN - UPCT.

Summary: The use of dielectric materials in communications applications such as microwave heating applications exists a precise knowledge of the dielectric properties. The methods used so far do not provide the desired accuracy in some applications and further restrictions on the shape and uniformity of the sample. Therefore in this thesis has been developed and validated techniques inverse measure of permitivity novel that, through an evolutionary process based on genetic algorithms, they are able to estimate the electric permitivity samples with arbitrary shapes and materials both homogeneous and heterogeneous. With prior knowledge studied in the literature review deals with the design of new techniques reverse. The inverse techniques designed based on the optimization of an evaluation function by comparing genetic algorithms scattering parameters measured on a rectangular waveguide and those calculated by several electromagnetic simulators. Therefore, in each of the techniques is a process of optimización-simulación which operates as follows: initially, the optimization algorithm proposed values permitivity; with these values is applied to calculate electromagnetic simulation parameters ispesión simulated. The optimization algorithm calculates the evaluation function and proposes other values primitividad diminish the error. It iterates the process until it complies with the requirements for termination. The optimization algorithm that guide this process optimización-simulación is a genetic algorithm. In some cases is accelerating the convergence of genetic algorithm using the method Quasi-Newton. Each of the techniques developed using a simulation platform specific. The analytical technique was implemented equations cuadripolos cascading allowing estimate parameters of the S microwave network. Materials used in this technique should completely fill the section of the waveguide. The technique uses two-dimensional finite element method to calculate the areas in ports and on the basis of these equations are used to obtain the parameters of the dispersion of the structure. These structures must be invariant in the shaft and the guía-onda (lesser dimension). Finally the technique makes use of three-dimensional integration method for obtaining finite S parameters of the sample under study. This show has complete freedom in its geometry. The three techniques have been experimentally validated and applied to the extent of various structures was obtained successfully permitivity of them all. On the other hand has been developed and studied a new process of adapting microwave ovens warming which is based on the change in the position of the sample into the cavity. The study concludes that there is an optimal point at which fungi efficiency is highest, and discusses the dependence on this point with optimal frequency, permitivity, shape and size of the sample. The procedure is to be developed by varying the position of the sample along one of the pillars of the cavity and go measuring its reflection coefficient. It uses the method of Levenberg-Marquardt to find the optimum position. The simulations carried out show that the optimum position remains constant for different dielectric constant and loss factors greater than unity. The method of adjusting the burden has shown great sensitivity to the frequency of work, which requires a precise knowledge of the working frequency microwave 8 s. furnace