NUMERICAL ANALYSIS

Author: GONZALEZ RODRIGUEZ PEDRO.
Year: 2004.
University: CARLOS III DE MADRID [More theses of this university] [www.uc3m.es].
Place of defense: ESCUELA POLITECNICA SUPERIOR.
Place of preparation: UNIVERSIDAD CARLOS III DE MADRID.

Summary: This thesis explores two issues of great importance in the field of petroleum engineering, simulation and characterization of reservoirs. The first part describes and analyzes the method of power lines as an alternative to the problem very efficient simulation of secondary recovery process. We analyze its stability and digital convergence, and the use of techniques to simulate operator division of deposits in which the gravity and capillary pressure are important. To reduce the scattering has been used numerical method front-tracking in solving the equation of maintenance on the power lines. The accuracy and efficiency of the method has been tested by comparing their results with those obtained with finite difference methods. The second part examines the problem of characterization of deposits raised as a problem in calculating reverse one or more parameters of the model. The problem solved in the thesis is to determine the spatial distribution of permeability in the reservoir so as to minimize the error in the production data model regard to the experimental data. To that end, it uses a method of propagation retro-propagación obtained very satisfactory results of convergence. There have also been included two regularization techniques that help stabilize the algorithm and also allow adding certain types of information about the characteristics of the parameter or parameters to be calculated.

Author: SELGAS BUZNEGO VIRGINIA.
Year: 2005.
University: OVIEDO [More theses of this university] [www.uniovi.es].
Place of defense: SALA DE USOS MULTIPLES DE LA ESCUELA.
Place of preparation: FACULTAD DE MATEMATICAS DE LA UNIVERSIDAD DE SANTIAGO.

Summary: In this thesis we design and analyze a new numerical method for solving Maxwell equations cuasiestaticas raised in R3. This problem is apparent model of the Maxwell equations when despise the flow of movement and its use is very widespread in electrical engineering. As a first step, we assume that fields (magnetic and electric) with a sinusoidal behavior over time and that the domain that represents the driver is simply related. In this situation, we get a variational formulation raised in the region driving. We incorporate information from the field to our distant formulation through integral equations on the border of the computational domain. We propose to this Galerkin formulation of a scheme based on the simultaneous application of the finite element method Nedelec edge and boundary element method. We tested both the continuing problem as the discreet are raised. We show that the scheme has a numerical asymptotic convergence of optimal order depending on the parameter discrtización. We obtain numerical results that support our theoretical assertions. Then consider the case of a driver not merely related. Here, we introduce a computational bounded domain that contains the region of interest (the driver). This involves a restriction on the linear magnetic field, we try introducing a multiplier lagrange. We get with this technique variational formulation of a mixed approach that using a method of combining finite element Galerkin of Nedelec and Raviart-Thomas. Here also demonstrated that the continuous and discrete formulations are unique solution and provide an analysis of convergence of the method number. Finally we consider the problem of evolution in time without topological restrictions on the conductive zone. For this problem parabolic we deduce a variational formulation that is suitable for processing numerical finite element and boundary elements. Under assumption of regularity on the problem data, we provide an analysis of convergence of the scheme semi-discreto in space that we have proposed.

Author: LIFANTE NAVARRETE CONCEPCIO.
Year: 2005.
University: POLITÉCNICA DE CATALUÑA [More theses of this university] [www.upc.edu].
Place of defense: a sala de conferències de l'ETSEIAT:.
Place of preparation: ETSEIB, EDIFICI H PLANTA 8 Campus SUD.

Author: BELTRAN ALVAREZ CARLOS.
Year: 2005.
University: CANTABRIA [More theses of this university] [www.unican.es].
Place of defense: FACULTAD DE CIENCIAS.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: In the year 2000, the winner of the Fields medal Stephen Smale proposed 18 math problems for the next century. The number 17 of these problems question on the existence of an algorithm that approximates system solutions multivariate equations with complex coefficients, in a time polilnomial in half in the size of input. This thesis presents the first probabilistic solution to this problem. That is, an algorithm is described with the property that, given a system of polynomial equations, find an approximate solution in polynomial time, accepting a small probability of error that can be adjusted depending on the needs and resources. As a preliminary step to solving this problem, it introduces many intermediate results to analyze the behavior of the average amounts associated with the complexity of resolution, as well as the stability of the problem. In particular, they draw heights volume of tubes and pipes intersection with varieties that allow estimation using a technique generally all problems in the number of conditioning linear and non-linear, in a widely generalized. The results are studied both from a standpoint of continuous computing as from a discreet, contributed to the latter objective heights finest known until early transfer of discrete continuous outcomes, particularly in the case of defined problems design mode. Other results also show purely geometric and algebraic with self-interest, and other amounts are estimated assistants some relevance, as the average standard solutions of a system of polynomial equations with complex coefficients.

Author: DADVAND POOYAN.
Year: 2006.
University: POLITÉCNICA DE CATALUÑA [More theses of this university] [www.upc.edu].
Place of defense: Sala de Seminarios del C.I.de M.N. en I..
Place of preparation: EDIFICI C1 Campus NORD.

Summary: The world of computing simulation has experienced great progresses in recent years and requires more exigent multidisciplinary challenges to satisfy the new upcoming demands. Increasing the importance of solving multi-disciplinary problems makes developers put more attention to these problems and deal with difficulties involved in developing software in this area. Conventional finite element codes have several difficulties in dealing with multi-disciplinary problems. Many of these codes are designed and implemented for solving a certain type of problems, generally involving a single field. Extending these codes to deal with another field of analysis usually consists of several problems and large amounts of modifications and implementations. Some typical difficulties are: predefined set of degrees of freedom per node, data structure with fixed set of defined variables, global list of variables for all entities, domain based interfaces, IO restriction in reading new data and writing new results and algorithm definition inside the code. A common approach is to connect different solvers via a master program which implements the interaction algorithms and also transfers data from one solver to another. This approach has been used successfully in practice but results duplicated implementation and redundant overhead of data storing and transferring which may be significant depending to the solvers data structure. The objective of this thesis is to design and implement a framework for building multi-disciplinary finite element programs. Generality, reusability, extendibility, good performance and memory efficiency are considered to be the main points in design and implementation of this framework. Preparing the structure for team development is another objective because usually a team of experts in different fields are involved in the development of multi-disciplinary code. Kratos, the framework created in this work, provides several tools for easy implementation of finite element applications and also provides a common platform for natural interaction of its applications in different ways. This is done not only by a number of innovations but also by collecting and reusing several existing works. In this work an innovative variable base interface is designed and implemented which is used at different levels of abstraction and showed to be very clear and extendible. Another innovation is a very efficient and flexible data structure which can be used to store any type of data in a type-safe manner. An extendible IO is also created to overcome another bottleneck in dealing with multi-disciplinary problems. Collecting different concepts of existing works and adapting them to coupled problems is considered to be another innovation in this work. Examples are using an interpreter, different data organizations and variable number of dofs per node. The kernel and application approach is used to reduce the possible conflicts arising between developers of different fields and layers are designed to reflect the working space of different developers also considering their programming knowledge. Finally several technical details are applied in order to increase the performance and efficiency of Kratos which makes it practically usable. This work is completed by demonstrating the framework’s functionality in practice. First some classical single field applications like thermal, fluid and structural applications are implemented and used as benchmark to prove its performance. These applications are used to solve coupled problems in order to demonstrate the natural interaction facility provided by the framework. Finally some less classical coupled finite element algorithms are implemented to show its high flexibility and extendibility.

Author: HERRERO VIÑAS PAU.
Year: 2006.
University: GIRONA [More theses of this university] [www.udg.es].
Place of defense: ESCOLA POLITÈCNICA SUPERIOR.
Place of preparation: UNIVERSITAT DE GIRONA.

Summary: A restriction real quantified, Quantified Royal Constraint (QRC) in English, is a mathematical formalism that allows modeling a large number of physical problems represented by systems of nonlinear equations and logical quantified on real variables. The QRCs appear large fields, com or control engineering, electrical engineering or biology. Different approaches have been proposed for solving QRCs (peeliminación of quantifiers and methods approximate), but all of them have major limitations due to its computational complexity. In this thesis, presents a new methodology for solving QRCs based on the analysis Intervelar Modal, a mathematical theory developed by researchers at the University of Barcelona and the University of Girona. With respect to existing methods, the proposed methodology resolved, in an efficient manner, a broad class of QRCs.