RESOLUTION OF DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES

Author: GONZÁLEZ IBÁÑEZ DAVID.
Year: 2003.
University: ZARAGOZA [www.unizar.es].
Place of defense: CENTRO POLITÉCNICO SUPERIOR.
Place of preparation: CENTRO POLITÉCNICO SUPERIOR Y FACULTAD DE CIENCIAS.

Summary: The development of numerical methods for simulating physical phenomena has sufirdo in these last decades significant progress, both by the advancement of information technology in place to deal with more complex problems, such as the emergence of new numerical simulation techniques. The difficulties that offers the most developed and most popular method of Finite elements, such as automatic generation of a mesh computational domain in the study or restrictions should be imposed on it have forced the emergence of new technologies, yet developing, which disappears grid computing as the basis of its study. These methods without presenting mesh however certain shortcomings in its implementation, stressing that most of them offer a poor approximation of the essential conditions contour due to non interpolante (but approximant) of the functions of the form of these methods, why The approximation domain convex or not formed by several materials requires special techniques to ensure compliance of the methods. In recent years there has developed a method without mesh, following the philosophy of this kind of methods, it comes to improving some of the shortcomings that appear in these methods. This method is called the Method of Natural Elements (MEN). It is strictly interpolante since its formulation and enforcement of the boundary conditions and interface very similar to the method of Finite Elements. Although this method does not solve all the problems that initially raised methods without mesh, which can highlight the need to develop numerical one paper to reduce errors due to the numerical integration, is a major step towards building an alternative to efficient the technique Finite elements in those problems where they show weaknesses. One of the aspects that are discussed in this thesis has been to develop new techniques applied to the numerical integration MEN. It has been noted how the use of a technique of integration Nodal stabilized offers highly satisfactory results besides being very proper technique for using an approximation using Natural Elements because of the nature of their construction, for being based on the construction of the Diagram the Voronoi and Delaunay triangulation, to share the same philosophy. The extension of the approach to problems in 3 dimensions also offers excellent results, leaving evinced a clear alternative to the widespread use of the Finite Elements in some kind of trouble. One feature not previously commented on the characteristics of the MEN is compliance with the paradigm of the partition of the drive. This feature allows for the enrichment of joint approaches in excess of the volume lock that usually presents techniques Finite elements and Natural Elements in the simulation means incompressible. Consequently, there have been various algorithms to simulate guarantees these problems. It has been proven numerically status LBB through a test widely due to widespread Chapelle and Bathe. A good test to test the ability of the method is its application to Fluid Dynamics. The use of this technique under a Lagrangian point of view (usually these problems are used under a Euleriana) combined with the method of characteristics, which offers very attractive properties for the technique used by the MEN and behaves in a manner reliable such simulations. Again, the MEN is shown as a promising alternative to the use of the method of Finite Elements in this kind of problems.

Author: PEREZ DEL PALOMAR ALDEA AMAYA.
Year: 2003.
University: ZARAGOZA [www.unizar.es].
Place of defense: CENTRO POLITECNICO SUPERIOR.
Place of preparation: CENTRO POLITECNICO SUPERIOR.

Summary: THESIS DOCTORAL THIS IS ENGLOBADA WITHIN THE BIOMECÁNICA, DISCIPLINE TO APPLY THE PRINCIPLES FOR CHARACTERIZATION OF MECHANICAL SYSTEMS BIOLOGICAL. WITHIN THE LARGE FIELD THIS INCLUDES DISCIPLINE, THESIS ON THIS STUDY HAS BEEN FOCUSING ON THE CHARACTERIZATION OF SOFT TISSUE BIOLOGICAL AND INCLUDING THE CARTÍLAGO AND THE IMPLEMENTATION OF THESE MODELS TO THE BEHAVIOR OF THE BIOMECÁNICA CHARACTERIZATION OF A JOINT. KEY OBJECTIVES OF THIS HAVE BEEN THESIS TWO: FIRST PLACE IN THE DEVELOPMENT OF A NEW MODEL FOR BEHAVIOR FOR CARTÍLAGO IN BIG DEFORMACIONES, SIMULATING ITS MAIN FEATURES MECHANICAL HOW IS YOUR CHARACTER BIFÁSICO WITH THE INTRODUCTION OF THE PERMEABILIDAD AND POROSIDAD DEPENDENT THE DEFORMACIÓN, HIS CHARACTER INCOMPRESIBLE, AND THEIR BEHAVIOR ANISÓTROPO DUE TO THE LIKELIHOOD OF AN IMPORTANT NETWORK FIBROSA FORMADA BY FIBERS ON COLLAGEN YOU CONFIEREN AN IMPORTANT RESISTANCE TRACCIÓN; YEN SECOND PLACE THE IMPLEMENTATION OF THIS MODEL BEHAVIOR TO A REAL AS IS ELEMENT THE DISCO ARTICULAR OF COMPATIBILITY TEMPOROMANDIBULAR (ATM) HUMAN. THE ELECTION OF IMPLEMENTATION OF THE MODEL TO MTA HAS PROPICIADA BY THE HIGH NUMBER PATOLOGÍAS ASSOCIATED WITH THE SAME AND GROWING INTEREST OF MEDICAL SPECIALISTS IN THE KNOWLEDGE OF THIS BIOMECÁNICA COMPLEJA COMPATIBILITY. HOW TO CONCLUSIONS THESIS LEARNED IN THIS MAY BE IMPORTANT IN FIRST PLACE THAT THE PROPOSED MODEL BEHAVIOR FOR CARTÍLAGO CHARACTERIZES THE RESPONSE OF THE SAME IN BIG DEFORMACIONES FOR EXAMPLES OF VALIDATION ESTUDIADOS. FURTHER. THE INTRODUCTION OF THIS MODEL IN THE DISCO ARTICULAR OF THE ATM ALLOWED PREDECIR THAT IN THE EVENT OF THE ATM SANA THE AREA THAT ABSORBE MORE TENSION IS THE SIDE OF THE AREA INTERMEDIATE DISCO ARTICULAR, AND HOW IS THIS AREA LATER DISPLACE OCCURS WHEN A MOVING PAST DISK ARTICULAR. THE MOST IMPORTANT CONTRIBUTIONS ORIGINAL THESIS LEARNED IN THIS HAVE BEEN THE FOLLOWING: DEVELOPMENT OF A MODEL POROHIPERELÁSTICO FIBRADO IN BIG DEFORMACIONES FOR SOFT TISSUE HIDRATADOS IN PARTICULAR FOR CARTÍLAGO, THE INTRODUCTION OF THE RESTRICTION INCOMPRESIBILIDAD IN TISSUE BIFÁSICOS FROM AN APPROACH LAGRANGIANO ENHANCE THE LINEARIZATION Consistency OF THIS MODEL FOR ACHIEVING THE SPEED OF CONVERGENCE CUADRÁTICA IN THE SCHEME ITERATIVO RESOLUTION, THE MAKING OF A COMPLETE MODEL OF THREE-DIMENSIONAL ATM THAT INCORPORATES THE TEMPORARY, THE MANDÍBULA, ARTICULARES THE DISCS AND LIGAMENTOS MORE IMPORTANT THE INTRODUCTION OF A MODEL BEHAVIOR OF REAL FOR DISC ARTICULAR FOR THE SIMULATION OF COMPATIBILITY PATOLÓGICA AS BOTH HEALTHY AND THE STUDY OF THE INFLUENCE OF DIFFERENT TECHNIQUES QUIRÚRGICAS ON THE BEHAVIOR OF COMPATIBILITY.

Author: PEREZ ANSON MARIA ANGELES.
Year: 2003.
University: ZARAGOZA [www.unizar.es].
Place of defense: CENTRO POLITECNICO SUPERIOR.
Place of preparation: CENTRO POLITECNICO SUPERIOR.

Summary: THESIS DOCTORAL THIS IS ENGLOBA WITHIN THE LINE OF INQUIRY KNOWN TO NOMBREDE BIOMECÁNICA, CENTRÁNDOSE IN THE COMPUTER SIMULATION OF THE PROBLEM OF LASPRÓTESIS HIP CEMENTADAS. IN PARTICULAR, THE GOAL OF THE THESIS DOCTORAL IS LASIMULACIÓN OF DETERIORATION OF CEMENT AND INTERFACES. OBJECTIVE IS TO GET SUCH HAS DEVELOPED A MODEL FOR DAMAGES FOR INTERFAZCEMENTO-PRÓTESIS SIMULATING THE PROGRESSIVE DETERIORATION OF THE SAME AS WELL AS A MODEL FOR DAÑOPARA THE CEMENT TO ALLOW PREDECIR THE DEGRADATION OF THE SAME STRUCTURE INCLUDING NOSÓLO PROPERTIES VISCOELÁSTICAS OF CEMENT, BUT ALSO HOW DOES THE PROCESS DECIERRE OF GRIETAS A COMPRESSION AND NON LINEARITY PROCESS ACUMULACIÓN.ESTOS MODELS HAVE BEEN APPLIED TO THE STUDY OF DETERIORATION OF CEMENT AND THE INTERFAZCEMENTO-PRÓTESIS THREE MODELS COMMERCIAL PRÓTESIS HIP CEMENTADAS CONDIFERENTE FINISHING SURFACE: EXETER, PLUS ELITE AND ABG II REALIZANDO ALSO A ANÁLISISCOMPARATIVO BETWEEN ELLAS.DE LEARNED THE FINDINGS HIGHLIGHT THE NEED TO MAINSTREAM IN THIS KIND DESIMULACIONES THE DETERIORATION OF THE INTERFACE CEMENTO-PRÓTESIS, AND THAT IS A FACTOR DETERMINANTEEN STABILITY OF IMPLANTE AND FAILURE END OF SETTING. INTERFACE IS NOT ESTÁCOMPLETAMENTE SUELTA OR UNITED, BUT WHAT A PHYSICALLY GEOMETRY ADHESION TO ADVANCES SEVA DETERIORANDO UNDER THE PROCESS CÍCLICO LOADING AND UNLOADING AT THAT ESTANSOMETIDAS THESE PRÓTESIS. IN ADDITION THE MODEL OF DETERIORATION DEVELOPED FOR CEMENTOINCORPORA ASPECTS TO THE TIME THAT HAVE NOT CONSIDERING ACERCANDO LASSIMULACIONES INCREASINGLY TO ACTUAL MISMO.LOS MODEL BEHAVIOR DEVELOPED ALLOW ALSO MAKING COMPARISON BETWEEN DIVERSASPRÓTESIS HIP AND ALLOW DISTINGUIR THE IMPLANTS NOT ONLY BY THERE IS SUPERFICIAL SINOTAMBIÉN FOR FINISHING GEOMETRY.

Author: Cueto-Felgueroso Landeira Luis.
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: This thesis proposes the use of a class of techniques very precise approximation eespacial measure, mobile least squares (MLS) in the development of numerical schemes applied to problem solving aerodynamic and hydrodynamic. It presents, firstly, a Lagrangian particle formulation applied to flow problems with free surfaces, based on the method Smoothed Particle Hydrodynamics (SPH). One objective of this work is to clarify the wording of any SPH method using a Galerkin scheme to derive the equations discrete. In this context it is possible to analyze, and improve reinterpret various standard procedures in the literature on methods SPH, giving greater rigor and consistency to the entire formulation. It also proposes a combination of approaches MLS and diagrams upwind finite volume, applied to solving the equations for compressible flow (Euler and Navier-Stokes) and water shortly profindas (Shallow Waters) in unstructured meshes. Such methods of approximation is particularly competitive for the reconstruction of a particular function and its successive arising from the values of this function in a variety of venues scattered, which has suggested using approximations MLS for the construction of schemes very high order in unstructured meshes, representing an interesting alternative to existing methods at present. The schemes proposed for edcuaciones of compressible flow and shallow waters are based on the method of generalized Godunov, with reconstructions polynomial to pieces obtained by developments in Taylor series. In practice, the use of such methods has been severely limited by the need for approximation techniques to estimate the resulting high order of the variable flow from their average values in the various cells. The low power of the techniques employed in the literature that has led the vast majority of existing formulations are only second-order (linear reconstructions to pieces). This thesis has been implemented reconstructions linear, quadratic and cubic assess the resulting approximations necessary by least squares mobile and base cúbidca of polynomials. Such reconstructions allow increasing order of the scheme without increasing the number of degrees of freedom of the problem. It presents various application examples which demonstrate the suitability of the proposed methodology.

Author: Moreta Santos Ma. Jesús.
Year: 2004.
University: VALLADOLID [www.uva.es].
Place of defense: Facultad de Ciencias. Universidad de Valladolid.
Place of preparation: Facultad de Ciencias. Universidad de Valladolid.

Summary: As Indica title, the aim of this thesis has been the study of solving equations in the second order partial derivatives of time using methods Runge-Kutta_Nystrà ¶ m (RKN) to integrate numerically time. It is well known that the methods RKN, used widely in the literature, so naturally appear as a generalization of the methods Runge-Kutta when these are applied in the discretization of equations of second order in time, which previously had been transformed into a the system of first order in time. For these methods we studied the stability and the reduction of order that arises when integrated into Partial differential equations using the method of lines, as well as how to avoid this reduction of order. It has also been studied stability when the operator space is the generator of a cosine function and temporary integrator is a rational method designed to integrate equations of second order in time.

Author: GONZALEZ MARCO DANIEL.
Year: 2004.
University: POLITÉCNICA DE CATALUÑA [www.upc.edu].
Place of defense: SALA 212 (SALA DE CONFERÈNCIES).
Place of preparation: EDIFICI D1 Campus NORD.

Summary: Rising population and the increase of economic activities and tourism in the coastal regions, generates increasing uses and pressures in these areas, where it is increasingly common expansion and construction of ports, protection works, walks at sea, and so on. These actions cause significant changes in the means by which the waves move, generating scenarios sometimes unwanted, being therefore necessary studies wave to achieve a greater understanding of the same power and prevent harmful effects on the coast. This thesis has focused on the characterization of the digital wave propagation in irregular regions in shallow and deep water, including the surf zone. This has been done within a framework of implementing the Maritime Engineering and Operations forecast. It has developed a model of energy propagation of waves based on the equation Mild-Slope, code LIMWAVE. Its characteristics have enabled the development of new terms and methodologies closure, improving their performance with respect to existing models with similar characteristics, making it possible to broaden their applicability. To that end, it has defined a new model of closure to characterize the wave transmission through porous structures emerged, the model LIMPORE, assuming an improvement in the numerical modeling of wave in the porous medium. It has also developed a methodology for characterizing transmission of waves by rebases, including its effect on shaping 2DH structures exempt. It had also implemented a method to characterize the âprimeraâ reflection of the waves. It is worth mentioning that the main limitation of the model of propagation of wave energy is its inability to solve reflection. Using this methodology, this problem is partially addressed, playing in the waves reflected scenarios unsophisticated, as a dam exempted. The model LIMWAVE has been extensively validated as a whole. They have reproduced the main cases for validating analytical solution known, as well as laboratory tests and field trials, which were measured data available. This process of development and validation of the model LIMWAVE has helped narrow the limits of its applicability. This has also enabled the development of applications that focus on two areas, the functional design of structures with low peak coronation (LCS) and the operational wave forecasting. Regarding the functional design of LCS, the work has helped advance the knowledge of hydrodynamic behavior of this type of protection structures, culminating in contributing to the development of some Guidelines for the design of such structures within the project European DELOS. Finally, with regard to the operational wave forecasting, two systems are designed prediction applicable to ports and beaches, based on the nested model LIMWAVE models of generation and propagation of waves. The results show the applicability of the model developed, as well as strategies nested row, for this purpose. In this area, has been designed and conducted a campaign field along a transect perpendicular to the coast, from shallow to deep water, including measures in the surf zone. These data have led to calibrate and validate the model LIMWAVE and strategy ani 8 given pair 2b7 to forecast operational wave at the beach.

Author: PEREZ SINUSIA ESTER.
Year: 2004.
University: PÚBLICA DE NAVARRA [www.unavarra.es].
Place of defense: EDIFICIO DE LOS MADROÑOS.
Place of preparation: UNIVERSIDAD DE ZARAGOZA.

Summary: This thesis is focused on the study of two and three dimensional singularly-perturbed convection-diffusion problems of parabolic and elliptic type defined over different unbounded and bounded domains that present, besides the small perturbation parameter, another source of singular behaviour for the solution: discontinuities of the boundary/initial data or of their derivatives. The difficulty originated by discontinuities of the Dirichlet data is a subject of recent interest because there are not many theoretical nor numerical results about this problem. In this thesis, we analyze the effect that jump discontinuities of the boundary/initial conditions or of their derivatives has on the singular behaviour of the solution. For this purpose we consider several examples of parabolic or elliptic convection-diffusion singularly perturbed problems with constant coefficients defined in bounded and unbounded domains in 2 or 3 dimensions with discontinuous data (in the Dirichlet conditions or in its derivatives). For every one of the examples analyzed, we obtain an exact representation of the solution in terms of a Laplace or Fourier integral or in terms of a series of Fourier integrals. Then, using the classical asymptotic method for integrals which contain saddle points near a pole of the integrand, we construct, for every analyzed problem, an asymptotic expansion of the solution in the singular limit in which the perturbation parameter goes to 0. The first term of this expansion contains always an error function (in three dimensions it contains a product of error functions). These expansions are not valid near the discontinuities of the Dirichlet data. We use distributional methods for asymptotic expansions of integrals to derive convergent expansions of the solution of every problem near de discontinuities in terms of powers of the distance to the discontinuity. Most of the analyzed examples show that the first term of this second expansion is a linear function of the angle and independent of the convection vector. The main conclusion of the thesis is the appearance of the error function as a basic approximant of the solution of all the analyzed problems in the singular limit. Moreover, the argument of this error function is always the same (it depends only in the character parabolic or elliptic of the problem). We study the universality of the error function as approximant of the solution of more general singular perturbation problems defined in more general domains and other equations like convection-diffusion-reaction equations. The asymptotic expansions obtained in this thesis may be used to design uniformly convergent numerical methods for other more complicated singularly perturbed problems with discontinuous Dirichlet data.

Author: Gómez Díaz Héctor.
Year: 2005.
University: A CORUÑA [www.udc.es].
Place of defense: E.T.S. de Inge. de Caminos, Canales y Puertos.
Place of preparation: E.T.S. de Inge. de Caminos, Canales y Puertos.

Summary: This thesis proposes a new methodology (consisting of a mathematical model and a numerical model) for the resolution of problems of transport convección-difusión engineering. The proposed wording is based on a constitutive equation developed on the basis of the law of Cattaneo and removes some of the disadvantages of the design based on Fick's law, for example, the prediction of transport to speed infinite. Two algorithms have been proposed for solving numerical mathematical model introduced. The first one is based on the method of Taylor-Galerkin and the second scheme is a type discontinuous Galerkin. By the first method are solved several cases of interest in engineering, and engineering point of view that can be applied to real problems. With the algorithm type discontinnuous Galerkin are resolved classic examples of convection dominant obtained in all cases very good results (stable solutions with discontinuities captured in one or two cells) without the need to perform any kind of stabilization. In addition, it utliza algorithm type discontinuous Galerkin for the numerical simulation of the evolution of an accidental spillage in a port area using the actual geometry of the port of A Coruna. Finally, it is proposed the use of the mathematical model presented with numerical formulation type discontinuous Galerkin as an effective methodology for solving problems convección-difusión engineering.

Author: FERREIRO FERREIRO ANA MARÍA.
Year: 2005.
University: SEVILLA [www.us.es].
Place of defense: E.T.S. DE ARQUITECTURA.
Place of preparation: FACULTAD DE MATEMÁTICAS.

Summary: The report deals with the simulation of carrying sediment caused by the evolution of a fluid, both one-dimensional and two-dimensional domains. The mathematical model is considered to dock system shallow water along with an equation for carrying sediment. That model falls within the systems Hyperbolic not conservative. For the one-dimensional numerical solution is obtained through a method of generalized Roe of the first order, and through broad expanses of order scheme Roe widespread, based on reconstructions of state type WENO. It proposes a method reconstructions limiters flow combining the scheme linealizado of Lax-Wendroff with the method of Roe, using functions cleansing flow to determine the use of one or the other. The two-dimensional approximation is done using the method of lines using a method of Roe widespread. On the other hand, addresses the deduction of high-order schemes based on reconstructions of state that extend schemes built for the high-order one-dimensional problem. In addition, a study is conducted on the order of convergence of the scheme and ownership of well balanced. It uses a reconstruction of state-type MUSCL order two for unstructured meshes, proposing a limiter pending more robust than the usual. It conducted various numerical test (academic and experimental) that allow pre different schemes submitted, noting the improved precision with widespread patterns of Roe high-order systems Hyperbolic not conservative. On the other hand, focuses on the development of a tool post itself, PostDF 2D and 3D, developed with open source, which allows you to view the temporal evolution of troubleshooting solutions obtained by hydraulic methods of finite volumes. It describes the main features of PostDF, as well as the tools used in their implementation.

Author: RIVAS ULLOA JUDITH.
Year: 2005.
University: PAÍS VASCO [www.ehu.es].
Place of defense: FACULTAD DE CIENCIA Y TECNOLOGÍA.
Place of preparation: FACULTAD DE CIENCIA Y TECNOLOGÍA.

Summary: The thesis is presented that analyzes methods based on spectral functions Hermite applied to scalar hyperbolic equations in a spatial dimension, both linear and non-linear, raised in the whole real line. The idea of a spectral method is to approximate the exact solution of the problem given by a linear combination of the basic functions, which in this paper are the features of Hermite. The way to calculate the ratios vary depending on the spectral method considered. Here are studying methods Galerkin methods and placement pseudoespectrales. In the case of linear equations, we showed the convergence of the two methods in a space L2 with a weight appropriate to the functions of Hermite form an orthogonal basis, with the help of equivalence theorem of Lax-Richmyer. When it comes to non-linear equations, because the solutions developed discontinuities, we introduce certain amount of viscosity to stabilize the numerical method. We tested the convergence of the methods of spectral viscosity towards the only solution of entropy in omega Lp spaces for any higher I and Q omega any subset open and bounded IR x (O, P). To do this, use results of the theory of compactness by offsetting measures and Young. The possible lack of regularity of the solutions of equations hyperbolic reduces the speed of convergence of approximations spectral. Therefore, we built a filter which increases the order of convergence. Finally, we performed numerical experiments that confirm the theoretical results demonstrated.

Author: Prieto Aneiros Andrs.
Year: 2006.
University: SANTIAGO DE COMPOSTELA [www.usc.es].
Place of defense: Facultad de Matemticas.
Place of preparation: Facultad de Matemticas.

Summary: The work presented in the course of the argument is framed in the frequency domain, ie under the hiptesis dependency armnica of variable weather. In fact, our attention is focused on problems propagacin acstica in the regime of low frequencies, where the discretizacin using a finite element method is an expensive and not feasible, from a computational point of view. In the first part, focusing our attention on the clculo of resonance frequencies and the frequency response of porous materials coupled with fluid acsticos campuses acotados. While the second part is dedicated to anlisis matemtico and numrico the technique of the PML, which also can be considered as a special case disipativo half. Finally, the last part of this work shows some computational applications involving porous media and using the technique of the PML to truncate the bounded domain that involves the problem of propagacin acstica The first part is devoted to the study of propagacin acstica in regime armnico to travs of porous materials. This kind of material is widely used in various applications do passive noise control. These materials are well known for their ability to dissipate wave acsticas. Therefore, from a point of view acstico, porous materials possess significant advantages compared to other kinds of materials because they are lightweight and absorptive at the same time. This first part has two fundamental objectives. On the one hand, make a revisin of models of porous media response to the characteristics fsicas of materials, whether part slida rgida or elstica, stressing the difference between the models clsicos and those who appeared recently obtained by the techniques of homogeneizacin . Moreover, our attention also focuses on the Resolution numrica any of these models, providing tools numricas able to calculate as resonance frequencies and the frequency response systems acsticos involving these porous materials. The second part of the thesis is devoted to the study of the technique of the PML (Perfectly Matched Layers). First introduced in Partial differential equations that determine their behavior as originally Berenger made using the argument of separacin artificial variables of the problem (also known as `` splitting'') after giving a interpretacin physical as a way that does not produce disipativo the spurious reflections coupled with a fluid acstico. In fact, the technique of PML is the tool numrica that is used throughout this work to truncate the domain of computational problems dispersin acstica statements about not bounded domains. This technique makes it possible to reduce the dominance of these problems without disrupting too solution of the original problem. However, the study of the PML is not reduced to the simple utilization of the technique but along this part of the thesis proposes a modification that optimizes performance numricos obtained problems discretizados. More precisely, thus far to build layers PML used an absorbent limited function, an that tericamente appropriate, not produca results numricos ptimos on problems discretizados. Longo In this part adems to present this technique is discussed from a viewpoint terico and numrico the solution of these problems by using a non-integrable function absorbent. In the third part, there are some applications numricas the technique of PML and models of porous media which were studied in the first two parts. First, we compare two models di 8 ferentes 66d seeking to shape means disipativos: model Allard-Champoux, which can be understood as a means of reaccin extensive (provided that the field pressure in a space depends on the values of presin that there are around them) and the model impedance wall that is classified as a model reaccin locally (because the presin in impedance wall Only depends on what happens at that particular point space). The two models are compared in several problems dispersin acstica set forth in not bounded domains. Afterwards, the clculo coefficient absorcin is analyzed for patterns of porous media on the part slida rgida and for different types of panels reaccin locally. In all cases, carried out a anlisis preliminary wave flat and adems, the PML technique is used to truncate the computational domain of interest fsico in all problems.

Author: LAGUARDIA CUPERTINO JOSÉ JAVIER.
Year: 2006.
University: ZARAGOZA [www.unizar.es].
Place of defense: E. UNI. DE INGE. TÉCNI. INDUS. DE ZARAGOZA.
Place of preparation: CENTRO POLITÉCNICO SUPERIOR Y FACULTAD DE MATEMÁTICAS.

Summary: SUMMARY: The recent and ongoing development of a family of methods of numerical calculation methods called non-mesh, has opened new possibilities in this area, since this type of technology does not impose greater limitations regarding the relative position of the nodes, as does the method of Finite Elements (WEF), clearly predominant method since the mid-70's. However, this family of methods, which is in constant development, still has certain drawbacks, having employed in the field of very specific applications. The Method of Natural Elements (MEN), is a non-mesh method that has certain advantages compared to other methods and make it attractive for application to problems with complex geometry domains in fields such as biomechanics. The development of this thesis not only is in line expansion MEN face problems such as the growth of cracks and the interfaces between different materials, but it opens a new avenue in the discretization domain through complex geometry structures octree increasing speed access to data and reduce the cost of end computational method, which has been one of the disadvantages presented in front of the MEF. The text has been divided into six chapters containing independent without loss of coherence between them. The first and second chapter presents an introduction covering key aspects in the literature directly related to the scope of this work. They performed a description of the state of the art, purpose of the thesis and structure, as well as a broad introduction of the various existing methods without mesh, deepening the Method of Natural Elements, objective analysis and development work . The third chapter is an introduction to the techniques used for data processing, emphasizing the need to search neighborhood naturally in the context of the natural elements. It presents the advantages of using a tree structure Octree or for storing binary data, the method without getting adjusted to the mesh structure underlying data to achieve greater speed, both in terms of access to information, as in the calculation. The fourth chapter presents a study based on adaptive how structured storage Octree filed. It discusses the various techniques adaptatividad and uses the estimator Zienkiewicz-Zhu. Finally, we try to glimpse the potential of the method in the field of biomechanics some early yet linear approximations. Overall, the thesis provides an interesting development and application of smart structures Octree the Method of Natural Elements. A work of great originality which reverses great merit on its author, D. Jose Javier Laguardia Cupertino and give the category of doctoral an excellent job.