A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Interface discontinuity factors in the modal eigenspace of the multigroup diffusion matrix

Interface discontinuity factors based on the Generalized Equivalence Theory are commonly used in nodal homogenized diffusion calculations so that diffusion average values approximate heterogeneous higher order solutions. In this paper, an additional form of interface correction factors is presented in the frame of the Analytic Coarse Mesh Finite Difference Method (ACMFD), based on a correction of the modal fluxes instead of the physical fluxes. In the ACMFD formulation, implemented in COBAYA3 code, the coupled multigroup diffusion equations inside a homogenized region are reduced to a set of uncoupled modal equations through diagonalization of the multigroup diffusion matrix. Then, physical fluxes are transformed into modal fluxes in the eigenspace of the diffusion matrix. It is possible to introduce interface flux discontinuity jumps as the difference of heterogeneous and homogeneous modal fluxes instead of introducing interface discontinuity factors as the ratio of heterogeneous and homogeneous physical fluxes. The formulation in the modal space has been implemented in COBAYA3 code and assessed by comparison with solutions using classical interface discontinuity factors in the physical space

Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.

The flexibility matrix o timber composite beams with a discrete connection system

This work presents a method for the analysis of timber composite beams which considers the slip in the connection system, based on assembling the flexibility matrix of the whole structure. This method is based on one proposed by Tommola and Jutila (2001). This paper extends the method to the case of a gap between two pieces with an arbitrary location at the first connector, which notably broadens its practical application. The addition of the gap makes it possible to model a cracked zone in concrete topping, as well as the case in which forming produces the gap. The consideration of induced stresses due to changes in temperature and moisture content is also described, while the concept of equivalent eccentricity is generalized. This method has important advantages in connection with the current European Standard EN 1995-1-1: 2004, as it is able to deal with any type of load, variable section, discrete and non-regular connection systems, a gap between the two pieces, and variations in temperature and moisture content. Although it could be applied to any structural system, it is specially suited for the case of simple supported and continuous beams. Working examples are presented at the end, showing that the arrangement of the connection notably modifies shear force distribution. A first interpretation of the results is made on the basis of the strut and tie theory. The examples prove that the use of EC-5 is unsafe when, as a rule of thumb, the strut or compression field between the support and the first connector is at an angle with the axis of the beam of less than 60º.

Matrix-free time-stepping methods for the solution of TriGlobal instability problems

La inmensa mayoría de los flujos de relevancia ingenieril permanecen sin estudiar en el marco de la teoría de estabilidad global. Esto es debido a dos razones fundamentalmente, las dificultades asociadas con el análisis de los flujos turbulentos y los inmensos recursos computacionales requeridos para obtener la solución del problema de autovalores asociado al análisis de inestabilidad de flujos tridimensionales, también conocido como problema TriGlobal. En esta tesis se aborda el problema asociado con la tridimensionalidad. Se ha desarrollado una metodología general para obtener soluciones de problemas de análisis modal de las inestabilidades lineales globales mediante el acoplamiento de métodos de evolución temporal, desarrollados en este trabajo, con códigos de mecánica de fluidos computacional de segundo orden, utilizados de forma general en la industria. Esta metodología consiste en la resolución del problema de autovalores asociado al análisis de inestabilidad mediante métodos de proyección en subespacios de Krylov, con la particularidad de que dichos subespacios son generados por medio de la integración temporal de un vector inicial usando cualquier código de mecánica de fluidos computacional. Se han elegido tres problemas desafiantes en función de la exigencia de recursos computacionales necesarios y de la complejidad física para la demostración de la presente metodología: (i) el flujo en el interior de una cavidad tridimensional impulsada por una de sus tapas, (ii) el flujo alrededor de un cilindro equipado con aletas helicoidales a lo largo su envergadura y (iii) el flujo a través de una cavidad abierta tridimensinal en ausencia de homogeneidades espaciales. Para la validación de la tecnología se ha obtenido la solución del problema TriGlobal asociado al flujo en la cavidad tridimensional, utilizando el método de evolución temporal desarrollado acoplado con los operadores numéricos de flujo incompresible del código CFD OpenFOAM (código libre). Los resultados obtenidos coinciden plentamente con la literatura. La aplicación de esta metodología al estudio de inestabilidades globales de flujos abiertos tridimensionales ha proporcionado por primera vez, información sobre la transición tridimensional de estos flujos. Además, la metodología ha sido adaptada para resolver problemas adjuntos TriGlobales, permitiendo el control de flujo basado en modificaciones de las inestabilidades globales. Finalmente, se ha demostrado que la cantidad moderada de los recursos computacionales requeridos para la solución del problema de valor propio TriGlobal usando este método numérico, junto a su versatilidad al poder acoplarse a cualquier código aerodinámico, permite la realización de análisis de inestabilidad global y control de flujos complejos de relevancia industrial. Abstract Most flows of engineering relevance still remain unexplored in a global instability theory context for two reasons. First, because of the difficulties associated with the analysis of turbulent flows and, second, for the formidable computational resources required for the solution of the eigenvalue problem associated with the instability analysis of three-dimensional base flows, also known as TriGlobal problem. In this thesis, the problem associated with the three-dimensionality is addressed by means of the development of a general approach to the solution of large-scale global linear instability analysis by coupling a time-stepping approach with second order aerodynamic codes employed in industry. Three challenging flows in the terms of required computational resources and physical complexity have been chosen for demonstration of the present methodology; (i) the flow inside a wall-bounded three-dimensional lid-driven cavity, (ii) the flow past a cylinder fitted with helical strakes and (iii) the flow over a inhomogeneous three-dimensional open cavity. Results in excellent agreement with the literature have been obtained for the three-dimensional lid-driven cavity by using this methodology coupled with the incompressible solver of the open-source toolbox OpenFOAM®, which has served as validation. Moreover, significant physical insight of the instability of three-dimensional open flows has been gained through the application of the present time-stepping methodology to the other two cases. In addition, modifications to the present approach have been proposed in order to perform adjoint instability analysis of three-dimensional base flows and flow control; validation and TriGlobal examples are presented. Finally, it has been demonstrated that the moderate amount of computational resources required for the solution of the TriGlobal eigenvalue problem using this method enables the performance of instability analysis and control of flows of industrial relevance.