Order 10 4 speedup in global linear instability analysis using matrix formation

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.

Advances in global instability computations: from incompressible to hypersonic flow

Esta tesis constituye un gran avance en el conocimiento del estudio y análisis de inestabilidades hidrodinámicas desde un punto de vista físico y teórico, como consecuencia de haber desarrollado innovadoras técnicas para la resolución computacional eficiente y precisa de la parte principal del espectro correspondiente a los problemas de autovalores (EVP) multidimensionales que gobiernan la inestabilidad de flujos con dos o tres direcciones espaciales inhomogéneas, denominados problemas de estabilidad global lineal. En el contexto del trabajo de desarrollo de herramientas computacionales presentado en la tesis, la discretización mediante métodos de diferencias finitas estables de alto orden de los EVP bidimensionales y tridimensionales que se derivan de las ecuaciones de Navier-Stokes linealizadas sobre flujos con dos o tres direcciones espaciales inhomogéneas, ha permitido una aceleración de cuatro órdenes de magnitud en su resolución. Esta mejora de eficiencia numérica se ha conseguido gracias al hecho de que usando estos esquemas de diferencias finitas, técnicas eficientes de resolución de problemas lineales son utilizables, explotando el alto nivel de dispersión o alto número de elementos nulos en las matrices involucradas en los problemas tratados. Como más notable consecuencia cabe destacar que la resolución de EVPs multidimensionales de inestabilidad global, que hasta la fecha necesitaban de superordenadores, se ha podido realizar en ordenadores de sobremesa. Además de la solución de problemas de estabilidad global lineal, el mencionado desarrollo numérico facilitó la extensión de las ecuaciones de estabilidad parabolizadas (PSE) lineales y no lineales para analizar la inestabilidad de flujos que dependen fuertemente en dos direcciones espaciales y suavemente en la tercera con las ecuaciones de estabilidad parabolizadas tridimensionales (PSE-3D). Precisamente la capacidad de extensión del novedoso algoritmo PSE-3D para el estudio de interacciones no lineales de los modos de estabilidad, desarrollado íntegramente en esta tesis, permite la predicción de transición en flujos complejos de gran interés industrial y por lo tanto extiende el concepto clásico de PSE, el cuál ha sido empleado exitosamente durante las pasadas tres décadas en el mismo contexto para problemas de capa límite bidimensional. Típicos ejemplos de flujos incompresibles se han analizado en este trabajo sin la necesidad de recurrir a restrictivas presuposiciones usadas en el pasado. Se han estudiado problemas vorticales como es el caso de un vórtice aislado o sistemas de vórtices simulando la estela de alas, en los que la homogeneidad axial no se impone y así se puede considerar la difusión viscosa del flujo. Además, se ha estudiado el chorro giratorio turbulento, cuya inestabilidad se utiliza para mejorar las características de funcionamiento de combustores. En la tesis se abarcan adicionalmente problemas de flujos compresibles. Se presenta el estudio de inestabilidad de flujos de borde de ataque a diferentes velocidades de vuelo. También se analiza la estela formada por un elemento rugoso aislado en capa límite supersónica e hipersónica, mostrando excelentes comparaciones con resultados obtenidos mediante simulación numérica directa. Finalmente, nuevas inestabilidades se han identificado en el flujo hipersónico a Mach 7 alrededor de un cono elíptico que modela el vehículo de pruebas en vuelo HIFiRE-5. Los resultados comparan favorablemente con experimentos en vuelo, lo que subraya aún más el potencial de las metodologías de análisis de estabilidad desarrolladas en esta tesis. ABSTRACT The present thesis constitutes a step forward in advancing the frontiers of knowledge of fluid flow instability from a physical point of view, as a consequence of having been successful in developing groundbreaking methodologies for the efficient and accurate computation of the leading part of the spectrum pertinent to multi-dimensional eigenvalue problems (EVP) governing instability of flows with two or three inhomogeneous spatial directions. In the context of the numerical work presented in this thesis, the discretization of the spatial operator resulting from linearization of the Navier-Stokes equations around flows with two or three inhomogeneous spatial directions by variable-high-order stable finite-difference methods has permitted a speedup of four orders of magnitude in the solution of the corresponding two- and three-dimensional EVPs. This improvement of numerical performance has been achieved thanks to the high-sparsity level offered by the high-order finite-difference schemes employed for the discretization of the operators. This permitted use of efficient sparse linear algebra techniques without sacrificing accuracy and, consequently, solutions being obtained on typical workstations, as opposed to the previously employed supercomputers. Besides solution of the two- and three-dimensional EVPs of global linear instability, this development paved the way for the extension of the (linear and nonlinear) Parabolized Stability Equations (PSE) to analyze instability of flows which depend in a strongly-coupled inhomogeneous manner on two spatial directions and weakly on the third. Precisely the extensibility of the novel PSE-3D algorithm developed in the framework of the present thesis to study nonlinear flow instability permits transition prediction in flows of industrial interest, thus extending the classic PSE concept which has been successfully employed in the same context to boundary-layer type of flows over the last three decades. Typical examples of incompressible flows, the instability of which was analyzed in the present thesis without the need to resort to the restrictive assumptions used in the past, range from isolated vortices, and systems thereof, in which axial homogeneity is relaxed to consider viscous diffusion, as well as turbulent swirling jets, the instability of which is exploited in order to improve flame-holding properties of combustors. The instability of compressible subsonic and supersonic leading edge flows has been solved, and the wake of an isolated roughness element in a supersonic and hypersonic boundary-layer has also been analyzed with respect to its instability: excellent agreement with direct numerical simulation results has been obtained in all cases. Finally, instability analysis of Mach number 7 ow around an elliptic cone modeling the HIFiRE-5 flight test vehicle has unraveled flow instabilities near the minor-axis centerline, results comparing favorably with flight test predictions.

Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems

In this paper, several computational schemes are presented for the optimal tuning of the global behavior of nonlinear dynamical sys- tems. Specifically, the maximization of the size of domains of attraction associated with invariants in parametrized dynamical sys- tems is addressed. Cell Mapping (CM) tech- niques are used to estimate the size of the domains, and such size is then maximized via different optimization tools. First, a ge- netic algorithm is tested whose performance shows to be good for determining global maxima at the expense of high computa- tional cost. Secondly, an iterative scheme based on a Stochastic Approximation proce- dure (the Kiefer-Wolfowitz algorithm) is eval- uated showing acceptable performance at low cost. Finally, several schemes combining neu- ral network based estimations and optimiza- tion procedures are addressed with promising results. The performance of the methods is illus- trated with two applications: first on the well-known van der Pol equation with stan- dard parametrization, and second the tuning of a controller for saturated systems.

ITEM: Inter-Texture Error Measurement for 3D Meshes

We introduce a simple and innovative method to compare any two texture maps, regardless of their sizes, aspect ratios, or even masks, as long as they are both meant to be mapped onto the same 3D mesh. Our system is based on a zero-distortion 3D mesh unwrapping technique which compares two new adapted texture atlases with the same mask but different texel colors, and whose every texel covers the same area in 3D. Once these adapted atlases are created, we measure their difference with ITEM-RMSE, a slightly modified version of the standard RMSE defined for images. ITEM-RMSE is more meaningful and reliable than RMSE because it only takes into account the texels inside the mask, since they are the only ones that will actually be used during rendering. Our method is not only very useful to compare the space efficiency of different texture atlas generation algorithms, but also to quantify texture loss in compression schemes for multi-resolution textured 3D meshes.

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Experimental results on advanced inertial fusion schemes obtained within the HiPER project

This paper presents de results of experiments conducted within the Work Package 10 (fusion experimental programme) of the HiPER project. The aim of these experiments was to study the physics relevant for advanced ignition schemes for inertial confinement fusion, i.e. the fast ignition and the shock ignition. Such schemes allow to achieve a higher fusion gain compared to the indirect drive approach adopted in the National Ignition Facility in United States, which is important for the future inertial fusion energy reactors and for realising the inertial fusion with smaller facilities

A mathematical framework for new fault detection schemes in nonlinear stochastic continuous-time dynamical systems

n this work, a mathematical unifying framework for designing new fault detection schemes in nonlinear stochastic continuous-time dynamical systems is developed. These schemes are based on a stochastic process, called the residual, which reflects the system behavior and whose changes are to be detected. A quickest detection scheme for the residual is proposed, which is based on the computed likelihood ratios for time-varying statistical changes in the Ornstein–Uhlenbeck process. Several expressions are provided, depending on a priori knowledge of the fault, which can be employed in a proposed CUSUM-type approximated scheme. This general setting gathers different existing fault detection schemes within a unifying framework, and allows for the definition of new ones. A comparative simulation example illustrates the behavior of the proposed schemes.

The first renewable forward market mechanisms in the Iberian Electricity Market

A description of the first renewable forward market mechanisms in the Iberian Electricity Market is provided. A contract for difference mechanism is available in Spain since March 2011between the last resort suppliers and the special regime (renewables and cogeneration) settling the price differences between the equilibrium price of the forward regulated auctions for the last resort supply and the spot price of the corresponding delivery period. Regulated auctions of baseload futures of the Portuguese zone in which the Portuguese last resort supplier sells the special regime production exist since December 2011. The experience gained from renewables auctions in Latin America could be used in the Iberian Electricity market, complementing these first market mechanisms. Introduction of renewable auctions at least for the most mature technologies (i.e. wind) in Spain and Portugal providing a fair price for the renewable generation will be of utmost importance in the short term to diminish the tariff deficit caused by the massive deployment of the feed-in-tariff scheme. Liquidity in the forward markets will also increase as a result of the entry of renewable generation companies intending to maximize their profits due to gradual suppression of feed in tariff schemes.

Diffusion Gradient Temporal Difference for Cooperative Reinforcement Learning with Linear Function Approximation

We introduce a diffusion-based algorithm in which multiple agents cooperate to predict a common and global statevalue function by sharing local estimates and local gradient information among neighbors. Our algorithm is a fully distributed implementation of the gradient temporal difference with linear function approximation, to make it applicable to multiagent settings. Simulations illustrate the benefit of cooperation in learning, as made possible by the proposed algorithm.

Analysis and design of multirate synchronous sampling schemes for sparse multiband signals

We consider the problem of developing efficient sampling schemes for multiband sparse signals. Previous results on multicoset sampling implementations that lead to universal sampling patterns (which guarantee perfect reconstruction), are based on a set of appropriate interleaved analog to digital converters, all of them operating at the same sampling frequency. In this paper we propose an alternative multirate synchronous implementation of multicoset codes, that is, all the analog to digital converters in the sampling scheme operate at different sampling frequencies, without need of introducing any delay. The interleaving is achieved through the usage of different rates, whose sum is significantly lower than the Nyquist rate of the multiband signal. To obtain universal patterns the sampling matrix is formulated and analyzed. Appropriate choices of the parameters, that is the block length and the sampling rates, are also proposed.

Popularity based distribution schemes for P2P assisted streaming of VoD contents

The Video on Demand (VoD) service is becoming a dominant service in the telecommunication market due to the great convenience regarding the choice of content items and their independent viewing time. However, it comes with the downsides of high server storage and capacity demands because of the large variety of content items and the high amount of traffic generated for serving all requests. Storing part of the popular contents on the peers brings certain advantages but, it still has issues regarding the overall traffic in the core of the network and the scalability. Therefore, we propose a P2P assisted model for streaming VoD contents that takes advantage of the clients unused uplink and storage capacity to serve requests of other clients and we present popularity based schemes for distribution of both the popular and unpopular contents on the peers. The proposed model and the schemes prove to reduce the streaming traffic in the core of the network, improve the responsiveness of the system and increase its scalability.

Benchmarking of calculation schemes in Apollo2 and COBAYA3 for VVER lattices

This paper presents solutions of the NURISP VVER lattice benchmark using APOLLO2, TRIPOLI4 and COBAYA3 pin-by-pin. The main objective is to validate MOC based calculation schemes for pin-by-pin cross-section generation with APOLLO2 against TRIPOLI4 reference results. A specific objective is to test the APOLLO2 generated cross-sections and interface discontinuity factors in COBAYA3 pin-by-pin calculations with unstructured mesh. The VVER-1000 core consists of large hexagonal assemblies with 2mm inter-assembly water gaps which require the use of unstructured meshes in the pin-by-pin core simulators. The considered 2D benchmark problems include 19-pin clusters, fuel assemblies and 7-assembly clusters. APOLLO2 calculation schemes with the step characteristic method (MOC) and the higher-order Linear Surface MOC have been tested. The comparison of APOLLO2 vs.TRIPOLI4 results shows a very close agreement. The 3D lattice solver in COBAYA3 uses transport corrected multi-group diffusion approximation with interface discontinuity factors of GET or Black Box Homogenization type. The COBAYA3 pin-by-pin results in 2, 4 and 8 energy groups are close to the reference solutions when using side-dependent interface discontinuity factors.

Managing drought economic effects through insurance schemes based on local water availability.

In many arid or semi-arid Mediterranean regions, agriculture is dependent on irrigation. When hydrological drought phenomena occur, farmers suffer from water shortages, incurring important economic losses. Yet, there is not agricultural insurance available for lack of irrigation water. This work attempts to evaluate hydrological drought risk and its economic impact on crop production in order to provide the basis for the design of drought insurance for irrigated arable crops. With this objective a model that relates water availability with expected yields is developed. Crop water requirements are calculated from evapotranspiration, effective rainfall and soil water balance. FAO?s methodology and AquaCrop software have been used to establish the relationship between water allocations and crop yields. The analysis is applied to the irrigation zone ?Riegos de Bardenas?, which is located in the Ebro river basin, northeast Spain, to the main arable crops in the area. Results show the fair premiums of different hydrological drought insurance products. Whole-farm insurance or irrigation district insurance should be preferable to crop specific insurance due to the drought management strategies used by farmers.

Experimental study on bridge damage identification based on wavelet packet energy curvature difference method

Among those damage identification methods, the Wavelet Packet Energy Curvature Difference (WPECD) Method is an effective one. However, most of the existing methods rely on numerical simulation and are unverified via experiment, and very few of them have been applied to practice. In this paper, the validity of WPECD in structural damage identification is verified by a numerical example. A damage simulation experiment is taken on a real replaced girder at the Ziya River New Bridge in Cangzhou. Two damage cases are applied and the acceleration responses at the measuring points are obtained, based on which the damages are identified with the WPECD Method, and the influence of wavelet function and decomposition level is studied. The results show that the WPECD Method can identify structure damage efficiently and can be put into practice.