Unstructured spline spaces for isogeometric analysis based on spline manifolds

Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured T-splines. This allows us to prove the key properties that are needed for isogeometric analysis, such as linear independence and optimal approximation properties for $h$-refined meshes

Suitably graded THB-spline refinement and coarsening: Towards an adaptive isogeometric analysis of additive manufacturing processes

In the present work we introduce a complete set of algorithms to efficiently perform adaptive refinement and coarsening by exploiting truncated hierarchical B-splines (THB-splines) defined on suitably graded isogeometric meshes, that are called admissible mesh configurations. We apply the proposed algorithms to two-dimensional linear heat transfer problems with localized moving heat source, as simplified models for additive manufacturing applications. We first verify the accuracy of the admissible adaptive scheme with respect to an overkilled solution, for then comparing our results with similar schemes which consider different refinement and coarsening algorithms, with or without taking into account grading parameters. This study shows that the THB-spline admissible solution delivers an optimal discretization for what concerns not only the accuracy of the approximation, but also the (reduced) number of degrees of freedom per time step. In the last example we investigate the capability of the algorithms to approximate the thermal history of the problem for a more complicated source path. The comparison with uniform and non-admissible hierarchical meshes demonstrates that also in this case our adaptive scheme returns the desired accuracy while strongly improving the computational efficiency.Comment: 20 pages, 12 figure

Attitudes of residents towards tourism. The case of Benalmadena, Spain

Tourism is consumed in the place of production causing a series of impacts. These effects caused by tourism can be perceived positively or negatively by residents. The objective of this study is to analyze the attitude of the residents from the impacts of tourism in the town of Benalmádena, Spanish town that is located within the Costa del Sol. We used a quantitative methodology and we have carried out an extensive survey of 770 residents. Information has been collected through questionnaires and there have been exploratory and ANOVA analysis. The results are: the economic benefits are the most important elements sought and valued by the local population. However, they also recognize the negative effects of this dimension, in the same way as with the socio-cultural and environmental impacts.This study is to analyze the attitude of the residents from the impacts of tourism in the town of Benalmádena, Spanish. This is a mature destination framed in a pattern of sun and beach in 2012 has a total of 10,885 hotel places. Benalmádena tourism has a significant oscillation throughout the year, peaking in the months of July to September and the minimum between December and February.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Robust Model Predictive Control for Spacecraft Rendezvous with Online Prediction of Disturbance Bounds

IFAC Workshop Aerospace Guidance, Navigation and Flight Control Systems (AGNFCS' 09) Samara, RUSSIA June 30 - July 2, 2009A Model Predictive Controller is introduced to solve the problem of rendezvous of spacecraft, using the HCW model and including additive disturbances and line-of-sight constraints. It is shown that a standard MPC is not able to cope with disturbances. Then a robust Model Predictive Control that introduces the concepts of robust satisfaction of constraints is proposed. The formulation also includes a predictor of the disturbance properties which are needed in the robust algorithm. In simulations it is shown that the robust MPC scheme is able to handle not only additive disturbances (which are the ones used in the formulation) but also large multiplicative disturbances and unmodelled dynamics (due to eccentricity of the orbit of the target spacecraft)

Trajectory Planning for Spacecraft Rendezvous in Elliptical Orbits with On / Off Thrusters

The 19th World Congress of the International Federation of Automatic Control 2014 Cape Town, SudáfricaIn a previous work, the authors developed a trajectory planning algorithm for spacecraft rendezvous which computed optimal Pulse-Width Modulated (PWM) control signals, assuming that the target was moving in a circular Keplerian orbit. In this paper we extend the algorithm to the case of an elliptical target orbit with arbitrary eccentricity. Since the orbit is elliptical, the linear time-varying Tschauner-Hempel model is used, whose exact solution is possible by using true (or eccentric) anomaly instead of time (which is directly related to both via Kepler's equation). Unlike in the circular case, computing the PWM solution itself requires numerical integration. However, explicit linearization around the computed solution turns out to be possible and is exploited for rapidly improving the solution using linear programming (LP) techniques. The algorithm is initialized by solving the impulsive problem first; the impulses are converted to PWM signals, which are used as an initial guess. Using the explicit linearization and LP, the solution is refined until a (possibly local) optimal value is reached. The efficacy of the method is shown in a simulation study where it is compared to the impulsive-only approach

Sobre ἄλλως conjuntivo

This paper presents an identification and description, within a functional framework, of conjunctive uses of the adverb ἄλλως in several collocations with conjunctions and particles. The selected passages prove that the adverb was used in Ancient Greek prose in a variety of constructions expressing conditional, disjunctive, enumerative, adversative, additive and particularizing conjunction.El artículo presenta una identificación y descripción en un marco teórico funcional de empleos conjuntivos del adverbio ἄλλως en combinaciones varias con conjunciones y partículas. Los pasajes seleccionados demuestran que el adverbio fue usado en la prosa griega antigua en una variedad de construcciones en las que expresa conexión condicional, disyuntiva, enumerativa, aditiva y particularizadora

Model Predictive Control for Spacecraft Rendezvous in Elliptical Orbits with On/Off Thrusters

IFAC Workshop on Advanced Control and Navigation for Autonomous Aerospace Vehicles. 08/06/2015. SevillaIn previous works, the authors have developed a trajectory planning algorithm for spacecraft rendezvous which computed optimal Pulse-Width Modulated (PWM) control signals, for circular and eccentric Keplerian orbits. The algorithm is initialized by solving the impulsive problem first and then, using explicit linearization and linear programming, the solution is refined until a (possibly local) optimal value is reached. However, trajectory planning cannot take into account orbital perturbations, disturbances or model errors. To overcome these issues, in this paper we develop a Model Predictive Control (MPC) algorithm based on the open-loop PWM planner and test it for elliptical target orbits with arbitrary eccentricity (using the linear time-varying Tschauner-Hempel model). The MPC is initialized by first solving the open-loop problem with the PWM trajectory planning algorithm. After that, at each time step, our MPC saves time recomputing the trajectory by applying the iterative linearization scheme of the trajectory planning algorithm to the solution obtained in the previous time step. The efficacy of the method is shown in a simulation study where it is compared to MPC computed used an impulsive-only approach

Trajectory Planning for Spacecraft Rendezvous with On / Off Thrusters

18th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2The objective of this work is to present a trajectory planning algorithm for spacecraft rendezvous that is able to incorporate Pulse-Width Modulated (PWM) control signals. The algorithm is based on linearization around a previously computed solution. To initialize the algorithm, a first solution needs to be obtained. To do so, the trajectory planning problem is solved using Pulse-Amplitude Modulated (PAM) control signals; these are then converted to PWM signals, which are used as an initial guess. Iterating, the solution is refined until an optimal value is reached. Simulations show that this method converges after a few iterations. The algorithm is simple and fast, hence it could be implemented online or used together with a Model Predictive Controller