Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.

On the car sequencing problem: analysis and solution methods

This work deals with the car sequencing (CS) problem, a combinatorial optimization problem for sequencing mixed-model assembly lines. The aim is to find a production sequence for different variants of a common base product, such that work overload of the respective line operators is avoided or minimized. The variants are distinguished by certain options (e.g., sun roof yes/no) and, therefore, require different processing times at the stations of the line. CS introduces a so-called sequencing rule H:N for each option, which restricts the occurrence of this option to at most H in any N consecutive variants. It seeks for a sequence that leads to no or a minimum number of sequencing rule violations. In this work, CS’ suitability for workload-oriented sequencing is analyzed. Therefore, its solution quality is compared in experiments to the related mixed-model sequencing problem. A new sequencing rule generation approach as well as a new lower bound for the problem are presented. Different exact and heuristic solution methods for CS are developed and their efficiency is shown in experiments. Furthermore, CS is adjusted and applied to a resequencing problem with pull-off tables.

Geotechnical characterization of mixed sandy and silty soils using piezocone tests: Analysis of partial drainage phenomena and rate effects on the experimental soil response

The cone penetration test (CPT), together with its recent variation (CPTU), has become the most widely used in-situ testing technique for soil profiling and geotechnical characterization. The knowledge gained over the last decades on the interpretation procedures in sands and clays is certainly wide, whilst very few contributions can be found as regards the analysis of CPT(u) data in intermediate soils. Indeed, it is widely accepted that at the standard rate of penetration (v = 20 mm/s), drained penetration occurs in sands while undrained penetration occurs in clays. However, a problem arise when the available interpretation approaches are applied to cone measurements in silts, sandy silts, silty or clayey sands, since such intermediate geomaterials are often characterized by permeability values within the range in which partial drainage is very likely to occur. Hence, the application of the available and well-established interpretation procedures, developed for ‘standard’ clays and sands, may result in invalid estimates of soil parameters. This study aims at providing a better understanding on the interpretation of CPTU data in natural sand and silt mixtures, by taking into account two main aspects, as specified below: 1)Investigating the effect of penetration rate on piezocone measurements, with the aim of identifying drainage conditions when cone penetration is performed at a standard rate. This part of the thesis has been carried out with reference to a specific CPTU database recently collected in a liquefaction-prone area (Emilia-Romagna Region, Italy). 2)Providing a better insight into the interpretation of piezocone tests in the widely studied silty sediments of the Venetian lagoon (Italy). Research has focused on the calibration and verification of some site-specific correlations, with special reference to the estimate of compressibility parameters for the assessment of long-term settlements of the Venetian coastal defences.

[Herd problem: udder health. Retrospective study of farms assessed by the Swiss Bovine Health Service (BHS) from 1999 to 2004]

Data from 59 farms with complaints of udder health problems and insufficient quality of delivered milk that had been assessed by the Swiss Bovine Health Service (BHS) between 1999 and 2004 were retrospectively analysed. Data evaluated included farm characteristics such as farm size, herd size, average milk yield, milking system and housing system, deficits of the milking equipment and the milking practices, and bacteriological results of milk samples from all cows in lactation. The average size of the farms assessed by the BHS was larger than the size of the were evaluated, 42 showed obvious failures which the farm managers could have noticed. Only 5 of the 57 milkers carried out their work according to the generally valid guidelines of the National Mastitis Council. More than 2 basic mistakes were observed in the milking practices of 36 milkers. In 51 farms, mixed infections with several problem bacteria (those present in at least 20 % of the tested cows on a farm) were found. Staphylococcus aureus proved to be the most common problem germ. As the bacteria responsible for the herd problem (the sole problem bacteria detectable on a particular farm) Staphylococcus aureus was detected in 4 farms. The current study revealed that education in the area of milking techniques and milking practices of farmers should be improved in order to reduce the incidence of udder health problems on herd level. Staphylococcus aureus is the most important problem bacteria involved in herds with udder health problems in Switzerland. Staphylococcus aureus might be used in practice as the indicator germ for early recognition of management problems in dairy farms.

The Car Resequencing Problem with Pull-Off Tables

The car sequencing problem determines sequences of different car models launched down a mixed-model assembly line. To avoid work overloads of workforce, car sequencing restricts the maximum occurrence of labor-intensive options, e.g., a sunroof, by applying sequencing rules. We consider this problem in a resequencing context, where a given number of buffers (denoted as pull-off tables) is available for rearranging a stirred sequence. The problem is formalized and suited solution procedures are developed. A lower bound and a dominance rule are introduced which both reduce the running time of our graph approach. Finally, a real-world resequencing setting is investigated.

Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up

In reverse logistics networks, products (e.g., bottles or containers) have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP) is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.

A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

Index Tracking Using Data-Mining Techniques and Mixed-Binary Linear Programming

Index tracking has become one of the most common strategies in asset management. The index-tracking problem consists of constructing a portfolio that replicates the future performance of an index by including only a subset of the index constituents in the portfolio. Finding the most representative subset is challenging when the number of stocks in the index is large. We introduce a new three-stage approach that at first identifies promising subsets by employing data-mining techniques, then determines the stock weights in the subsets using mixed-binary linear programming, and finally evaluates the subsets based on cross validation. The best subset is returned as the tracking portfolio. Our approach outperforms state-of-the-art methods in terms of out-of-sample performance and running times.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

An empirical mixed model to quantify climate influence on the growth of Pinus halepensis Mill. stands in South-Eastern Spain

The influence of climate on forest stand composition, development and growth is undeniable. Many studies have tried to quantify the effect of climatic variables on forest growth and yield. These works become especially important because there is a need to predict the effects of climate change on the development of forest ecosystems. One of the ways of facing this problem is the inclusion of climatic variables into the classic empirical growth models. The work has a double objective: (i) to identify the indicators which best describe the effect of climate on Pinus halepensis growth and (ii) to quantify such effect in several scenarios of rainfall decrease which are likely to occur in the Mediterranean area. A growth mixed model for P. halepensis including climatic variables is presented in this work. Growth estimates are based on data from the Spanish National Forest Inventory (SNFI). The best results are obtained for the indices including rainfall, or rainfall and temperature together, with annual precipitation, precipitation effectiveness, Emberger?s index or free bioclimatic intensity standing out among them. The final model includes Emberger?s index, free bioclimatic intensity and interactions between competition and climate indices. The results obtained show that a rainfall decrease about 5% leads to a decrease in volume growth of 5.5?7.5% depending on site quality.

Finite element simulation of sandwich panels of laminated plaster and rockwool under mixed mode fracture

Sandwich panels of laminated gypsum and rock wool have shown large pathology of cracking due to excessive slabs deflection. Currently the most widespread use of this material is as vertical elements of division or partition, with no structural function, what justifies that there are no studies on the mechanism of fracture and mechanical properties related to it. Therefore, and in order to reduce the cracking problem, it is necessary to progress in the simulation and prediction of the behaviour under tensile and shear load of such panels, although in typical applications have no structural responsability.

A Multi Ant Colony Optimization algorithm for a Mixed Car Assembly Line

This paper presents an ant colony optimization algorithm to sequence the mixed assembly lines considering the inventory and the replenishment of components. This is a NP-problem that cannot be solved to optimality by exact methods when the size of the problem growth. Groups of specialized ants are implemented to solve the different parts of the problem. This is intended to differentiate each part of the problem. Different types of pheromone structures are created to identify good car sequences, and good routes for the replenishment of components vehicle. The contribution of this paper is the collaborative approach of the ACO for the mixed assembly line and the replenishment of components and the jointly solution of the problem.

Analyzing size-symmetric vs. size-asymmetric and intra-vs. inter-specific competition in beech (Fagus sylvatica L.) mixed stands

In mixed stands, inter-specific competition can be lower than intra-specific competition when niche complementarity and/or facilitation between species prevail. These positive interactions can take place at belowground and/or aboveground levels. Belowground competition tends to be size symmetric while the aboveground competition is usually for light and almost always size-asymmetric. Interactions between forest tree species can be explored analyzing growth at tree level by comparing intra and inter-specific competition. At the same time, possible causes of niche complementarity can be inferred relating intra and inter-specific competition with the mode of competition, i.e. size-symmetric or sizeasymmetric. The aim of this paper is to further our understanding of the interactions between species and to detect possible causes of competition reduction in mixed stands of beech (Fagus sylvatica L.) with other species: pine?beech, oak?beech and fir?beech. To test whether species growth is better explained by size-symmetric and/or size-asymmetric competition, five different competition structures where included in basal area growth models fitted using data from the Spanish National Forest Inventory for the Pyrenees. These models considered either size-symmetry only (Reineke?s stand density index, SDI), size-asymmetry only (SDI of large trees or SDI of small trees), or both combined. In order to assess the influence of the admixture, these indices were introduced in two different ways, one of which was to consider that trees of all species compete in a similar way, and the other was to split the stand density indices into intra- and inter-specific competition components. The results showed that in pine?beech mixtures, there is a slightly negative effect of beech on pine basal area growth while beech benefitted from the admixture of Scots pine; this positive effect being greater as the proportion of pine trees in larger size classes increases. In oak?beech mixtures, beech growth was also positively influenced by the presence of oaks that were larger than the beech trees. The growth of oak, however, decreased when the proportion of beech in SDI increased, although the presence of beech in larger size classes promoted oak growth. Finally, in fir?beech mixtures, neither fir nor beech basal area growth were influenced by the presence of the other species. The results indicate that size-asymmetric is stronger than size-symmetric competition in these mixtures, highlighting the importance of light in competition. Positive species interactions in size-asymmetric competition involved a reduction of asymmetry in tree size-growth relationships.

Managing daily surgery schedules in a teaching hospital: a mixed-integer optimization approach

Background: This study examined the daily surgical scheduling problem in a teaching hospital. This problem relates to the use of multiple operating rooms and different types of surgeons in a typical surgical day with deterministic operation durations (preincision, incision, and postincision times). Teaching hospitals play a key role in the health-care system; however, existing models assume that the duration of surgery is independent of the surgeon's skills. This problem has not been properly addressed in other studies. We analyze the case of a Spanish public hospital, in which continuous pressures and budgeting reductions entail the more efficient use of resources. Methods: To obtain an optimal solution for this problem, we developed a mixed-integer programming model and user-friendly interface that facilitate the scheduling of planned operations for the following surgical day. We also implemented a simulation model to assist the evaluation of different dispatching policies for surgeries and surgeons. The typical aspects we took into account were the type of surgeon, potential overtime, idling time of surgeons, and the use of operating rooms. Results: It is necessary to consider the expertise of a given surgeon when formulating a schedule: such skill can decrease the probability of delays that could affect subsequent surgeries or cause cancellation of the final surgery. We obtained optimal solutions for a set of given instances, which we obtained through surgical information related to acceptable times collected from a Spanish public hospital. Conclusions: We developed a computer-aided framework with a user-friendly interface for use by a surgical manager that presents a 3-D simulation of the problem. Additionally, we obtained an efficient formulation for this complex problem. However, the spread of this kind of operation research in Spanish public health hospitals will take a long time since there is a lack of knowledge of the beneficial techniques and possibilities that operational research can offer for the health-care system.

A framework for mixed-criticality partitioned real-time embedded systems

Los sistemas empotrados son cada día más comunes y complejos, de modo que encontrar procesos seguros, eficaces y baratos de desarrollo software dirigidos específicamente a esta clase de sistemas es más necesario que nunca. A diferencia de lo que ocurría hasta hace poco, en la actualidad los avances tecnológicos en el campo de los microprocesadores de los últimos tiempos permiten el desarrollo de equipos con prestaciones más que suficientes para ejecutar varios sistemas software en una única máquina. Además, hay sistemas empotrados con requisitos de seguridad (safety) de cuyo correcto funcionamiento depende la vida de muchas personas y/o grandes inversiones económicas. Estos sistemas software se diseñan e implementan de acuerdo con unos estándares de desarrollo software muy estrictos y exigentes. En algunos casos puede ser necesaria también la certificación del software. Para estos casos, los sistemas con criticidades mixtas pueden ser una alternativa muy valiosa. En esta clase de sistemas, aplicaciones con diferentes niveles de criticidad se ejecutan en el mismo computador. Sin embargo, a menudo es necesario certificar el sistema entero con el nivel de criticidad de la aplicación más crítica, lo que hace que los costes se disparen. La virtualización se ha postulado como una tecnología muy interesante para contener esos costes. Esta tecnología permite que un conjunto de máquinas virtuales o particiones ejecuten las aplicaciones con unos niveles de aislamiento tanto temporal como espacial muy altos. Esto, a su vez, permite que cada partición pueda ser certificada independientemente. Para el desarrollo de sistemas particionados con criticidades mixtas se necesita actualizar los modelos de desarrollo software tradicionales, pues estos no cubren ni las nuevas actividades ni los nuevos roles que se requieren en el desarrollo de estos sistemas. Por ejemplo, el integrador del sistema debe definir las particiones o el desarrollador de aplicaciones debe tener en cuenta las características de la partición donde su aplicación va a ejecutar. Tradicionalmente, en el desarrollo de sistemas empotrados, el modelo en V ha tenido una especial relevancia. Por ello, este modelo ha sido adaptado para tener en cuenta escenarios tales como el desarrollo en paralelo de aplicaciones o la incorporación de una nueva partición a un sistema ya existente. El objetivo de esta tesis doctoral es mejorar la tecnología actual de desarrollo de sistemas particionados con criticidades mixtas. Para ello, se ha diseñado e implementado un entorno dirigido específicamente a facilitar y mejorar los procesos de desarrollo de esta clase de sistemas. En concreto, se ha creado un algoritmo que genera el particionado del sistema automáticamente. En el entorno de desarrollo propuesto, se han integrado todas las actividades necesarias para desarrollo de un sistema particionado, incluidos los nuevos roles y actividades mencionados anteriormente. Además, el diseño del entorno de desarrollo se ha basado en la ingeniería guiada por modelos (Model-Driven Engineering), la cual promueve el uso de los modelos como elementos fundamentales en el proceso de desarrollo. Así pues, se proporcionan las herramientas necesarias para modelar y particionar el sistema, así como para validar los resultados y generar los artefactos necesarios para el compilado, construcción y despliegue del mismo. Además, en el diseño del entorno de desarrollo, la extensión e integración del mismo con herramientas de validación ha sido un factor clave. En concreto, se pueden incorporar al entorno de desarrollo nuevos requisitos no-funcionales, la generación de nuevos artefactos tales como documentación o diferentes lenguajes de programación, etc. Una parte clave del entorno de desarrollo es el algoritmo de particionado. Este algoritmo se ha diseñado para ser independiente de los requisitos de las aplicaciones así como para permitir al integrador del sistema implementar nuevos requisitos del sistema. Para lograr esta independencia, se han definido las restricciones al particionado. El algoritmo garantiza que dichas restricciones se cumplirán en el sistema particionado que resulte de su ejecución. Las restricciones al particionado se han diseñado con una capacidad expresiva suficiente para que, con un pequeño grupo de ellas, se puedan expresar la mayor parte de los requisitos no-funcionales más comunes. Las restricciones pueden ser definidas manualmente por el integrador del sistema o bien pueden ser generadas automáticamente por una herramienta a partir de los requisitos funcionales y no-funcionales de una aplicación. El algoritmo de particionado toma como entradas los modelos y las restricciones al particionado del sistema. Tras la ejecución y como resultado, se genera un modelo de despliegue en el que se definen las particiones que son necesarias para el particionado del sistema. A su vez, cada partición define qué aplicaciones deben ejecutar en ella así como los recursos que necesita la partición para ejecutar correctamente. El problema del particionado y las restricciones al particionado se modelan matemáticamente a través de grafos coloreados. En dichos grafos, un coloreado propio de los vértices representa un particionado del sistema correcto. El algoritmo se ha diseñado también para que, si es necesario, sea posible obtener particionados alternativos al inicialmente propuesto. El entorno de desarrollo, incluyendo el algoritmo de particionado, se ha probado con éxito en dos casos de uso industriales: el satélite UPMSat-2 y un demostrador del sistema de control de una turbina eólica. Además, el algoritmo se ha validado mediante la ejecución de numerosos escenarios sintéticos, incluyendo algunos muy complejos, de más de 500 aplicaciones. ABSTRACT The importance of embedded software is growing as it is required for a large number of systems. Devising cheap, efficient and reliable development processes for embedded systems is thus a notable challenge nowadays. Computer processing power is continuously increasing, and as a result, it is currently possible to integrate complex systems in a single processor, which was not feasible a few years ago.Embedded systems may have safety critical requirements. Its failure may result in personal or substantial economical loss. The development of these systems requires stringent development processes that are usually defined by suitable standards. In some cases their certification is also necessary. This scenario fosters the use of mixed-criticality systems in which applications of different criticality levels must coexist in a single system. In these cases, it is usually necessary to certify the whole system, including non-critical applications, which is costly. Virtualization emerges as an enabling technology used for dealing with this problem. The system is structured as a set of partitions, or virtual machines, that can be executed with temporal and spatial isolation. In this way, applications can be developed and certified independently. The development of MCPS (Mixed-Criticality Partitioned Systems) requires additional roles and activities that traditional systems do not require. The system integrator has to define system partitions. Application development has to consider the characteristics of the partition to which it is allocated. In addition, traditional software process models have to be adapted to this scenario. The V-model is commonly used in embedded systems development. It can be adapted to the development of MCPS by enabling the parallel development of applications or adding an additional partition to an existing system. The objective of this PhD is to improve the available technology for MCPS development by providing a framework tailored to the development of this type of system and by defining a flexible and efficient algorithm for automatically generating system partitionings. The goal of the framework is to integrate all the activities required for developing MCPS and to support the different roles involved in this process. The framework is based on MDE (Model-Driven Engineering), which emphasizes the use of models in the development process. The framework provides basic means for modeling the system, generating system partitions, validating the system and generating final artifacts. The framework has been designed to facilitate its extension and the integration of external validation tools. In particular, it can be extended by adding support for additional non-functional requirements and support for final artifacts, such as new programming languages or additional documentation. The framework includes a novel partitioning algorithm. It has been designed to be independent of the types of applications requirements and also to enable the system integrator to tailor the partitioning to the specific requirements of a system. This independence is achieved by defining partitioning constraints that must be met by the resulting partitioning. They have sufficient expressive capacity to state the most common constraints and can be defined manually by the system integrator or generated automatically based on functional and non-functional requirements of the applications. The partitioning algorithm uses system models and partitioning constraints as its inputs. It generates a deployment model that is composed by a set of partitions. Each partition is in turn composed of a set of allocated applications and assigned resources. The partitioning problem, including applications and constraints, is modeled as a colored graph. A valid partitioning is a proper vertex coloring. A specially designed algorithm generates this coloring and is able to provide alternative partitions if required. The framework, including the partitioning algorithm, has been successfully used in the development of two industrial use cases: the UPMSat-2 satellite and the control system of a wind-power turbine. The partitioning algorithm has been successfully validated by using a large number of synthetic loads, including complex scenarios with more that 500 applications.