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Adaptatividade em aprendizagem de máquina: conceitos e estudo de caso. / Adaptivity in machine learning: Concepts and case study.Stange, Renata Luiza 21 October 2011 (has links)
A aprendizagem incremental requer que o mecanismo de aprendizagem seja baseado no acúmulo dinâmico da informação extraída das experiências realizadas. A aprendizagem de máquina usando adaptatividade considera a integração de técnicas de aprendizagem de máquina simbólicas com técnicas adaptativas para a solução de problemas de aprendizagem. A palavra adaptatividade sugere a capacidade de modificação do conjunto de regras aprendidas em resposta a eventos que podem ocorrer durante o processo de aprendizagem, ou então autoajustes no conjunto de parâmetros. Os dispositivos adaptativos que possuem a capacidade de reter em suas regras informações extraídas de suas entradas podem acumular informações, para que sejam utilizadas quando forem necessárias. As estratégias de interesse para a incorporação da adaptatividade incluem a utilização de métodos e técnicas de aprendizagem de máquina, em particular as que implementam aprendizado supervisionado e tomada de decisão. O objetivo deste trabalho é explorar a utilização de técnicas adaptativas no processo de aprendizado por máquina, tanto de forma exclusiva como em conjunto com outras técnicas de aprendizagem. Para atingir este objetivo, propõe-se aqui a utilização de dispositivos adaptativos para representar o conhecimento adquirido através da aprendizagem incremental. Além disso, é feito um estudo de caso que combina aprendizagem de máquina com técnicas adaptativas para implementar um esquema de aprendizagem autônoma de estratégias, com o objetivo de vencer uma particular instância do jogo que é apresentado. A aprendizagem de um jogo exige a tomada de decisão, que é um processo complexo e dinâmico. Com a finalidade de fornecer um substrato geral para a criação, manipulação e análise de regras em problemas de tomada de decisão, utilizando tabelas de decisão adaptativas, a ferramenta de software Adapt-DT foi implementada. Um exemplo ilustrativo utilizando tabelas de decisão adaptativa como meio para a representação de conhecimento é apresentado, para exercitar a utilização da ferramenta. Isto permite concluir que os dispositivos adaptativos podem ser utilizados para representar o conhecimento adequadamente, com vantagens sobre outros métodos tradicionais. / Incremental learning requires a learning mechanism based on the information extracted from dynamically accumulated experiments. Adaptivity-oriented machine-learning combines adaptive techniques with symbolic ones for solving machine-learning problems. The term adaptivity means the ability of a learning process to change its own set of rules in response to events occurred during the learning process, or, equivalently, self-tuning the set of parameters. The adaptive devices with withhold information ability inside their rules, extracted from input from their own set of rules, can accumulate information to be used whenever they are necessary. The strategies of interest to adopt adaptivity include the use of machine learning techniques and methods, particularly the ones that implement supervised learning and decision-making. This work purposes to investigate the application of adaptive techniques in machine learning process, either exclusively and in cooperation with other techniques. In order to achieve this target, the use of adaptive devices to represent the knowledge gathered through incremental learning is proposed. Additionally, a case study that combines both machine learning and adaptive techniques to implement a scheme of autonomous learning strategies is also performed with the goal of winning an instance of the simple game. Decision-making is required to learning how to play a game, which is a complex and dynamic process. So as to provide a general framework for the creation, manipulation and analysis of rules in decision-making problems using adaptive decision tables, the Adapt-DT tool was implemented. An illustrative example using adaptive decision tables as a means to represent knowledge is introduced to the tool evaluation. This supports the conclusion that adaptive devices can be used to adequately represent the knowledge, with advantages over other traditional methods.
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Adaptatividade em aprendizagem de máquina: conceitos e estudo de caso. / Adaptivity in machine learning: Concepts and case study.Renata Luiza Stange 21 October 2011 (has links)
A aprendizagem incremental requer que o mecanismo de aprendizagem seja baseado no acúmulo dinâmico da informação extraída das experiências realizadas. A aprendizagem de máquina usando adaptatividade considera a integração de técnicas de aprendizagem de máquina simbólicas com técnicas adaptativas para a solução de problemas de aprendizagem. A palavra adaptatividade sugere a capacidade de modificação do conjunto de regras aprendidas em resposta a eventos que podem ocorrer durante o processo de aprendizagem, ou então autoajustes no conjunto de parâmetros. Os dispositivos adaptativos que possuem a capacidade de reter em suas regras informações extraídas de suas entradas podem acumular informações, para que sejam utilizadas quando forem necessárias. As estratégias de interesse para a incorporação da adaptatividade incluem a utilização de métodos e técnicas de aprendizagem de máquina, em particular as que implementam aprendizado supervisionado e tomada de decisão. O objetivo deste trabalho é explorar a utilização de técnicas adaptativas no processo de aprendizado por máquina, tanto de forma exclusiva como em conjunto com outras técnicas de aprendizagem. Para atingir este objetivo, propõe-se aqui a utilização de dispositivos adaptativos para representar o conhecimento adquirido através da aprendizagem incremental. Além disso, é feito um estudo de caso que combina aprendizagem de máquina com técnicas adaptativas para implementar um esquema de aprendizagem autônoma de estratégias, com o objetivo de vencer uma particular instância do jogo que é apresentado. A aprendizagem de um jogo exige a tomada de decisão, que é um processo complexo e dinâmico. Com a finalidade de fornecer um substrato geral para a criação, manipulação e análise de regras em problemas de tomada de decisão, utilizando tabelas de decisão adaptativas, a ferramenta de software Adapt-DT foi implementada. Um exemplo ilustrativo utilizando tabelas de decisão adaptativa como meio para a representação de conhecimento é apresentado, para exercitar a utilização da ferramenta. Isto permite concluir que os dispositivos adaptativos podem ser utilizados para representar o conhecimento adequadamente, com vantagens sobre outros métodos tradicionais. / Incremental learning requires a learning mechanism based on the information extracted from dynamically accumulated experiments. Adaptivity-oriented machine-learning combines adaptive techniques with symbolic ones for solving machine-learning problems. The term adaptivity means the ability of a learning process to change its own set of rules in response to events occurred during the learning process, or, equivalently, self-tuning the set of parameters. The adaptive devices with withhold information ability inside their rules, extracted from input from their own set of rules, can accumulate information to be used whenever they are necessary. The strategies of interest to adopt adaptivity include the use of machine learning techniques and methods, particularly the ones that implement supervised learning and decision-making. This work purposes to investigate the application of adaptive techniques in machine learning process, either exclusively and in cooperation with other techniques. In order to achieve this target, the use of adaptive devices to represent the knowledge gathered through incremental learning is proposed. Additionally, a case study that combines both machine learning and adaptive techniques to implement a scheme of autonomous learning strategies is also performed with the goal of winning an instance of the simple game. Decision-making is required to learning how to play a game, which is a complex and dynamic process. So as to provide a general framework for the creation, manipulation and analysis of rules in decision-making problems using adaptive decision tables, the Adapt-DT tool was implemented. An illustrative example using adaptive decision tables as a means to represent knowledge is introduced to the tool evaluation. This supports the conclusion that adaptive devices can be used to adequately represent the knowledge, with advantages over other traditional methods.
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Fast simulation of (nearly) incompressible nonlinear elastic material at large strain via adaptive mixed FEMBalg, Martina, Meyer, Arnd 19 October 2012 (has links) (PDF)
The main focus of this work lies in the simulation of the deformation of mechanical components which consist of nonlinear elastic, incompressible material and that are subject to large deformations. Starting from a nonlinear formulation one can derive a discrete problem by using linearisation techniques and an adaptive mixed finite element method. This turns out to be a saddle point problem that can be solved via a Bramble-Pasciak conjugate gradient method. With some modifications the simulation can be improved.
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Σχεδιασμός κι ανάπτυξη εξατομικευμένου και προσαρμοστικού συστήματος ηλεκτρονικής μάθησης, το μέλλον των Learning Management Systems / Design and development of a personalized and adaptive e-learning system, the future of Learning Management SystemsΣκουληκάρη, Αριάδνη - Ειρήνη 12 June 2015 (has links)
Τα τελευταία χρόνια η αυξανόμενη σημασία της πληροφορίας και της συνεχιζόμενης μάθησης έχει καταστήσει τη χρήση των τεχνολογιών πληροφορικής και επικοινωνιών (Τ.Π.Ε.) στην εκπαίδευση καθώς και την εξ αποστάσεως εκπαίδευση μέσω e-learning συστημάτων, ως επιτακτική ανάγκη.
Το κυριότερο πλεονέκτημα των e-learning συστημάτων είναι ότι παρέχουν τη δυνατότητα στον κόσμο να παρακολουθήσει ένα μάθημα, ακόμα κι ένα ολόκληρο πρόγραμμα σπουδών εξ αποστάσεως, μέσω της σύγχρονης και παγκοσμίως πλέον διαδεδομένης μεθόδου των online courses. Τα περισσότερα μεγάλης εμβέλειας και αναγνωρισιμότητας, πανεπιστήμια του εξωτερικού προσφέρουν online μαθήματα μέσω τεχνολογιών του διαδικτύου, χρησιμοποιώντας διαφάνειες, βιντεο-διαλέξεις και online εκπαιδευτικές δραστηριότητες. Ένας τομέας όμως στον οποίο υστερεί η εκπαίδευση εξ αποστάσεως, ακόμα και στα πιο πρόσφατα ανεπτυγμένα e-learning συστήματα, είναι ο τομέας της προσωποποίησης του σπουδαστή και εξατομίκευσης του συστήματος στις ανάγκες του.
Η παρούσα διπλωματική εργασία παρουσιάζει τις δυνατότητες που παρέχονται από τα ήδη υπάρχοντα συστήματα e-learning, την τωρινή κατάσταση με τα παρεχόμενα online μαθήματα από πανεπιστήμια του εξωτερικού και το ερευνητικό κενό που υπάρχει σχετικά με την «προσωποποίηση» (personalization) του σπουδαστή και την προσαρμογή (adaptation) του συστήματος στις ανάγκες του.
Μελετάται η μοντελοποίηση του χρήστη (user modeling), τα μαθησιακά προφίλ, ο εμπλουτισμός του προφίλ του σπουδαστή ώστε να παρέχει περισσότερες και αξιόλογες πληροφορίες, καθώς και οι δυνατότητες εξατομίκευσης του συστήματος στον εκάστοτε σπουδαστή, ώστε να επιτευχθεί η επιτάχυνση και αποτελεσματικότητα της ηλεκτρονικής μάθησης.
Στα πλαίσια της παρούσας διπλωματικής εργασίας σχεδιάστηκε και υλοποιήθηκε ένα σύστημα ηλεκτρονικής μάθησης, το οποίο στηρίζεται στο λογισμικό Moodle και έχουν αναπτυχθεί σε αυτό, νέες υπηρεσίες εξατομίκευσης και προσαρμοστικότητας του συστήματος στις ανάγκες και προτιμήσεις του εκπαιδευομένου. Το Moodle LMS (Modular Object Oriented Dynamic Learning Environment) είναι ελεύθερο λογισμικό διαχείρισης εκπαιδευτικού περιεχομένου και χρησιμοποιείται από πολλά πανεπιστήμια παγκοσμίως. Είναι ευέλικτο, εύκολο στην εκμάθηση και αρκετά ασφαλές για την ασύγχρονη εκπαίδευση από απόσταση. Ενσωματώνει πληθώρα λειτουργιών και δυνατοτήτων που επιτρέπουν στο διδάσκοντα να διαμορφώσει ένα καλά οργανωμένο και ευχάριστο μάθημα με ευρεία κλίμακα δραστηριοτήτων.
Στο εξατομικευμένο και προσαρμοστικό σύστημα ηλεκτρονικής μάθησης που αναπτύχθηκε, διαμορφώθηκε ένα μάθημα με πλούσιο εκπαιδευτικό υλικό, το οποίο απαρτίζουν πολλά και διαφορετικού τύπου μαθησιακά αντικείμενα (πηγές πληροφόρησης, δραστηριότητες, κ.α.). Εμπλουτίστηκε το προφίλ χρήστη με περισσότερες προσωπικές πληροφορίες γι αυτόν και στη συνέχεια αναπτύχθηκαν μαθησιακά μονοπάτια που στηρίζονται είτε στα πεδία προφίλ χρήστη, είτε στο μαθησιακό στυλ του εκπαιδευομένου, είτε σε άλλους παράγοντες που παρουσιάζονται αναλυτικά στην εργασία. Για την εξατομίκευση του συστήματος αναπτύχθηκε μία ενότητα «Pre-course test» η οποία περιλαμβάνει δύο νέες υπηρεσίες για την άντληση πληροφοριών του χρήστη, μορφωτικό υπόβαθρο, μαθησιακό στυλ, προηγούμενη γνώση στο αντικείμενο του μαθήματος κ.α. Τα αποτελέσματα που προκύπτουν από εκεί, αξιοποιούνται κατάλληλα για τη διαμόρφωση ομάδων των εκπαιδευομένων και για τις υπηρεσίες προσαρμοστικότητας του συστήματος.
Επίσης, στο διαδικτυακό αυτό σύστημα ηλεκτρονικής μάθησης έχουν αναπτυχθεί μαθησιακά αντικείμενα που ενισχύουν στη συνεργατική μάθηση, βελτιώνουν την ποιότητα του μαθήματος και έτσι αυξάνεται το κίνητρο του σπουδαστή. / Nowdays, e-learning environments have become increasingly popular in educational establishments. The rapid growth of e-learning has changed traditional learning behavior and presented a new situation to both educators (lecturers) and learners (students). The majority of current e-learning systems are based on Learning Management Systems (LMS), which allow students attending courses free from space and time limitations. They can attend the class anytime they are available and regardless of the place.
LMS are web-based educational systems that offer students an active role in their own education through a variety of learning activities and different kinds of learning content, that the educator has produced. Although this fact, most Learning Management Systems lack of personalization and adaptivity features. The modern trend in education is the production and organization of Massive Open Online Courses (MOOCs) from large and internationally recognized Universities. So, they focus on gathering too many people in these courses (MOOCs) and not on personalization and adaptivity.
Personalization in web-based systems means “attention to the user and his needs”. Web-based systems, such as e-commerce sites, focus on personalization by observing the user, his common actions and navigation paths, in order to understand his preferences and what he is looking for. So they differentiate each individual according to his interests, preferences, and generally his “profile”. Then, they adapt the content appropriately to his needs, and the user watches first the content that may interest him.
Traditional and commonly used e-learning platforms offer to their users same educational content, same learning activities and possibilities, and generally exactly the same content, with no further personalization support. Some existing open source e-Learning systems may support, under certain circumstances adaptation and personalization features, but need extension and elaboration to acquire sufficiently these characteristics.
Especially in the case of distance learning, that teacher and students have no face-to-face communication, learner’s personalization is essential in order the teacher to be aware of each learner’s characteristics. In e-learning systems, personalization could be achieved with an integrated user profile (student profile), which would include except from the classic information (name, surname, email) more specific and useful information. If the teacher had more information about each student, he could be able to guide him more effectively and evaluate him more correctly. In addition to that, if teacher was aware of each learner’s profile, meaning his learning style, interests, preferences and his previous knowledge of the course topics, he would be able to adapt the learning content to his needs. That would increase student’s satisfaction, motivation and consequently his participation in the course.
In this master thesis, a personalized and adaptive e-learning system has been developed. The development of this integrated personalized e-learning system, is based on a very popular open source LMS, which in this case is used for further extension and development of new features. The most suitable LMS for implementing those new features is Moodle (Modular Object-oriented Dynamic Learning Environment), due to its modularity and extensibility as well as its vast community of users. There have been added new features in order to enrich student’s profile and adjust learning material to the learner, depending on his profile and learning progress. The teacher has the ability to organize suitable learning objects and learning paths for each student, depending on particular user profile fields, learning styles and student’s performance. This personalized and adaptive e-learning system increases student’s motivation and participation.
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Schemes and Strategies to Propagate and Analyze Uncertainties in Computational Fluid Dynamics ApplicationsGeraci, Gianluca 05 December 2013 (has links) (PDF)
In this manuscript, three main contributions are illustrated concerning the propagation and the analysis of uncertainty for computational fluid dynamics (CFD) applications. First, two novel numerical schemes are proposed : one based on a collocation approach, and the other one based on a finite volume like representation in the stochastic space. In both the approaches, the key element is the introduction of anon-linear multiresolution representation in the stochastic space. The aim is twofold : reducing the dimensionality of the discrete solution and applying a time-dependent refinement/coarsening procedure in the combined physical/stochastic space. Finally, an innovative strategy, based on variance-based analysis, is proposed for handling problems with a moderate large number of uncertainties in the context of the robust design optimization. Aiming to make more robust this novel optimization strategies, the common ANOVA-like approach is also extended to high-order central moments (up to fourth order). The new approach is more robust, with respect to the original variance-based one, since the analysis relies on new sensitivity indexes associated to a more complete statistic description.
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Adaptive sequential feature selection in visual perception and pattern recognition / Adaptive sequentielle Featureasuwahl in visuelle Wahrnehmung und MustererkennungAvdiyenko, Liliya 08 October 2014 (has links) (PDF)
In the human visual system, one of the most prominent functions of the extensive feedback from the higher brain areas within and outside of the visual cortex is attentional modulation. The feedback helps the brain to concentrate its resources on visual features that are relevant for recognition, i. e. it iteratively selects certain aspects of the visual scene for refined processing by the lower areas until the inference process in the higher areas converges to a single hypothesis about this scene.
In order to minimize a number of required selection-refinement iterations, one has to find a short sequence of maximally informative portions of the visual input. Since the feedback is not static, the selection process is adapted to a scene that should be recognized. To find a scene-specific subset of informative features, the adaptive selection process on every iteration utilizes results of previous processing in order to reduce the remaining uncertainty about the visual scene.
This phenomenon inspired us to develop a computational algorithm solving a visual classification task that would incorporate such principle, adaptive feature selection. It is especially interesting because usually feature selection methods are not adaptive as they define a unique set of informative features for a task and use them for classifying all objects. However, an adaptive algorithm selects features that are the most informative for the particular input. Thus, the selection process should be driven by statistics of the environment concerning the current task and the object to be classified. Applied to a classification task, our adaptive feature selection algorithm favors features that maximally reduce the current class uncertainty, which is iteratively updated with values of the previously selected features that are observed on the testing sample. In information-theoretical terms, the selection criterion is the mutual information of a class variable and a feature-candidate conditioned on the already selected features, which take values observed on the current testing sample. Then, the main question investigated in this thesis is whether the proposed adaptive way of selecting features is advantageous over the conventional feature selection and in which situations.
Further, we studied whether the proposed adaptive information-theoretical selection scheme, which is a computationally complex algorithm, is utilized by humans while they perform a visual classification task. For this, we constructed a psychophysical experiment where people had to select image parts that as they think are relevant for classification of these images. We present the analysis of behavioral data where we investigate whether human strategies of task-dependent selective attention can be explained by a simple ranker based on the mutual information, a more complex feature selection algorithm based on the conventional static mutual information and the proposed here adaptive feature selector that mimics a mechanism of the iterative hypothesis refinement.
Hereby, the main contribution of this work is the adaptive feature selection criterion based on the conditional mutual information. Also it is shown that such adaptive selection strategy is indeed used by people while performing visual classification.
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Spasiba: a context-aware adaptive mobile advisorRudkovskiy, Alexey 01 April 2010 (has links)
This thesis presents the design and analysis of Spasiba, a context-aware mobile advisor. We argue that current context-aware mobile applications exhibit significant flaws with respect to (1) limited use of context information, (2) incomplete or irrelevant content generation, and (3) low usability. The proposed model attempts to tackle these limitations by advancing the usage and manipulation of context information, automating the back-end systems in terms of self-management and seamless extensibility, and shifting the logic away from the client side. A distinguishing characteristic of Spasiba is the proactive approach to notifying the user of information of interest. In this proactive approach, the user subscribes to the service and receives content updates as the context changes. This proposed model is realised in a proof-of-concept prototype that uses a Nokia Web Runtime widget as the client application. The widget, which sports an elegant, touch-optimised interface, collects multiple context parameters to deliver high-quality results. The server-side architecture employs the publish/subscribe paradigm for managing the active users and Comet—for proactively notifying the clients of updated information of interest. IRS-III, a Semantic Web Services broker, handles the process of content generation. The prototype employs nine data sources, seven of which are open API web services and two of which are regular web pages, to deliver diverse and complete results. A simple autonomic element, implemented with the help of aspect-oriented programming, ensures partial self-management of the back-end systems. Spasiba is evaluated by means of a case study that involves a tourist couple visiting Victoria. The application assists the tourist couple with finding attractions, relevant stores, and places serving food.
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Context management and self-adaptivity for situation-aware smart software systemsVillegas Machado, Norha Milena 25 February 2013 (has links)
Our society is increasingly demanding situation-aware smarter software (SASS)
systems, whose goals change over time and depend on context situations. A system
with such properties must sense their dynamic environment and respond to changes
quickly, accurately, and reliably, that is, to be context-aware and self-adaptive. The problem addressed in this dissertation is the dynamic management of context information, with the goal of improving the relevance of SASS systems' context-aware capabilities with respect to changes in their requirements and execution environment. Therefore, this dissertation focuses on the investigation of dynamic context management and self-adaptivity to: (i) improve context-awareness and exploit context information to enhance quality of user experience in SASS systems, and (ii) improve the dynamic capabilities of self-adaptivity in SASS systems. Context-awareness and self-adaptivity pose signi cant challenges for the engineering of SASS systems. Regarding context-awareness, the rst challenge addressed in this dissertation is the impossibility of fully specifying environmental entities and the corresponding monitoring requirements at design-time. The second challenge arises from the continuous evolution of monitoring requirements due to changes in the system caused by self-adaptation. As a result, context monitoring strategies must be modeled and managed in such a way that they support the addition and deletion of context types and monitoring conditions at runtime. For this, the user must be integrated into the dynamic context management process. Concerning self-adaptivity, the third challenge is to control the dynamicity of adaptation goals, adaptation mechanisms, and monitoring infrastructures, and the way they a ect each other in the adaptation process. This is to preserve the eff ectiveness of context monitoring requirements and thus self-adaptation. The fourth challenge, related also to self-adaptivity,concerns the assessment of adaptation mechanisms at runtime to prevent undesirable system states as a result of self-adaptation. Given these challenges, to improve context-awareness we made three contributions. First, we proposed the personal context sphere concept to empower users to control
the life cycle of personal context information in user-centric SASS systems. Second, we proposed the SmarterContext ontology to model context information and its monitoring requirements supporting changes in these models at runtime. Third, we proposed an effi cient context processing engine to discover implicit contextual facts from context information speci fied in changing context models. To improve self-adaptivity we made three contributions. First, we proposed a framework for the identi cation of adaptation properties and goals, which is useful to evaluate self-adaptivity and to derive monitoring requirements mapped to adaptation goals. Second, we proposed a reference model for designing highly dynamic self-adaptive systems, for which the continuous pertinence between monitoring mechanisms and both changing system goals and context situations is a major concern. Third, we proposed a model with explicit validation and veri cation (V&V) tasks for
self-adaptive software, where dynamic context monitoring plays a major role. The seventh contribution of this dissertation, the implementation of Smarter-Context infrastructure, addresses both context-awareness and self-adaptivity. To evaluate our contributions, qualitatively and quantitatively, we conducted several comprehensive literature reviews, a case study on user-centric situation-aware online shopping, and a case study on dynamic governance of service-oriented applications. / Graduate
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Efficient and Reliable Simulation of Quantum Molecular DynamicsKormann, Katharina January 2012 (has links)
The time-dependent Schrödinger equation (TDSE) models the quantum nature of molecular processes. Numerical simulations based on the TDSE help in understanding and predicting the outcome of chemical reactions. This thesis is dedicated to the derivation and analysis of efficient and reliable simulation tools for the TDSE, with a particular focus on models for the interaction of molecules with time-dependent electromagnetic fields. Various time propagators are compared for this setting and an efficient fourth-order commutator-free Magnus-Lanczos propagator is derived. For the Lanczos method, several communication-reducing variants are studied for an implementation on clusters of multi-core processors. Global error estimation for the Magnus propagator is devised using a posteriori error estimation theory. In doing so, the self-adjointness of the linear Schrödinger equation is exploited to avoid solving an adjoint equation. Efficiency and effectiveness of the estimate are demonstrated for both bounded and unbounded states. The temporal approximation is combined with adaptive spectral elements in space. Lagrange elements based on Gauss-Lobatto nodes are employed to avoid nondiagonal mass matrices and ill-conditioning at high order. A matrix-free implementation for the evaluation of the spectral element operators is presented. The framework uses hybrid parallelism and enables significant computational speed-up as well as the solution of larger problems compared to traditional implementations relying on sparse matrices. As an alternative to grid-based methods, radial basis functions in a Galerkin setting are proposed and analyzed. It is found that considerably higher accuracy can be obtained with the same number of basis functions compared to the Fourier method. Another direction of research presented in this thesis is a new algorithm for quantum optimal control: The field is optimized in the frequency domain where the dimensionality of the optimization problem can drastically be reduced. In this way, it becomes feasible to use a quasi-Newton method to solve the problem. / eSSENCE
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Enhancing the scaled boundary finite element methodVu, Thu Hang January 2006 (has links)
[Truncated abstract] The scaled boundary finite element method is a novel computational method developed by Wolf and Song which reduces partial differential equations to a set of ordinary linear differential equations. The method, which is semi-analytical, is suitable for solving linear elliptic, parabolic and hyperbolic partial differential equations. The method has proved to be very efficient in solving various types of problems, including problems of potential flow and diffusion. The method out performs the finite element method when solving unbounded domain problems and problems involving stress singularities and discontinuities. The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. Consequently, to a greater extent than the finite element method, it is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, no systematic study had been performed so far into the use of elements of higher order, and no consideration made of p adaptivity. . . The primal problem is solved normally using the basic scaled boundary finite element method. The dual problem is solved by the new technique using the fundamental solution. A guaranteed upper error bound based on the Cauchy-Schwarz inequality is derived. A iv goal-oriented p-hierarchical adaptive procedure is proposed and implemented efficiently in the scaled boundary finite element method.
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