In this dissertation we present an analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric and symmetrizable hyperbolic systems of conservation laws. We explicitly write the leading term of the local DG error, which is spanned by Legendre polynomials of degree p and p+1 when p-th degree polynomial spaces are used for the solution. For special hyperbolic systems, where the coefficient matrices are nonsingular, we show that the leading term of the error is spanned by (p+1)-th degree Radau polynomials. We apply these asymptotic results to observe that projections of the error are pointwise O(h^p+2)-superconvergent in some cases and establish superconvergence results for some integrals of the error. We develop an efficient implicit residual-based a posteriori error estimation scheme by solving local finite element problems to compute estimates of the leading term of the discretization error. For smooth solutions we obtain error estimates that converge to the true error under mesh refinement. We first show these results for linear symmetric systems that satisfy certain assumptions, then for general linear symmetric systems. We further generalize these results to linear symmetrizable systems by considering an equivalent symmetric formulation, which requires us to make small modifications in the error estimation procedure. We also investigate the behavior of the discretization error when the Lax-Friedrichs numerical flux is used, and we construct asymptotically exact a posteriori error estimates. While no superconvergence results can be obtained for this flux, the error estimation results can be recovered in most cases. These error estimates are used to drive h- and p-adaptive algorithms and assess the numerical accuracy of the solution. We present computational results for different fluxes and several linear and nonlinear hyperbolic systems in one, two and three dimensions to validate our theory. Examples include the wave equation, Maxwell's equations, and the acoustic equation. / Ph. D.

Modeling or simulating Complex Adaptive Systems (CASs) is both important and challenging. As the name suggests, CASs are systems consisting of large numbers of interacting adaptive compartments. They are studied across a wide range of disciplines and have unique properties. They model such systems as multicellular organisms, ecosystems, social networks, and many more. They are complex, in the sense that they are dynamical, nonlinear, and heterogeneous systems that cannot be simply scaled up/down. However, they are self-organized, in the sense that they can evolve into specific structures/patterns without guidance from outside sources. Modeling/Simulating CASs is challenging, not only because of the high complexity, but also because of the difficulty in explaining the underlying mechanism behind self-organization. The goal of this research is to provide a modeling framework as well as a simulation platform to advance the study of CASs. We argue that there are common principles behind self-organization processes of different systems across different domains. We explore, analyze, and perform experiments into these principles. We propose and implement modeling templates such as short-term and long-term adaptivity. We incorporate techniques from systems theory, employing computing paradigms, including multi-agent system and asynchronous message passing. We also consider an application from the biological domain to model and simulate under our framework, treating it as a CAS for validation purposes. / Ph. D.

More and more challenging designs are required everyday in today¿s industries. The traditional trial and error procedure commonly used for mechanical parts design is not valid any more since it slows down the design process and yields suboptimal designs. For structural components, one alternative consists in using shape optimization processes which provide optimal solutions. However, these techniques require a high computational effort and require extremely efficient and robust Finite Element (FE) programs. FE software companies are aware that their current commercial products must improve in this sense and devote considerable resources to improve their codes. In this work we propose to use the Cartesian Grid Finite Element Method, cgFEM as a tool for efficient and robust numerical analysis. The cgFEM methodology developed in this thesis uses the synergy of a variety of techniques to achieve this purpose, but the two main ingredients are the use of Cartesian FE grids independent of the geometry of the component to be analyzed and an efficient hierarchical data structure. These two features provide to the cgFEM technology the necessary requirements to increase the efficiency of the cgFEM code with respect to commercial FE codes. As indicated in [1, 2], in order to guarantee the convergence of a structural shape optimization process we need to control the error of each geometry analyzed. In this sense the cgFEM code also incorporates the appropriate error estimators. These error estimators are specifically adapted to the cgFEM framework to further increase its efficiency. This work introduces a solution recovery technique, denoted as SPR-CD, that in combination with the Zienkiewicz and Zhu error estimator [3] provides very accurate error measures of the FE solution. Additionally, we have also developed error estimators and numerical bounds in Quantities of Interest based on the SPR-CD technique to allow for an efficient control of the quality of the numerical solution. Regarding error estimation, we also present three new upper error bounding techniques for the error in energy norm of the FE solution, based on recovery processes. Furthermore, this work also presents an error estimation procedure to control the quality of the recovered solution in stresses provided by the SPR-CD technique. Since the recovered stress field is commonly more accurate and has a higher convergence rate than the FE solution, we propose to substitute the raw FE solution by the recovered solution to decrease the computational cost of the numerical analysis. All these improvements are reflected by the numerical examples of structural shape optimization problems presented in this thesis. These numerical analysis clearly show the improved behavior of the cgFEM technology over the classical FE implementations commonly used in industry. / Cada d'¿a dise¿nos m'as complejos son requeridos por las industrias actuales. Para el dise¿no de nuevos componentes, los procesos tradicionales de prueba y error usados com'unmente ya no son v'alidos ya que ralentizan el proceso y dan lugar a dise¿nos sub-'optimos. Para componentes estructurales, una alternativa consiste en usar procesos de optimizaci'on de forma estructural los cuales dan como resultado dise¿nos 'optimos. Sin embargo, estas t'ecnicas requieren un alto coste computacional y tambi'en programas de Elementos Finitos (EF) extremadamente eficientes y robustos. Las compa¿n'¿as de programas de EF son conocedoras de que sus programas comerciales necesitan ser mejorados en este sentido y destinan importantes cantidades de recursos para mejorar sus c'odigos. En este trabajo proponemos usar el M'etodo de Elementos Finitos basado en mallados Cartesianos (cgFEM) como una herramienta eficiente y robusta para el an'alisis num'erico. La metodolog'¿a cgFEM desarrollada en esta tesis usa la sinergia entre varias t'ecnicas para lograr este prop'osito, cuyos dos ingredientes principales son el uso de los mallados Cartesianos de EF independientes de la geometr'¿a del componente que va a ser analizado y una eficiente estructura jer'arquica de datos. Estas dos caracter'¿sticas confieren a la tecnolog'¿a cgFEM de los requisitos necesarios para aumentar la eficiencia del c'odigo cgFEM con respecto a c'odigos comerciales. Como se indica en [1, 2], para garantizar la convergencia del proceso de optimizaci'on de forma estructural se necesita controlar el error en cada geometr'¿a analizada. En este sentido el c'odigo cgFEM tambi'en incorpora los apropiados estimadores de error. Estos estimadores de error han sido espec'¿ficamente adaptados al entorno cgFEM para aumentar su eficiencia. En esta tesis se introduce un proceso de recuperaci'on de la soluci'on, llamado SPR-CD, que en combinaci'on con el estimador de error de Zienkiewicz y Zhu [3], da como resultado medidas muy precisas del error de la soluci'on de EF. Adicionalmente, tambi'en se han desarrollado estimadores de error y cotas num'ericas en Magnitudes de Inter'es basadas en la t'ecnica SPR-CD para permitir un eficiente control de la calidad de la soluci'on num'erica. Respecto a la estimaci'on de error, tambi'en se presenta un proceso de estimaci'on de error para controlar la calidad del campo de tensiones recuperado obtenido mediante la t'ecnica SPR-CD. Ya que el campo recuperado es por lo general m'as preciso y tiene un mayor orden de convergencia que la soluci'on de EF, se propone sustituir la soluci'on de EF por la soluci'on recuperada para disminuir as'¿ el coste computacional del an'alisis num'erico. Todas estas mejoras se han reflejado en esta tesis mediante ejemplos num'ericos de problemas de optimizaci'on de forma estructural. Los resultados num'ericos muestran claramente un mejor comportamiento de la tecnolog'¿a cgFEM con respecto a implementaciones cl'asicas de EF com'unmente usadas en la industria. / Nadal Soriano, E. (2014). Cartesian grid FEM (cgFEM): High performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/35620

L’objectif principal de la thèse est de répondre à des questions liées aux étapes clé d’un processus de l’adaptation de modèles de plaques. Comme l’adaptativité dépend des estimateurs d’erreurs fiables, une part importante du rapport est dédiée au développement des méthodes numériques pour les estimateurs d’erreurs aussi bien dues à la discrétisation qu’au choix du modèle. Une comparaison des estimateurs d’erreurs de discrétisation d’un point de vue pratique est présentée. Une attention particulière est prêtée a la méthode de résiduels équilibrés (en anglais, "equilibrated residual method"), laquelle est potentiellement applicable aux estimations des deux types d’erreurs, de discrétisation et de modèle.Il faut souligner que, contrairement aux estimateurs d’erreurs de discrétisation, les estimateurs d’erreur de modèle sont plus difficiles à élaborer. Le concept de l’adaptativité de modèles pour les plaques est implémenté sur la base de la méthode de résiduels équilibrés et de la famille hiérarchique des éléments finis de plaques. Les éléments finis dérivés dans le cadre de la thèse, comprennent aussi bien les éléments de plaques minces et que les éléments de plaques épaisses. Ces derniers sont formulés en s’appuyant sur une théorie nouvelle de plaque, intégrant aussi les effets d’étirement le long de l’épaisseur. Les erreurs de modèle sont estimées via des calculs élément par élément. Les erreurs de discrétisation et de modèle sont estimées d’une manière indépendante, ce qui rend l’approche très robuste et facile à utiliser. Les méthodes développées sont appliquées sur plusieurs exemples numériques. Les travaux réalisés dans le cadre de la thèse représentent plusieurs contributions qui visent l’objectif final de la modélisation adaptative, ou une procédure complètement automatique permettrait de faire un choix optimal du modèle de plaques pour chaque élément de la structure. / The primary goal of the thesis is to provide some answers to the questions related to the key steps in the process of adaptive modeling of plates. Since the adaptivity depends on reliable error estimates, a large part of the thesis is related to the derivation of computational procedures for discretization error estimates as well as model error estimates. A practical comparison of some of the established discretization error estimates is made. Special attention is paid to what is called equilibrated residuum method, which has a potential to be used both for discretization error and model error estimates. It should be emphasized that the model error estimates are quite hard to obtain, in contrast to the discretization error estimates. The concept of model adaptivity for plates is in this work implemented on the basis of equilibrated residuum method and hierarchic family of plate finite element models.The finite elements used in the thesis range from thin plate finite elements to thick plate finite elements. The latter are based on a newly derived higher order plate theory, which includes through the thickness stretching. The model error is estimated by local element-wise computations. As all the finite elements, representing the chosen plate mathematical models, are re-derived in order to share the same interpolation bases, the difference between the local computations can be attributed mainly to the model error. This choice of finite elements enables effective computation of the model error estimate and improves the robustness of the adaptive modeling. Thus the discretization error can be computed by an independent procedure.Many numerical examples are provided as an illustration of performance of the derived plate elements, the derived discretization error procedures and the derived modeling error procedure. Since the basic goal of modeling in engineering is to produce an effective model, which will produce the most accurate results with the minimum input data, the need for the adaptive modeling will always be present. In this view, the present work is a contribution to the final goal of the finite element modeling of plate structures: a fully automatic adaptive procedure for the construction of an optimal computational model (an optimal finite element mesh and an optimal choice of a plate model for each element of the mesh) for a given plate structure.

[pt] Este trabalho apresenta uma metodologia para geração de malhas adaptativas de elementos finitos 2D e 3D usando modeladores geométricos com multi-regiões e superfícies paramétricas. A estratégia adaptativa adotada é fundamentada no refinamento independente das curvas, superfícies e sólidos. Inicialmente as curvas são refinadas, no seu espaço paramétrico, usando uma técnica de partição binária da curva (binary-tree). A discretização das curvas é usada como dado de entrada para o refinamento das superfícies. A discretização destas é realizada no seu espaço paramétrico e utiliza uma técnica de avanço de fronteira combinada com uma estrutura de dados do tipo quadtree para gerar uma malha não estruturada de superfície. Essas malhas de superfícies são usadas como dado de entrada para o refinamento dos domínios volumétricos. A discretização volumétrica combina uma estrutura de dados do tipo octree juntamente com a técnica de avanço de fronteira para gerar uma malha sólida não estruturada de elementos tetraédricos. As estruturas de dados auxiliares dos tipos binary-tree, quadtree e octree são utilizadas para armazenar os tamanhos característicos dos elementos gerados no refinamento das curvas, superfícies e regiões volumétricas. Estes tamanhos característicos são definidos pela estimativa de erro numérico associado à malha global do passo anterior do processo adaptativo. A estratégia adaptativa é implementada em dois modeladores: o MTOOL (2D) e o MG (3D), que são responsáveis pela criação de um modelo geométrico, podendo ter, multi-regiões, onde no caso 3D as curvas e superfícies são representadas por NURBS. / [en] This work presents a methodology for adaptive generation of 2D and 3D finite-element meshes using geometric modeling with multi- regions and parametric surfaces. The adaptive strategy adopted in this methodology is based on independent refinements of curves, surfaces and solids. Initially, the model´s curves are refined using a binary-partition algorithm in parametric space. The discratizetion of these curves is used as input for the refinement of adjacent surfaces. Surface discretization is also performed in parametric space and employs a quadtree-based refinement coupled to an advancing-front technique for the generation of an unstructured triangulation. These surface meshes are used as input for the refinement adjacent volumetric domains. Volume discretization combines an octree refinement with an advancing-front technique to generate an unstructural mesh of tetrahedral elements. In all stages of the adaptive strategy, the refinement of curves, surface meshes and solid meshes is based on estimated numerical errors associated to the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes into account metric distortions between parametric and Cartesian spaces and high curvatures of the model´s geometric entities. The adaptive strategies are implemented in two different modelers: MTOOL (2D) and MG (3D), which are responsible for the creation of a geometric model with multi-regions, where for case 3D the curves and surfaces are represented by NURBS, and for the interactive and automatic finite-element mesh generation associated to surfaces and solid regions. Numerical examples of the simulation of engineering problems are presented in order to validate the methodology proposed in this work.

This research is concerned with the self-adaptive numerical solution of the neutral particle radiation transport problem. Radiation transport is an extremely challenging computational problem since the governing equation is seven-dimensional (3 in space, 2 in direction, 1 in energy, and 1 in time) with a high degree of coupling between these variables. If not careful, this relatively large number of independent variables when discretized can potentially lead to sets of linear equations of intractable size. Though parallel computing has allowed the solution of very large problems, available computational resources will always be finite due to the fact that ever more sophisticated multiphysics models are being demanded by industry. There is thus the pressing requirement to optimize the discretizations so as to minimize the effort and maximize the accuracy. One way to achieve this goal is through adaptive phase-space refinement. Unfortunately, the quality of discretization (and its solution) is, in general, not known a priori; accurate error estimates can only be attained via the a posteriori error analysis. In particular, in the context of the finite element method, the a posteriori error analysis provides a rigorous error bound. The main difficulty in applying a well-established a posteriori error analysis and subsequent adaptive refinement in the context of radiation transport is the strong coupling between spatial and angular variables. This research attempts to address this issue within the context of the second-order, even-parity form of the transport equation discretized with the finite-element spherical harmonics method. The objective of this thesis is to develop a posteriori error analysis in a coupled space-angle framework and an efficient adaptive algorithm. Moreover, the mesh refinement strategy which is tuned for minimizing the error in the target engineering output has been developed by employing the dual argument of the problem. This numerical framework has been implemented in the general-purpose neutral particle code EVENT for assessment.

Die vorliegende Dissertation präsentiert neue wissenschaftliche Konzepte und Lösungen zur Erstellung, Durchführung und Auswertung von Befragungen, die sich einfacher an unterschiedliche Nutzungsszenarien anpassen lassen und für den Einsatz in virtuellen Organisationen besser geeignet sind als herkömmliche Online-Befragungen. Die dabei berücksichtigten Adaptionsaspekte umfassen Inhalt und Umfang der Befragung, die Umsetzung in unterschiedliche Präsentationsmedien, -formate und Befragungsmodi sowie das adaptive Verhalten während der Interaktion. Eine wesentliche Grundlage bildet die inhaltsorientierte Beschreibung adaptiver und adaptierbarer Befragungen durch die hier vorgeschlagene deklarative Beschreibungssprache AXSML. Diese berücksichtigt insbesondere die Wechselwirkungen der unterschiedlichen Adaptionsaspekte in Verbindung mit der Forderung nach einer medien- und modusübergreifenden Vergleichbarkeit der Ergebnisse multimodaler Befragungen. Für diese Beschreibungssprache werden Transformationsregeln vorgestellt, die eine adäquate Umsetzung einer Befragung in verschiedene Präsentationsmedien und Befragungsformen ermöglichen. Eine damit einhergehende inhaltliche Anpassung an das Einsatzszenario erfolgt automatisiert und erfordert keine speziellen Fachkenntnisse auf dem Gebiet des Befragungsdesigns. Die Auswertung der Befragungsrückläufe wird ebenfalls deklarativ beschrieben, berücksichtigt adaptionsbedingte Fehlwerte und erlaubt die Nutzung verschiedenster Berechnungsmodelle zur Aggregation der Rücklaufdaten. Da Erstellung und Wartung adaptiver und adaptierbarer Befragungen sehr komplex sind, werden Konzepte und Lösungen zur Unterstützung des Autorenprozesses vorgestellt, die den notwendigen Aufwand reduzieren. Um die gleichzeitige Durchführung einer großen Zahl von Untersuchungen in vielen unterschiedlichen Teams und die Anpassung der Befragung durch Nicht-Fachexperten zu gewährleisten, wurde eine IT-Stützung des Befragungsprozesses konzipiert und umgesetzt, welche den Anforderungen an die organisatorische Einbindung der Befragung in virtuellen Unternehmen gerecht wird.

In this thesis we focus on multiscale and multiphysics problems. We derive a posteriori error estimates for a one way coupled multiphysics problem, using the dual weighted residual method. Such estimates can be used to drive local mesh refinement in adaptive algorithms, in order to efficiently obtain good accuracy in a desired goal quantity, which we demonstrate numerically. Furthermore we prove existence and uniqueness of finite element solutions for a two way coupled multiphysics problem. The possibility of deriving dual weighted a posteriori error estimates for two way coupled problems is also addressed. For a two way coupled linear problem, we show numerically that unless the coupling of the equations is to strong the propagation of errors between the solvers goes to zero. We also apply a variational multiscale method to both an elliptic and a hyperbolic problem that exhibits multiscale features. The method is based on numerical solutions of decoupled local fine scale problems on patches. For the elliptic problem we derive an a posteriori error estimate and use an adaptive algorithm to automatically tune the resolution and patch size of the local problems. For the hyperbolic problem we demonstrate the importance of how to construct the patches of the local problems, by numerically comparing the results obtained for symmetric and directed patches.

This work develops finite element methods with high order stabilization, and robust and efficient adaptive algorithms for Large Eddy Simulation of turbulent compressible flows. The equations are approximated by continuous piecewise linear functions in space, and the time discretization is done in implicit/explicit fashion: the second order Crank-Nicholson method and third/fourth order explicit Runge-Kutta methods. The full residual of the system and the entropy residual, are used in the construction of the stabilization terms. These methods are consistent for the exact solution, conserves all the quantities, such as mass, momentum and energy, is accurate and very simple to implement. We prove convergence of the method for scalar conservation laws in the case of an implicit scheme. The convergence analysis is based on showing that the approximation is uniformly bounded, weakly consistent with all entropy inequalities, and strongly consistent with the initial data. The convergence of the explicit schemes is tested in numerical examples in 1D, 2D and 3D. To resolve the small scales of the flow, such as turbulence fluctuations, shocks, discontinuities and acoustic waves, the simulation needs very fine meshes. In this thesis, a robust adjoint based adaptive algorithm is developed for the time-dependent compressible Euler/Navier-Stokes equations. The adaptation is driven by the minimization of the error in quantities of interest such as stresses, drag and lift forces, or the mean value of some quantity. The implementation and analysis are validated in computational tests, both with respect to the stabilization and the duality based adaptation. / QC 20110627

Title: Novel Methods for Natural Language Generation in Spoken Dialogue Systems Author: Ondřej Dušek Department: Institute of Formal and Applied Linguistics Supervisor: Ing. Mgr. Filip Jurčíček, Ph.D., Institute of Formal and Applied Linguistics Abstract: This thesis explores novel approaches to natural language generation (NLG) in spoken dialogue systems (i.e., generating system responses to be presented the user), aiming at simplifying adaptivity of NLG in three respects: domain portability, language portability, and user-adaptive outputs. Our generators improve over state-of-the-art in all of them: First, our gen- erators, which are based on statistical methods (A* search with perceptron ranking and sequence-to-sequence recurrent neural network architectures), can be trained on data without fine-grained semantic alignments, thus simplifying the process of retraining the generator for a new domain in comparison to previous approaches. Second, we enhance the neural-network-based gener- ator so that it takes preceding dialogue context into account (i.e., user's way of speaking), thus producing user-adaptive outputs. Third, we evaluate sev- eral extensions to the neural-network-based generator designed for producing output in morphologically rich languages, showing improvements in Czech generation. In...