Mathematical modeling of physical processes often leads to systems of differential and algebraic equations involving quantities of interest. A computer model created based on these equations can be numerically integrated to predict future states of the system and its evolution in time. This thesis investigates current methods in numerical time-stepping schemes, identifying a number of important features needed to speed up and increase the accuracy of the solutions. The focus is on developing new methods suitable for large-scale applications with multiple physical processes, potentially with significant differences in their time-scales. Various families of new methods are introduced with special attention to multirating, low computational cost implicitness, high order of convergence, and robustness. For each family, the order condition theory is discussed and a number of examples are derived. The accuracy and stability of the methods are investigated using standard analysis techniques and numerical experiments are performed to verify the abilities of the new methods. / Doctor of Philosophy / Mathematical descriptions of physical processes are often in the form of systems of differential equations describing the time-evolution of a phenomenon. Computer simulations are realizations of these equations using well-known discretization schemes. Numerical time-stepping methods allow us to advance the state of a computer model using a sequence of time-steps. This thesis investigates current methods in time-stepping schemes, identifying a number of additional features needed to improve the speed and accuracy of simulations, and devises new methods suitable for large-scale applications where multiple processes of different physical nature drive the equations, potentially with significant differences in their time-scales. Various families of new methods are introduced with proper mathematical formulations provided for creating new ones on demand. The accuracy and stability of the methods are investigated using standard analysis techniques. These methods are then used in numerical experiments to investigate their abilities.

The transient time-domain simulation, of the circuit response, is a fundamental component in the Computer-Aided Design tools of all integrated circuit and systems. It is typically desirable that a method adopted in the transient circuit simulator be of high- order and numerically stable. The two requirements, however, proved to be in conflict with each other, especially in the larger class of methods that were used in traditional circuit simulators. Recent work based on utilizing the Obreshkov formula has proved that it is possible to combine the high order with the numerical stability. The objective of this thesis is to show how the present implementation of the Obreshkov- based method can be improved and generalized to handle different types of circuits. The first aspect of improvement targets the computation of the high-order derivatives re- quired by the Obreshkov formula. The second aspect of improvement, presented in the thesis, develops a generalized formulation that takes into account the presence of non- linear memory elements, whose nonlinearity is based on a capacitive or inductive-based nonlinear model.

This thesis investigates the numerical treatment of nonlinear eigenvalue problems. These problems are defined by the condition $T(lambda) v = boldsymbol{0}$, with $T: C to C^{n times n}$, where we seek to compute the scalar-vector pairs, $lambda in C$ and nonzero $ v in C^{n}$. The first contribution of this work connects recent contour integration methods to the theory and practice of system identification. This observation leads us to explore rational interpolation for system realization, producing a Loewner matrix contour integration technique. The second development of this work studies the application of rational interpolation to the function $T(z)^{-1}$, where we use the poles of this interpolant to approximate the eigenvalues of $T$. We then expand this idea to several iterative methods, where at each step the approximate eigenvalues are taken as new interpolation points. We show that the case where one interpolation point is used is theoretically equivalent to Newton's method for a particular scalar function. / Master of Science / This thesis investigates the numerical treatment of nonlinear eigenvalue problems. The solutions to these problems often reveal characteristics of an underlying physical system. One popular methodology for handling these problems uses contour integrals to compute a set of the solutions. The first contribution of this work connects these contour integration methods to the theory and practice of system identification. This leads us to explore other techniques for system identification, resulting in a new method. Another common methodology approximates the nonlinear problem directly. The second development of this work studies the application of rational interpolation for this purpose. We then use this idea to form several iterative methods, where at each step the approximate solutions are taken to be new interpolation points. We show that the case where one interpolation point is used is theoretically equivalent to Newton’s method for a particular scalar function.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / AnimaÃÃo baseada em FÃsica ganhou muita atenÃÃo dos pesquisadores nas Ãltimas duas dÃcadas, por causa dos desafios de realismo e desempenho propostos pelas indÃstrias de filme e jogos, bem como pelas aplicaÃÃes de realidade virtual e comÃrcio eletrÃnico. Consequentemente, foram feitos avanÃos significativos nessa Ãrea, e vÃrias abordagens foram propostas, tanto para a modelagem de tecidos, quanto para a simulaÃÃo de seu comportamento dinÃmico. Modelar tecido como um sistema massa-mola tem sido uma tÃcnica amplamente utilizada, por causa de sua simplicidade, e porque ela permite soluÃÃes numÃricas mais eficientes para as equaÃÃes diferenciais que governam o problema. Esses mÃtodos de integraÃÃo sÃo divididos em duas categorias principais: os mÃtodos explÃcitos e os mÃtodos implÃcitos. Um conhecimento mais aprofundado sobre o uso desses mÃtodos no contexto de simulaÃÃo dinÃmica de tecidos ainda à pertinente. Dessa forma, o objetivo desta dissertaÃÃo à analisar os mÃtodos de integraÃÃo mais comumente usados na literatura sobre simulaÃÃo de tecidos baseados em sistemas de partÃculas, para entender melhor suas vantagens e desvantagens. Um estudo comparativo desses mÃtodos à feito, considerando os critÃrios de realismo de animaÃÃo, esforÃo computacional e estabilidade numÃrica. / Physically based cloth animation has gained much attention from researchers in the last two decades, due to the challenges of realism and performance placed by the film and game industries, as well as by the applications of virtual reality and e-commerce. Consequently, there have been overwhelming achievements in this area, and several approaches have been proposed for modeling and simulating the dynamic behavior of cloth. Modeling cloth as a mass-spring system has been widely used, because of its simplicity and since it leads to more efficient numerical solutions to the governing differential equations. These numerical integration methods are divided into two main categories: explicit integration methods and implicit integration methods. A deeper understanding about their use in cloth simulations is still in order. Thus, the objective of this work is to analyze the integration methods most commonly used in the literature of cloth simulation, based on particle systems, to understand the advantages and disadvantages of their use. A comparative study of those methods is done, considering the criteria of animation realism, computational effort and numerical stability.

Customer-centric business approaches have been theorized over the last decades (Sheth, Sisodia and Sharma, 2000; Sheth, Sethia and Srinivas, 2011; Rajagopal, 2020). However, the active usage of customer input for a successful product portfolio strategy is widespread but not yet fully implemented (Cooper, Edgett and Kleinschmidt, 2002). The co-creation aspects of having two equal partners in performing the product portfolio structuring task is a key issue for managers (Rajagopal, 2020). The aim is to find how customer input can be used as an important influencing factor for the product portfolio strategy. This aim is achieved through an analysis of the most commonly used influencing factors and the expert's assessment of information gathering procedures and their categorisation, supported by the Edvardsson et al. (2012) framework. Furthermore, a framework by Voss (2012) is examined regarding customer integration into project portfolio management to investigated possible additions. As an appropriate method, an exploratory approach with a single case study and semi-structured interviews of experts of the field is selected. The primary data of this case study is compared with a structured literature review, which consists of the latest theories on customer integration into the product portfolio strategy. Four major results are found. First, product portfolio strategy is mainly driven by financial input and not yet by customer input. Second, customer input should be collected through multiple channels. Thirdly, customer input is assessed as being a useful factor for the product portfolio strategy. Fourths the execution of input gathering is currently performed more towards past performances than for future-oriented input as needs and wishes for the product portfolio structuring. Finally, managerial implications with a method is provided for the collection, storage, analysis and distribution of customer input. In conclusion, the implementation fidelity of the future related customer input is not yet performed but desired. The approach of input collection from customers is considered to be valuable, however a suitable method is needed. Furthermore, two new connections can be made for the structuring phase of Voss’s framework and avenues for future research of the customer input integration are presented. / Över de senaste årtiondena har det teoretiserats kring affärmodeller koncentrerade kring konsumenterna (Sheth, Sisodia och Sharma, 2000; Sheth, Sethia och Srinivas, 2011; Rajagopal, 2020). Idèn att använda konsumenternas åsikter för att utveckla strategier kring sortimentet är välkänd, men ännu inte helt implementerad (Cooper, Edgett and Kleinschmidt, 2002). Frågorna kring hur två affärspartners tillsammans ska strukturera sina sortiment är av stor vikt för chefer (Rajagopal, 2020). Målet är att undersöka hur konsumenternas feedback kan användas för att påverka strategin avseende sortimentet. Detta uppnås genom en analys av de vanligaste fallen där kunderna påverkat strategin, samt utlåtanden från experter om insamling av information. Vidare undersöks ett ramverk från Voss (2012) vars syfte är att involvera kunderna i utformningen av sortimentet. En fallstudie samt öppna intervjufrågor till experter inom ämnet lade grunden till detta. Den viktigaste datan från studien jämfördes med aktuella teorier kring integration av kunder i utvecklingen av sortimentet. Resultatet visade framför allt fyra tydliga samband. Det första var att strategier kring sortiment framför allt drivs av finansiella faktorer, och inte konsumentkritik. Det andra var att feedback från kunderna borde samlas in från flera olika kanaler. Det tredje var att kundernas kritik värderades högt i utformningen av sortimentet, och det fjärde var att insamlingen av kritik från kunderna ofta fokuserar på utvärdering av tidigare sortiment, istället för att ta in önskemål från kunder om ändringar av sortimentet. Slutligen tillhandahålls en metod för insamling, förvaring, analys och distribution av kundernas kritik. Sammanfattningsvis är exaktheten för insamling av framtidsorienterad kritik ännu inte bra nog, men värderad högt. Att jobba tillsammans med kunderna anses mer värdefullt, speciellt när en lämplig metod är tillgänglig. Dessutom kan två nya kopplingar göras för strukturen i Voss's ramverk, och tillvägagångssätt för framtida forskning på konsumentkritik presenteras.

The topic of structural dynamics involves an ample actuation field since the most of nature actions are time dependent. The analyses of structures in aerospace engineering, offshore engineering, civil engineering and others might be realized including the inertial effects since they have important role in reliability and safety of them. Due to the various nonlinearities that can be present in the dynamic analysis, the preview of the dynamic behavior of a structure can become a complex task. That analysis is generally executed using computational numeric algorithms improved for spatial and temporal discretization where computational requirements are excessive. Techniques based on element-by-element concept have gained recognition due to its increasing efficiency caused by the recent development of parallel computers. This work is focused on time integration algorithms for nonlinear dynamic problems formulated by the finite element approach. Besides, the considered algorithms have been prepared to be used, in the future, on parallel computational architectures. The main algorithms for nonlinear structural dynamics and alternatives of implementation of the element-by-element techniques are studied. The software MATLAB has been used for implementation of some algorithms, whose features are analyzed by examples. Some characteristics as computational cost, number of iterations and solutions quality are observed for nonlinear quasistatic and dynamic problems, adopting several spatial and temporal discretization levels. / A dinâmica de estruturas compreende uma vasta área de atuação visto que as ações da natureza são geralmente variáveis com o tempo. Análises de aeronaves, estruturas offshore, estruturas sujeitas a terremotos, entre outras, devem ser realizadas considerando também os efeitos inerciais, que têm papel importante na performance e segurança dessas estruturas. A análise do comportamento dinâmico dessas estruturas é bastante complexa em virtude das diversas não linearidades que podem estar presentes. Atualmente, essas análises são realizadas utilizando-se algoritmos numéricos computacionais para discretização espacial e temporal, exigindo, em geral, grandes esforços computacionais. Com o advento dos clusters de computadores na década de 90, o emprego de algoritmos numéricos paralelos utilizando a técnica elemento por elemento tem se difundido e se mostrado eficiente na solução desses problemas. Nesse contexto, este trabalho está direcionado ao estudo de algoritmos de integração no tempo para problemas de dinâmica não linear de estruturas pelo método dos elementos finitos, que possibilitem seu uso futuro em arquiteturas computacionais paralelas. Os principais algoritmos para dinâmica não linear de estruturas são revisados, assim como as alternativas de implementação através da utilização da técnica elemento por elemento. Em seguida, utilizando-se o programa computacional MATLAB, implementam-se alguns desses algoritmos e avaliam-se suas características através de exemplos ilustrativos. Observam-se, nesses exemplos, características como custo computacional, número de iterações e qualidade das respostas geradas para problemas quase estáticos e dinâmicos não lineares considerando-se diversos níveis de discretização espacial e temporal.

This work introduces a time adaptive strategy that uses a refinement estimator based on the geometric indicator of curvature. The developed methodology is suitable for problems of numerical time integration present, for example, in the study of bodies subjected to dynamical loads. The refinement estimator demands low computational resources, being easily applied to several direct integration methods. Trying to interact these methods, an object oriented library that uses the developed scheme of adaptation is built. The main idea of this tool is to incorporate this scheme, in an easy way, in existing computational codes that employ direct integration methods. Examples of dynamic solid bodies are presented, ilustrating the technique and library usage in existing applications. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho introduz uma estratégia de adaptação no tempo que utiliza um estimador de refinamento baseado no indicador geométrico curvatura. A metodologia desenvolvida é aplicada ao problema de integração numérica temporal, presente, por exemplo, no estudo do comportamento de corpos submetidos a cargas dinâmicas. O estimador de refinamento formulado demanda pouco esforço computacional, sendo facilmente aplicado aos diversos métodos de integração direta existentes. Visando a interação com esses métodos, constrói-se uma biblioteca orientada a objetos que incorpora a técnica de adaptação desenvolvida. A idéia principal desta ferramenta é prover, de forma fácil, a técnica de adaptação concebida a códigos computacionais existentes e que fazem uso dos referidos métodos de integração. Apresentam-se exemplos de dinâmica de corpos sólidos que ilustram o potencial de utilização da técnica e o uso da biblioteca em aplicações existentes.

Doctor Scientiae - DSc / Robust Spectral Methods for Solving Option Pricing Problems by Edson Pindza PhD thesis, Department of Mathematics and Applied Mathematics, Faculty of Natural Sciences, University of the Western Cape Ever since the invention of the classical Black-Scholes formula to price the financial derivatives, a number of mathematical models have been proposed by numerous researchers in this direction. Many of these models are in general very complex, thus closed form analytical solutions are rarely obtainable. In view of this, we present a class of efficient spectral methods to numerically solve several mathematical models of pricing options. We begin with solving European options. Then we move to solve their American counterparts which involve a free boundary and therefore normally difficult to price by other conventional numerical methods. We obtain very promising results for the above two types of options and therefore we extend this approach to solve some more difficult problems for pricing options, viz., jump-diffusion models and local volatility models. The numerical methods involve solving partial differential equations, partial integro-differential equations and associated complementary problems which are used to model the financial derivatives. In order to retain their exponential accuracy, we discuss the necessary modification of the spectral methods. Finally, we present several comparative numerical results showing the superiority of our spectral methods.

Cross-border mergers and acquisitions (M&A) have become a prominent internationalization and growth strategy of today’s global business landscape. However, the practice faces significant failure in terms of value creation. To this end, the post-merger integration of information systems (IS) is critical for the failure rate of M&As due to the complexity and ambiguity of how and what systems should be consolidated. Research has been carried out to provide frameworks illustrating IS integration methods and the relationship between business strategies and IS integration strategies but omits potential factors that influence the level of IS integration. Hence, the aim of this study is to examine what factors influence how information systems are integrated in cross-border M&As. This was carried out through a qualitative multiple-case study of 9 Swedish multinational corporations with recent M&A activity. The study finds that there are five IS integration methods, one of which was added by this study in order to cover all levels of how IS are integrated. Additionally, a mixture of factors was found to influence specific IS integration methods where the M&A context, design of the IS integration, and organizational characteristics were on a general level found to be most influential. This suggests previous findings focused on alignment of business strategies and IS integration strategies need a nuanced view to further explain the failure rates of M&As.

Made available in DSpace on 2016-12-23T14:05:52Z (GMT). No. of bitstreams: 1 Diogo Folador Rossi.pdf: 4782694 bytes, checksum: c76f1cce52a07536be399c535f2db153 (MD5) Previous issue date: 2013-03-22 / Esse trabalho apresenta o uso de métodos de adaptação automática dos incrementos de tempo utilizados na integração numérica passo-a-passo das análises dinâmicas de sistemas estruturais, no domínio do tempo, em estruturas de um e de múltiplos graus de liberdade. Buscou-se comparar as performances das diferentes estratégias adaptativas estudadas. Inicialmente, foi feita uma revisão dos principais processos adotados na solução numérica das equações de equilíbrio dinâmico de sistemas de um grau de liberdade, se concentrando na família de métodos de Newmark, discutindo seus mais amplos aspectos. Posteriormente foi tratado o problema de estruturas de múltiplos graus de liberdade, descrevendo a formação das matrizes estruturais envolvidas através do conceito do método dos elementos finitos e da análise matricial de estruturas, considerando o amortecimento estrutural do tipo viscoso e proporcional, e generalizando os processos de solução numérica das equações dinâmicas. Em seguida foi descrito o escopo de um programa computacional que aplicasse a teoria desenvolvida em análise de estruturas de pórticos planos, o qual foi construído no ambiente de programação do software Matlab. As estratégias de adaptação do incremento de tempo são analisadas na sequência, escolhendo-se três algoritmos principais a serem abordados na implementação, dentre os vários disponíveis, por se basearem em conceitos distintos uns dos outros. Por fim, são apresentados exemplos numéricos resolvidos, onde se comparam as performances das diferentes estratégias adaptativas e se propõem melhorias e diretrizes de aplicação das mesmas / This work presents methods of automatic adaptive time increment used in numerical step-by-step integration analyses of structural systems, in time domain, for single and multi-degree-of-freedom structures. The main purpose was to compare the different strategies performances. Initially, the major processes formulations adopted in the numerical solution of dynamic equilibrium equations were shown for single-degree-of-freedom systems, focusing on the Newmark family of integration methods, discussing about its various aspects. Later, the problem of multi-degree-of-freedom systems was discussed, by describing the structural matrix formulations, considering viscous and proportional structural damping, and generalizing the numerical solution of dynamic equations. Then, it is described a computational program that apply the developed theory on plane frame structures analysis, which was built in the programing software Matlab. The adaptive strategies of time increment are then analyzed, having three major algorithms been chosen to be addressed in the implementation, among the various others available, because they are based on three different concepts. Finally, several numerical examples are presented, on which the performances of the different adaptive strategies are compared, and improvements and guidelines for application are suggested