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With the advances in process technology, comes the domination of interconnect in the overall propagation delay in modern VLSI designs. Hence, interconnect synthesis techniques, such as buffer insertion, wire sizing and layer assignment play critical roles in the successful timing closure for EDA tools. In this thesis, while our aim is to satisfy timing constraints, accounting for the overhead caused by these optimization techniques is of another primary concern. We utilized a Lagrangian relaxation method to minimize the usage of buffers and metal resources to meet the timing constraints. Compared with the previous work that extended traditional Van Ginneken’s algorithm, which allows for bumping up the wire from thin to thick given significant delay improvement, our approach achieved around 25% reduction in buffer + wire capacitance under the same timing budget.

Elliptic obstacle problems are formulated to find either superharmonic solutions or minimal surfaces that lie on or over the obstacles, by incorporating inequality constraints. This dissertation investigates simple iterative algorithms based on the successive over-relaxation (SOR) method. It introduces subgrid methods to reduce accuracy deterioration occurring near the free boundary when the mesh grid does not match with the free boundary. For nonlinear obstacle problems, a method of gradient-weighting is introduced to solve the problem more conveniently and efficiently. The iterative algorithm is analyzed for convergence for both linear and nonlinear obstacle problems. Parabolic initial-boundary value problems with nonsmooth data show either rapid transitions or reduced smoothness in its solution. For those problems, specific numerical methods are required to avoid spurious oscillations as well as unrealistic smoothing of steep changes in the numerical solution. This dissertation investigates characteristics of the θ-method and introduces a variable-θ method as a synergistic combination of the Crank-Nicolson (CN) method and the implicit method. It suppresses spurious oscillations, by evolving the solution implicitly at points where the solution shows a certain portent of oscillations or reduced smoothness, and maintains as a similar accuracy as the CN method with smooth data. An effective strategy is suggested for the detection of points where the solution may introduce spurious oscillations (the wobble set); the resulting variable-θ method is analyzed for its accuracy and stability. After a theory of morphogenesis in chemical cells was introduced in 1950s, much attention had been devoted to the numerical solution of reaction-diffusion (RD) equations. This dissertation studies a nonoscillatory second-order time-stepping procedure for RD equations incorporating with variable-θ method, as a perturbation of the CN method. We also perform a sensitivity analysis for the numerical solution of RD systems to conclude that it is much more sensitive to the spatial mesh resolution than the temporal one. Moreover, to enhance the spatial approximation of RD equations, this dissertation investigates the averaging scheme, that is, an interpolation of the standard and skewed discrete Laplacian operator and introduce the simple optimizing strategy to minimize the leading truncation error of the scheme.

Bakgrund: I Sverige bistår barnmorskan vid den normala förlossningen och har en nyckelroll i att stödja kvinnan till avslappning under förlossningen. Avslappning minskar känsligheten för förlossningssmärta och främjar förloppet. Det ingår i barnmorskans förhållningssätt och yrkeskunskap. Syfte: Att beskriva barnmorskors erfarenhet av att stödja den födande till avslappning med dyktekniken under värkarbete. Metod: Kvalitativ deskriptiv design med individuella intervjuer. Nio legitimerade barnmorskor som stött den födande kvinnan till avslappning med dyktekniken under värkarbete intervjuades. Resultat: Resultatet beskrivs utifrån barnmorskans upplevelse och erfarenhet av att stödja födande kvinnor till avslappning med dyktekniken under värkarbete. Ett övergripande tema i analysen var hur dyktekniken är ett verktyg för barnmorskan att i barnafödandet stödja kvinnan till avslappning och för att göra hennes partner delaktig. Hur barnmorskan gjorde detta kan förstås genom följande kategorier som utkristalliserades genom analysen: dyktekniken ger positiva effekter för kvinnan och hennes partner i födandet, kvinnans förberedelse till att använda dyktekniken, dyktekniken stärker partnerns delaktighet samt barnmorskans förhållningssätt till dyktekniken. Slutsats: Flera faktorer styr kvinnornas val att välja aktiv avslappning. De intervjuade barnmorskorna delade med sig av sina erfarenheter om att stödja den födande kvinnan till avslappning under värkarbete. Barnmorskorna informerade, guidade med ord och stödde aktivt kvinnan till djup avslappning för att hantera värkarna. / Background: In Sweden, the midwife manages normal childbirth. The midwife has a key role in supporting the woman to relax during birth. Relaxation reduces the sensitivity to labor pain and promotes the process. It is part of the midwife's approaches and professional knowledge. Objective: To describe the midwives' experience of supporting the woman giving birth with the Dive Relaxation Method during the labor pain. Method: A qualitative and descriptive design using individual interviews. Nine licensed midwives who have supported women during labor to relaxation with the dive relaxation method were interviewed. Results: The result can be described on the basis of the midwife's experience and the experience of supporting women in labor to relaxation with the dive relaxation method during the labor pain. An overall theme in the analysis was how the method is a tool for the midwife to support the woman during childbirth to relaxation and to make her partner participate. How the midwife support the woman can be understood by the categories that were taken out of the analysis: the dive relaxation method has positive effects for the woman and her partner during childbirth, the woman's preparation for using the method, the method strengthens the partner's participations and the midwife's approach to the method. Conclusion: Several factors control women's choice to choose active relaxation. The interviewed midwives shared their experience about supporting the woman to relaxation during labor pain. The midwives informed, guided with words and actively supported the woman to deep relaxation to manage the pain.

Nesta tese discute-se a necessidade de se desenvolver novas ferramentas para auxiliar o projeto e análise de estruturas de cabos e membranas. Esse tipo de estrutura, essencialmente não linear, é geralmente analisada por meio do Método dos Elementos Finitos, combinado com o Método de Newton-Raphson, para a resolução do sistema de equações não lineares resultante. Porém, a ausência de um campo de tensão de tração sobre toda estrutura composta por elementos finitos de cabos e membranas pode gerar uma matriz de rigidez tangente indeterminada, levando à divergência da solução pelo Método de Newton-Raphson. O Método da Relaxação Dinâmica é uma alternativa interessante para resolver problemas não lineares complicados de equilíbrio estático, na qual o problema do equilíbrio estático é resolvido por uma análise dinâmica, com integração no tempo. A resposta transiente é fictícia e não tem significado físico, entretanto a parte estacionária é a solução do problema de equilíbrio estático. Nesta tese, apresenta-se uma contextualização histórica sobre o Método da Relaxação Dinâmica, apontando as contribuições mais relevantes já desenvolvidas por outros autores. Propõe-se um procedimento de sintonia da massa dos elementos, capaz de uniformizar as condições impostas ao incremento de tempo, para se obter estabilidade do processo de integração numérica. Implementam-se as formulações dos elementos finitos adotados, bem como um algoritmo de enrugamento para os elementos de membrana e diversas rotinas de pós-processamento, no programa de elementos finitos SATS (A System for the Analysis of Taut Structures), desenvolvido pelo autor desta tese, em colaboração com seu orientador. A implementação desenvolvida é aplicada a uma série de exemplos relativos ao projeto e análise de estruturas de cabos e membranas, permitindo verificar a eficiência dos procedimentos de amortecimento e cinético e de sintonia de massa propostos. / This thesis discusses the need to develop new tools to assist the design and analysis of cables and membrane structures. This type of structures, essentially non-linear is generally analyzed using the Finite Element Method, where in most cases the solution is obtained by the Newton-Raphson Method. However, the absence of a tension stress field over the entire structure composed only with cable and membrane finite element can generate a non-positive definite tangent stiffness matrix, leading to the divergence of Newton-Raphson iterations. The Method of Dynamic Relaxation is an interesting alternative to solve complicated nonlinear problems of static equilibrium, replaced by an equivalent dynamic analysis. The transient solution is fictitious and without physical meaning, and the stationary phase provides the static equilibrium solution. This thesis presents a historical contextualization of the Dynamic Relaxation Method, highlighting the most relevant contributions already developed by other authors. A procedure for the tuning of the element masses is proposed, which is capable of making uniform the restrictions imposed to the time steps in order to preserve the stability of the numerical integration. Some adopted finite element formulations are implemented, as well as an algorithm for representing the wrinkling of membrane elements and several post-processing routines, in the SATS (A System for the Analysis of Taut Structures) finite element program, developed by the author of this thesis, in collaboration with his advisor. The developed implementation is applied to a series of examples on the design and analysis of cables and membrane structures, allowing verification of the efficiency of the procedures proposed for kinetic damping and mass tuning.

Nesta tese discute-se a necessidade de se desenvolver novas ferramentas para auxiliar o projeto e análise de estruturas de cabos e membranas. Esse tipo de estrutura, essencialmente não linear, é geralmente analisada por meio do Método dos Elementos Finitos, combinado com o Método de Newton-Raphson, para a resolução do sistema de equações não lineares resultante. Porém, a ausência de um campo de tensão de tração sobre toda estrutura composta por elementos finitos de cabos e membranas pode gerar uma matriz de rigidez tangente indeterminada, levando à divergência da solução pelo Método de Newton-Raphson. O Método da Relaxação Dinâmica é uma alternativa interessante para resolver problemas não lineares complicados de equilíbrio estático, na qual o problema do equilíbrio estático é resolvido por uma análise dinâmica, com integração no tempo. A resposta transiente é fictícia e não tem significado físico, entretanto a parte estacionária é a solução do problema de equilíbrio estático. Nesta tese, apresenta-se uma contextualização histórica sobre o Método da Relaxação Dinâmica, apontando as contribuições mais relevantes já desenvolvidas por outros autores. Propõe-se um procedimento de sintonia da massa dos elementos, capaz de uniformizar as condições impostas ao incremento de tempo, para se obter estabilidade do processo de integração numérica. Implementam-se as formulações dos elementos finitos adotados, bem como um algoritmo de enrugamento para os elementos de membrana e diversas rotinas de pós-processamento, no programa de elementos finitos SATS (A System for the Analysis of Taut Structures), desenvolvido pelo autor desta tese, em colaboração com seu orientador. A implementação desenvolvida é aplicada a uma série de exemplos relativos ao projeto e análise de estruturas de cabos e membranas, permitindo verificar a eficiência dos procedimentos de amortecimento e cinético e de sintonia de massa propostos. / This thesis discusses the need to develop new tools to assist the design and analysis of cables and membrane structures. This type of structures, essentially non-linear is generally analyzed using the Finite Element Method, where in most cases the solution is obtained by the Newton-Raphson Method. However, the absence of a tension stress field over the entire structure composed only with cable and membrane finite element can generate a non-positive definite tangent stiffness matrix, leading to the divergence of Newton-Raphson iterations. The Method of Dynamic Relaxation is an interesting alternative to solve complicated nonlinear problems of static equilibrium, replaced by an equivalent dynamic analysis. The transient solution is fictitious and without physical meaning, and the stationary phase provides the static equilibrium solution. This thesis presents a historical contextualization of the Dynamic Relaxation Method, highlighting the most relevant contributions already developed by other authors. A procedure for the tuning of the element masses is proposed, which is capable of making uniform the restrictions imposed to the time steps in order to preserve the stability of the numerical integration. Some adopted finite element formulations are implemented, as well as an algorithm for representing the wrinkling of membrane elements and several post-processing routines, in the SATS (A System for the Analysis of Taut Structures) finite element program, developed by the author of this thesis, in collaboration with his advisor. The developed implementation is applied to a series of examples on the design and analysis of cables and membrane structures, allowing verification of the efficiency of the procedures proposed for kinetic damping and mass tuning.

We explore the paradigm shift in quantum computing and quantum information science, emphasizing the synergy between hardware advancements and algorithm development. Only now have the recent advances in quantum computing hardware, despite a century of quantum mechanics, unveiled untapped potential, requiring innovative algorithms for full utilization. Project 1 addresses quantum applications in radiative reactions, overcoming challenges in many-fermion physics due to imaginary time evolution, stochastic methods like Monte Carlo simulations, and the associated sign problem. The methodology introduces the Electromagnetic Transition System and a general two-level system for computing radiative capture reactions. Project 2 utilizes Variational Quantum Eigensolver (VQE) to address the difficulties in adiabatic quantum computations, highlighting Singular Value Decomposition (SVD) in quantum computing. Results demonstrate an accurate ground state wavefunction match with only a 0.016% energy error. These projects advance quantum algorithm design, error mitigation, and SVD integration, showcasing quantum computing’s transformative potential in computational science.

L’objectif principal de cette thèse concerne l’étude, la conception et la mise en œuvre numérique de schémas volumes finis associés aux solveurs de type Godunov. On s’intéresse à des systèmes hyperboliques de lois de conservation non linéaires, avec une attention particulière sur les équations d’Euler et les équations MHD idéale. Tout d’abord, nous dérivons un solveur de Riemann simple et véritablement multidimensionnelle, pouvant s’appliquer à tout système de lois de conservation. Ce solveur peut être considéré comme une généralisation 2D de l’approche HLL. Les ingrédients de base de la dérivation sont : la consistance avec la formulation intégrale et une utilisation adéquate des relations de Rankine-Hugoniot. Au final nous obtenons des expressions assez simples et applicables dans les contextes des maillages structurés et non structurés. Dans un second temps, nous nous intéressons à la préservation, au niveau discret, de la contrainte de divergence nulle du champ magnétique pour les équations de la MHD idéale. Deux stratégies sont évaluées et nous montrons comment le solveur de Riemann multidimensionnelle peut être utilisé pour obtenir des simulations robustes à divergence numérique nulle. Deux autres points sont abordés dans cette thèse : la méthode de relaxation pour un système Euler-Poisson pour des écoulements gravitationnels en astrophysique, la formulation volumes finis en coordonnées curvilignes. Tout au long de la thèse, les choix numériques sont validés à travers de nombreux résultats numériques. / The main objective of this thesis concerns the study, design and numerical implementation of finite volume schemes based on the so-Called Godunov-Type solvers for hyperbolic systems of nonlinear conservation laws, with special attention given to the Euler equations and ideal MHD equations. First, we derive a simple and genuinely two-Dimensional Riemann solver for general conservation laws that can be regarded as an actual 2D generalization of the HLL approach, relying heavily on the consistency with the integral formulation and on the proper use of Rankine-Hugoniot relations to yield expressions that are simple enough to be applied in the structured and unstructured contexts. Then, a comparison between two methods aiming to numerically maintain the divergence constraint of the magnetic field for the ideal MHD equations is performed and we show how the 2D Riemann solver can be employed to obtain robust divergence-Free simulations. Next, we derive a relaxation scheme that incorporates gravity source terms derived from a potential into the hydrodynamic equations, an important problem in astrophysics, and finally, we review the design of finite volume approximations in curvilinear coordinates, providing a fresher view on an alternative discretization approach. Throughout this thesis, numerous numerical results are shown.

Le but de cette thèse est de calculer l'optimum d'un polynôme sur un ensemble semi-algébrique et les points où cet optimum est atteint. Pour atteindre cet objectif, nous combinons des méthodes de base de bord avec la hiérarchie de relaxation convexe de Lasserre afin de réduire la taille des matrices de moments dans les problèmes de programmation semi-définie positive (SDP). Afin de vérifier si le minimum est atteint, nous apportons un nouveau critère pour vérifier l'extension plate de Curto Fialkow utilisant des bases orthogonales. En combinant ces nouveaux résultats, nous fournissons un nouvel algorithme qui calcule l'optimum et les points minimiseurs. Nous décrivons plusieurs expérimentations et des applications dans différents domaines qui prouvent la performance de l'algorithme. Au niveau théorique nous prouvons aussi la convergence finie d'une hiérarchie SDP construite à partir d'un idéal de Karush-Kuhn-Tucker et ses conséquences dans des cas particuliers. Nous étudions aussi le cas particulier où les minimiseurs ne sont pas des points de KKT en utilisant la variété de Fritz-John. / The objective of this thesis is to compute the optimum of a polynomial on a closed basic semialgebraic set and the points where this optimum is reached. To achieve this goal we combine border basis method with Lasserre's hierarchy in order to reduce the size of the moment matrices in the SemiDefinite Programming (SDP) problems. In order to verify if the minimum is reached we describe a new criterion to verify the flat extension condition using border basis. Combining these new results we provide a new algorithm which computes the optimum and the minimizers points. We show several experimentations and some applications in different domains which prove the perfomance of the algorithm. Theorethically we also prove the finite convergence of a SDP hierarchie contructed from a Karush-Kuhn-Tucker ideal and its consequences in particular cases. We also solve the particular case where the minimizers are not KKT points using Fritz-John Variety.

Ces travaux portent sur la modélisation et la simulation numérique des effets du déplacement d'un corps indéformable dans un écoulement multiphasique compressible. Ils se placent dans le cas où plusieurs objets sont en mouvement ou dans le cas où un objet est en mouvement dans un milieu aux géométries complexes. L'étude ne peut alors pas être placée dans le référentiel lié à l'objet en mouvement. Le modèle est basé sur une méthode multiphasique à interfaces diffuses où les différentes phases sont en équilibre mécanique. Le système régissant l'écoulement fluide est augmenté d'une équation d'advection. Cette dernière s'applique sur une fonction Level Set dont le niveau zéro permet de localiser le mobile dans l'espace. Des termes de couplage sont ajoutés au membre de droite des équations d'évolution de la quantité de mouvement et de l'énergie totale. Ces termes sont composés d'un facteur du type pénalisation et d'un facteur du type relaxation de vitesses. Cette nouvelle méthode permet de simuler des cas complexes où peuvent interagir des mobiles à hautes vitesses, des ondes de choc et des interfaces liquide/gaz. / This work deals with modelling and the numerical simulation of the effects of a moving rigid body on a multiphase flow. Here more than one object is moving, or an object is moving in a complex geometry domain. So the reference frame linked to the moving body can't be used. The model is build on a multiphase diffuse interface method with mechanical equilibrium. An advection equation is added. It applies on a Level Set function used to track the moving body. Coupling terms are added to the momentum equation and to the total energy equation. These terms are made of a penalization factor and a velocity relaxation factor. This new method allows to simulate complex cases where can interact high velocity objects, shock waves and liquid / gas interfaces.