This thesis develops the methodology for solving initial boundary value problems with the use of summation-by-parts discretizations. The combination of high orders of accuracy and a systematic approach to construct provably stable boundary and interface procedures makes this methodology especially suitable for scientific computations with high demands on efficiency and robustness. Most classes of high order methods can be applied in a way that satisfies a summation-by-parts rule. These include, but are not limited to, finite difference, spectral and nodal discontinuous Galerkin methods. In the first part of this thesis, the summation-by-parts methodology is extended to the time domain, enabling fully discrete formulations with superior stability properties. The resulting time discretization technique is closely related to fully implicit Runge-Kutta methods, and may alternatively be formulated as either a global method or as a family of multi-stage methods. Both first and second order derivatives in time are considered. In the latter case also including mixed initial and boundary conditions (i.e. conditions involving derivatives in both space and time). The second part of the thesis deals with summation-by-parts discretizations on multi-block and hybrid meshes. A new formulation of general multi-block couplings in several dimensions is presented and analyzed. It collects all multi-block, multi-element and  hybrid summation-by-parts schemes into a single compact framework. The new framework includes a generalized description of non-conforming interfaces based on so called summation-by-parts preserving interpolation operators, for which a new theoretical accuracy result is presented.

<p>Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. </p><p>A method for performing <i>ab initio </i>MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored.</p><p>Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. </p><p>Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as <i>N log N</i>, where <i>N </i>is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs.</p><p>Finally, an outlook is given and some directions for further developments are suggested.</p>

In this thesis we will investigate how the SBP-SAT finite difference method behave with and without an interface. As model problem, we consider the heat equation with piecewise constant coefficients. The thesis is split in two main parts. In the first part we look at the heat equation in one-dimension, and in the second part we expand the problem to a two-dimensional domain. We show how the SAT-parameters are chosen such that the scheme is dual consistent and stable. Then, we perform numerical experiments, now looking at the static case. In the one-dimensional case we see that the second order SBP-SAT method with an interface converge with an order of two, while the second order SBP-SAT method without an interface converge with an order of one.

O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

Doctor of Philosophy (PhD) / With improvements in actuation technology and sensory systems, it is becoming increasingly feasible to create powered exoskeletal garments that can assist with the movement of human limbs. This class of robotics referred to as human-machine interfaces will one day be used for the rehabilitation of paralysed, damaged or weak upper and lower extremities. The focus of this project was the development of an exoskeletal interface for the rehabilitation of the hands. A novel sensor was designed for use in such a device. The sensor uses simple optical mechanisms centred on a spring to measure force and position simultaneously. In addition, the sensor introduces an elastic element between the actuator and its corresponding hand joint. This will allow series elastic actuation (SEA) to improve control and safely of the system. The Hand Rehabilitation Device requires multiple actuators. To stay within volume and weight constraints, it is therefore imperative to reduce the size, mass and efficiency of each actuator without losing power. A method was devised that allows small efficient actuating subunits to work together and produce a combined collective output. This work summation method was successfully implemented with Shape Memory Alloy (SMA) based actuators. The actuation, sensory, control system and human-machine interface concepts proposed were evaluated together using a single-joint electromechanical harness. This experimental setup was used with volunteer subjects to assess the potentials of a full-hand device to be used for therapy, assessment and function of the hand. The Rehabilitation Glove aims to bring significant new benefits for improving hand function, an important aspect of human independence. Furthermore, the developments in this project may one day be used for other parts of the body helping bring human-machine interface technology into the fields of rehabilitation and therapy.

Methods for performing large-scale parallel Molecular Dynamics(MD) simulations are investigated. A perspective on the field of parallel MD simulations is given. Hardware and software aspects are characterized and the interplay between the two is briefly discussed. A method for performing ab initio MD is described; the method essentially recomputes the interaction potential at each time-step. It has been tested on a system of liquid water by comparing results with other simulation methods and experimental results. Different strategies for parallelization are explored. Furthermore, data-parallel methods for short-range and long-range interactions on massively parallel platforms are described and compared. Next, a method for treating electrostatic interactions in MD simulations is developed. It combines the traditional Ewald summation technique with the nonuniform Fast Fourier transform---ENUF for short. The method scales as N log N, where N is the number of charges in the system. ENUF has a behavior very similar to Ewald summation and can be easily and efficiently implemented in existing simulation programs. Finally, an outlook is given and some directions for further developments are suggested.

Akustiska kanaler för undervattenskommunikation är flervägskanaler där ljudet reflekteras från havets yta och botten och bryts vid ljudhastighetsförändringar. I grunt vatten är impulssvaret långt jämfört med symbolernas tidslängd i ett utskickat meddelande. Detta orsakar intersymbolinterferens, vilket gör det svårt att återskapa meddelandet. Denna avhandling behandlar fysikalisk modellering av kommunikationskanalen. Sådan modellering kan öka insikten om de svårigheter som finns vid design av kommunikationssystem och kan vara till hjälp vid utveckling av lämpliga modulationstekniker och avkodningsalgoritmer. Ljudutbredningen simuleras med en strålgångsmetod med reflektionskoefficienter beräknade för plana vågor. I artikel 4 och 5 utvidgas modellen till en algoritm för gaussisk strålsummation. De viktigaste vetenskapliga bidragen är följande. Artikel 1: Aktuell kunskap om impulssvaret hos kommunikationskanalen gör det betydligt lättare att tolka det mottagna meddelandet. I denna artikel studeras tidsvariabiliteten hos impulssvaret i termer av bitfelssannolikhet när ett gammalt impulssvar används för kanalutjämning. Tidsvariabiliteten visar sig variera avsevärt med mottagarpositionen, inte bara när det gäller avståndet till sändaren, utan även när det gäller placeringen i djupled. Artikel 2: En hybridmetod presenteras, där strålgång i ett avståndsberoende medium kombineras med lokal fullfältsmodellering av interaktionen med havsbottnen. Metoden används för simuleringar av akustisk kommunikation i grunt vatten. Artikel 3: För att kunna göra tillförlitliga simuleringar av ljudutbredning behöver man god kunskap om mediets ljudhastighetsprofil --- information som inte alltid är tillgänglig. I denna artikel används den hybrida strålgångsmetoden från artikel 2 för att skatta ljudhastighetsprofilen från kommunikationsdata. Miljöparametrarna som beräknats genom inversionen minskar avvikelsen mellan simulerade och observerade skattningar av impulssvaret jämfört med avvikelsen då en uppmätt, två dagar gammal ljudhastighetsprofil används vid simuleringen. Miljömodellen används också för en genomgång av alternativa käll- och mottagarpositioner. Artikel 4: Gaussisk strålsummation är en vågutbredningsmodell som liknar strålgång men kan ge korrekta resultat i strålgångens singulära områden, som skuggzoner och kaustikor. I denna artikel diskuteras hur några olika val av den komplexa strålparametern $\epsilon$ fungerar i grunda vågledare. Bäst resultat erhålls om man väljer $\epsilon$ så att strålen blir smal i punkten närmast mottagaren och får en plan vågfront där. Artikel 5: En adaptiv metod för gaussisk strålsummation i grunda vågledare presenteras. Algoritmen ger en noggrannhet som är bättre än eller minst lika bra som strålgångens, även i grunda vågledare med en starkt djupberoende ljudhastighet. / Acoustic underwater communication channels are multipath channels where sound is reflected from the surface and the bottom of the sea and refracted by sound speed variations. In shallow water, the impulse response is typically long compared to the time length of the symbols in a transmitted message. This causes inter-symbol interference, which makes the message difficult to decode. This thesis deals with physical modelling of the communication channel. Such modelling can provide insight into the difficulties of communication system design and may serve as an aid in the development of appropriate modulation techniques and decoding algorithms. The sound propagation is simulated by a ray tracing method with plane-wave reflection coefficients, in papers 4 and 5 expanded to a Gaussian beam summation algorithm. The main scientific contributions are the following. Paper 1: Up-to-date knowledge of the impulse response of the communication channel considerably simplifies the extraction of information from a detected signal. In this paper the time variability of the impulse response is studied in terms of the bit-error rate, when an old impulse response is used for channel equalisation. The time variability is found to vary significantly with the receiver position, not only in range, but also in depth. Paper 2: A hybrid raytrace method is presented, combining ray tracing in a range-dependent water column with local full-field modelling of the seabed interaction. The method is applied to simulations of acoustic communication in shallow water. Paper 3: To be able to make reliable simulations of sound propagation, one needs to know, quite accurately, the sound speed profile of the medium --- information which is not always available. In this paper the hybrid raytrace method from paper 2 is used to estimate the sound speed profile from communication data. The environmental model obtained by the inversion reduces the mismatch between the modelled and the observed impulse response estimates, compared to the mismatch with a two-days-old sound speed profile. The model is also used to investigate alternative source-receiver configurations. Paper 4: Gaussian beam summation is a wave propagation model similar to ray tracing, which can yield correct results in singular regions like shadow zones and caustic points. In this paper some different choices of the complex beam parameter $\epsilon$ are discussed for shallow waveguides. Best results are observed when $\epsilon$ is chosen so that each beam is narrow at the point where it is closest to the receiver and has a plane wavefront there. Paper 5: An adaptive method for Gaussian beam summation in shallow waveguides is presented. The algorithm yields better or at least as good accuracy as ray tracing, even in shallow waveguides with a strongly depth-dependent sound speed profile. / QC 20100819

Doctor of Philosophy (PhD) / With improvements in actuation technology and sensory systems, it is becoming increasingly feasible to create powered exoskeletal garments that can assist with the movement of human limbs. This class of robotics referred to as human-machine interfaces will one day be used for the rehabilitation of paralysed, damaged or weak upper and lower extremities. The focus of this project was the development of an exoskeletal interface for the rehabilitation of the hands. A novel sensor was designed for use in such a device. The sensor uses simple optical mechanisms centred on a spring to measure force and position simultaneously. In addition, the sensor introduces an elastic element between the actuator and its corresponding hand joint. This will allow series elastic actuation (SEA) to improve control and safely of the system. The Hand Rehabilitation Device requires multiple actuators. To stay within volume and weight constraints, it is therefore imperative to reduce the size, mass and efficiency of each actuator without losing power. A method was devised that allows small efficient actuating subunits to work together and produce a combined collective output. This work summation method was successfully implemented with Shape Memory Alloy (SMA) based actuators. The actuation, sensory, control system and human-machine interface concepts proposed were evaluated together using a single-joint electromechanical harness. This experimental setup was used with volunteer subjects to assess the potentials of a full-hand device to be used for therapy, assessment and function of the hand. The Rehabilitation Glove aims to bring significant new benefits for improving hand function, an important aspect of human independence. Furthermore, the developments in this project may one day be used for other parts of the body helping bring human-machine interface technology into the fields of rehabilitation and therapy.

O modelo de Ising dipolar bidimensional inclui, além da interação ferromagnética entre os primeiros vizinhos, interações de longo alcance entre os momentos de dipolo magnético dos spins. A presença da interação dipolar muda completamente o sistema, apresentando um rico diagrama de fase, cujas características têm originado inúmeros estudos na literatura. Além disso, a possibilidade de explicar fenômenos observados em filmes magnéticos ultrafinos, os quais possuem diversas aplicações em àreas tecnológicas, também motiva o estudo deste modelo. O estado fundamental ferromagnético do modelo de Ising puro é alterado para uma série de fases do tipo faixas, as quais consistem em domínios ferromagnéticos de largura $h$ com magnetizações opostas. A largura das faixas depende da razao $\\delta$ das intensidades dos acoplamentos ferromagnético e dipolar. Através de simulações de Monte Carlo e técnicas de repesagem em histogramas múltiplos identificamos as temperaturas críticas de tamanho finito para as transições de fase quando $\\delta=2$, o que corresponde a $h=2$. Calculamos o calor específico e a susceptibilidade do parâmetro de ordem, no intervalo de temperaturas onde as transições são observadas, para diferentes tamanhos de rede. As técnicas de repesagem permitem-nos explorar e identificar máximos distintos nessas funções da temperatura e, desse modo, estimar as temperaturas críticas de tamanho finito com grande precisão. Apresentamos evidências numéricas da existência de uma fase nemática de Ising para tamanhos grandes de rede. Em nossas simulações, observamos esta fase para tamanhos de rede a partir de $L=48$. Para verificar o quanto a interação dipolar de longo alcance afeta as estimativas físicas, nós calculamos o tempo de autocorrelação integrado nas séries temporais da energia. Inferimos daí quão severo é o critical slowing down (decaimento lento crítico) para esse sistema próximo às transições de fase termodinâmicas. Os resultados obtidos utilizando um algoritmo de atualização local foram comparados com os resultados obtidos utilizando o algoritmo multicanônico. / Two-dimensional spin model with nearest-neighbor ferromagnetic interaction and long-range dipolar interactions exhibit a rich phase diagram, whose characteristics have been exploited by several studies in the recent literature. Furthermore, the possibility of explain observed phenomena in ultrathin magnetic films, which have many technological applications, also motivates the study of this model. The presence of dipolar interaction term changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases, which consist of ferromagnetic domains of width $h$ with opposite magnetization. The width of the stripes depends on the ratio $\\delta$ of the ferromagnetic and dipolar couplings. Monte Carlo simulations and reweighting multiple histograms techniques allow us to identify the finite-size critical temperatures of the phase transitions when $\\delta=2$, which corresponds to $h=2$. We calculate, for different lattice sizes, the specific heat and susceptibility of the order parameter around the transition temperatures by means of reweighting techniques. This allows us to identify in these observables, as functions of temperature, the distinct maxima and thereby to estimate the finite-size critical temperatures with high precision. We present numerical evidence of the existence of a Ising nematic phase for large lattice sizes. Our results show that simulations need to be performed for lattice sizes at least as large as $L=48$ to clearly observe the Ising nematic phase. To access how the long-range dipolar interaction may affect physical estimates we also evaluate the integrated autocorrelation time in energy time series. This allows us to infer how severe is the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions. The results obtained using a local update algorithm are compared with results obtained using the multicanonical algorithm.

Dans le cadre des recherches menées sur les SFR (Sodium cooled Fast Reactor), le CEA souhaite développer une instrumentation innovante et spécifique à ces réacteurs. Le travail présenté concerne la mesure par ultrasons, de la température du sodium à la sortie des têtes des assemblages du coeur du réacteur. Cette instrumentation implique la propagation d'ultrasons dans du sodium liquide, thermiquement inhomogène et turbulent. Le milieu provoque des déviations du faisceau acoustique qu'il faut prévoir et quantifier pour envisager d'employer les ultrasons comme moyen de mesure dans un coeur de réacteur SFR.Pour cela un code nommé AcRaLiS (Acoustic Ray in Liquid Sodium) a été implémenté. Une étude thermo-hydraulique précise du sodium a tout d'abord été menée afin de proposer une description adaptée du milieu et de choisir le modèle de propagation acoustique adéquat. Puis une implémentation a été réalisée afin de permettre la simulation rapide de la propagation d'ondes de plusieurs mégahertz dans ce milieu particulier. Ce code prévoit les déviations et l'évolution de l'intensité du faisceau acoustique. Deux expériences ont ensuite été conçues et réalisées pour vérifier ce code. La première, nommée UPSilon, innove en remplaçant le sodium par de l'huile de silicone afin d'avoir une inhomogénéité thermique stable pendant l'expérience. Elle permet de déterminer la validité du code AcRaLiS dans des inhomogénéités thermiques. La seconde, nommée IKHAR, permet d'étudier en eau l'influence de la turbulence sur la propagation d'ondes, en exploitant les instabilités de Kelvin-Helmholtz. Les conclusions et les perspectives sont présentées en élargissant à d'autres domaines d'application. / In the frame of research on Sodium cooled Fast nuclear Reactor (SFR), CEA aims to develop an innovative instrumentation, specific to these reactors. The present work relates to the measurement of the sodium temperature at the outlet of the assemblies of the reactor's core by an ultrasonic method. This instrumentation involves the propagation of ultrasonic waves in liquid sodium, thermally inhomogeneous and turbulent. Environment causes deviations of the acoustic beam that must be understood to predict and quantify to consider ultrasound as a measure means in a core of SFR reactor. To determine the magnitude of these influences, a code named AcRaLiS (Acoustic Ray in Liquid Sodium) has been implemented. In a first step, a thermal-hydraulic study specific to the medium, was conducted to provide an adequate description of the environment and choose a suitable acoustic propagation model. Then an implementation has been performed to allow rapid simulations of the wave propagation at several megahertz in this particular environment. This code provides ultrasounds deviations and changes in beam intensity.Two experiments were designed and conducted to verify the code. The first, named UPSilon innovates by replacing sodium by silicone oil in order to have a stable thermal inhomogeneity during the experiment. It allows to determine the validity of the code AcRaLiS with thermal inhomogeneities. The second, called IKHAR allows to study the influence of water turbulence on the propagation of waves, using the Kelvin-Helmholtz instabilities. Conclusions and perspectives are presented, including perspectives for other application domains.