As CPU clock frequencies plateau and the doubling of CPU cores per processor exacerbate the memory wall, hybrid core computing, utilizing CPUs augmented with FPGAs and/or GPUs holds the promise of addressing high-performance computing demands, particularly with respect to performance, power and productivity. While traditional approaches to benchmark high-performance computers such as SPEC, took an architecture-based approach, they do not completely express the parallelism that exists in FPGA and GPU accelerators. This thesis follows an application-centric approach, by comparing the sustained performance of two key computational idioms, with respect to performance, power and productivity. Specifically, a complex, single precision, floating-point, 1D, Fast Fourier Transform (FFT) and a Molecular Dynamics modeling application, are implemented on state-of-the-art FPGA and GPU accelerators. As results show, FPGA floating-point FFT performance is highly sensitive to a mix of dedicated FPGA resources; DSP48E slices, block RAMs, and FPGA I/O banks in particular. Estimated results show that for the floating-point FFT benchmark on FPGAs, these resources are the performance limiting factor. Fixed-point FFTs are important in a lot of high performance embedded applications. For an integer-point FFT, FPGAs exploit a flexible data path width to trade-off circuit cost and speed of computation, improving performance and resource utilization. GPUs cannot fully take advantage of this, having a fixed data-width architecture. For the molecular dynamics application, FPGAs benefit from the flexibility in creating a custom, tightly-pipelined datapath, and a highly optimized memory subsystem of the accelerator. This can provide a 250-fold improvement over an optimized CPU implementation and 2-fold improvement over an optimized GPU implementation, along with massive power savings. Finally, to extract the maximum performance out of the FPGA, each implementation requires a balance between the formulation of the algorithm on the platform, the optimum use of available external memory bandwidth, and the availability of computational resources; at the expense of a greater programming effort. / Master of Science

The display of an Airy function via an optical image processing technique is demonstrated. Using a two-dimensional object with a cubic amplitude transmittance, one can observe a Fourier transformed image of which intensity variation is identical to that of the Airy function. A lens system is used to achieve the Fourier transformation of the object which is a two-dimensional binary filter. A set of computer simulations are performed prior to the optical experiments. Using the same method of optical display, the transient wave propagation in a dispersive medium is optically displayed based on the analogous relationship found between two equations: One is the Fourier form of a transient wave field propagating in a dispersive medium and the other is an equation of the diffraction pattern of an object constructed with two juxtaposed two-dimensional filters. A theoretical analysis is provided along with computer simulations. The use of a Spatial Light Modulator is proposed as the source of the input object in the optical experiment. / Master of Science

Dans ce travail réalisé au Centre de Morphologie Mathématique and IFPEN, on s'intéresse à la microstructure et aux propriétés physiques d'alumines mésoporeuses. Il s'agit d'un supporte de catalyseur utilisés notamment dans les processus industriels de raffinage du pétrole. Fortement poreux, ce matériau est formé de ''plaquettes'' distribuées de manière désordonnée à l'échelle de la dizaine de nanomètres. Les propriétés de transport de masse du support de catalyseur sont fortement influencées par la morphologie de la microstructure poreuse. Ce travail porte sur la modélisation de la microstructure et des propriétés de transport des alumines mésoporeuses, à l'aide d'outils numériques et théoriques dérivés de l'analyse d'image et de la théorie des ensembles aléatoires. D'une part, on met en place des méthodes de caractérisation et de modélisation des microstructures, qui s'appuient sur, entre autre, des images obtenues par microscopie électronique en transmission (MET) et des courbes de porosimétrie azote. D'autre part, on utilise des méthodes d'homogénéisation numérique à champs complets par transformées de Fourier rapide (FFT).Dans un premier temps, le matériau est caractérisé expérimentalement par porosimétrie azote et résonance magnétique nucléaire à gradient de champ pulsé (RMN-GCP). Les images MET sont obtenus sur des échantillons d'épaisseur variable, filtrées et caractérisés par des fonctions de corrélation, notamment. Le bruit à haute fréquence issu de la membrane de carbone est identifié et pris en compte dans la modélisation de l'imagerie MET. À partir des images MET 2D, un modèle aléatoire à deux échelles est proposé pour représenter la microstructure 3D. Il prend en compte la forme des plaquettes d'alumines, leurs tailles, les effets d'alignement locaux et d'agrégation, qui sont identifiés numériquement. La procédure est validée à l'aide de comparaisons entre modèle et images expérimentales, en terme notamment de fonctions de corrélation et de surface spécifique, mesurées par porosimétrie azote.Dans un deuxième temps, une méthode de simulation des courbes d'isothermes de porosimétrie dans des milieux poreux périodiques ou aléatoires est développée. Basée sur des opérations morphologiques simples, elle étend un travail antérieur sur la porosimétrie au mercure. L'adsorption multicouche à basse pression est simulée à l'aide d'une dilatation tandis que les ménisques de l'interface vapeur-liquide intervenant pendant l'adsorption sont simulés à l'aide de fermetures de la phase solide par des éléments structurants sphériques. Pour simuler la désorption, une combinaison de fermetures et de bouchages de trou est utilisée. Le seuil de désorption est obtenu par une analyse de la percolation de la phase gazeuse. La méthode, d'abord validée sur des géométries simples, est comparée à des résultats antérieurs. Elle prédit une hystérésis et les distributions de pores associées à la porosimétrie. Nous l'appliquons aux modèles de microstructures 3D d'alumines mésoporeuses et proposons un modèle à trois échelles afin de rendre compte du seuil de pression pendant la désorption. En plus de la courbe de désorption, ce modèle reproduit les fonctions de corrélation mesurées sur les images MET.Dans un troisième temps, la diffusion de Fick, la perméabilité de Darcy, et les propriétés élastiques sont prédits à l'aide de calculs de champs complets par FFT sur des réalisations des modèles d'alumines mésoporeuses à deux et trois échelles. Les coefficients de diffusion effectifs et les facteurs de tortuosité sont prédits à partir de l'estimation du flux. Sont étudiés les effets de forme, d'alignement et d'agrégation des plaquettes sur les propriétés de diffusion à grande échelle. Les prédictions numériques sont validées au moyen des résultats expérimentaux obtenus par méthode RMN-GCP. / In a work made at Centre de Morphologie Mathématique and IFPEN, we study the microstructure and physical properties of mesoporous alumina. This is a catalyst carrier used in the petroleum refining industry. Highly porous, it contains disordered ''platelets'' at the nanoscale. The mass transport properties of the catalyst carrier are strongly influenced by the morphology of the porous microstructure. We focus on the modeling of the microstructure and of transport properties of mesoporous alumina, using numerical and theoretical tools derived from image analysis and random sets models. On the one hand, methods are developed to characterize and model the microstructure, by extracting and combining information from transmission electron microscope (TEM) images and nitrogen porosimetry curves, among others. On the other hand, the numerical homogenization relies on full-field Fourier transform computations (FFT).The material is first characterized experimentally by nitrogen porosimetry and pulse-field gradient nuclear magnetic resonance (PFG-NMR). TEM images, obtained on samples of various thicknesses are filtered and measured in terms of correlation function. The high-frequency noise caused by carbon membrane support is identified and integrated in the TEM image model. Based on the 2D TEM images, a two-scale random set model of 3D microstructure is developed. It takes into account the platelet shape, platelet size, local alignments and aggregations effects which are numerically identified. The procedure is validated by comparing the model and experimental images in terms of correlation function and specific surface area estimated by nitrogen porosimetry.Next, a procedure is proposed to simulate porosimetry isotherms in general porous media, including random microstructures. Based on simple morphological operations, it extends an earlier approach of mercury porosimetry. Multilayer adsorption at low pressure is simulated by a dilation operation whereas the menisci of the vapor-liquid interface occurring during adsorption are simulated by closing the solid phase with spherical structuring elements. To simulate desorption, a combination of closing and hole-filling operations is used. The desorption threshold is obtained from a percolation analysis of the gaseous phase. The method, validated first on simple geometries, is compared to previous results of the literature, allowing us to predict the hysteresis and pore size distribution associated to porosimetry. It is applied on 3D microstructures of mesoporous alumina. To account for the pressure threshold during desorption, we propose a refined three-scale model for mesoporous alumina, that reproduces the correlation function and the desorption branch of porosimetry isotherms.Finally, Fick diffusion, Darcy permeability, and elastic moduli are numerically predicted using the FFT method and the two-scale and three-scale models of mesoporous alumina. The hindering effects in diffusion are estimated by the Renkin's equation. The effective diffusion coefficients and the tortuosity factors are estimated from the flux field, taking into account hindering effects. The effects of platelet shape, alignment and aggregation on the diffusion property are studied. The numerical estimation is validated from experimental PFG-NMR results.

Du fait de leurs propriétés physiques et chimiques exceptionnelles à haute température par rapport aux métaux, les composites de carbure de silicium (SiC) sont étudiés comme éventuel matériau de gainage du combustible nucléaire dans les réacteurs de fusion ou fission avancée futurs, ainsi que, depuis plus récemment, dans les réacteurs à eau légère existants. Les tubes composites SiC/SiC tressés en 2D, fabriqués par procédé d'infiltration chimique en phase vapeur (CVI), présentent un comportement mécanique anisotrope, faiblement déformable (~ 1%). La maîtrise des relations entre la microstructure, l’endommagement et le comportement macroscopique est essentielle pour optimiser précisément le dimensionnement structurel de ce matériau pour les applications envisagées. Un paramètre de fabrication important est l'angle de tressage, angle entre les torons de fibres et l'axe du tube. L'objectif de ce travail est de fournir une compréhension détaillée de la relation endommagement-microstructure, en particulier des effets de l'angle de tressage sur les mécanismes d’endommagement. Dans ce but, une étude combinant observations expérimentales à macro et micro-échelle et simulations numériques est menée. Les tubes composites sont d’abord étudiés par des essais de traction in situ sous tomographie par rayons X. Les expériences ont été réalisées sur la ligne PSICHE du synchrotron SOLEIL sous faisceau rose polychromatique. Les images tridimensionnelles sont analysées par la technique de corrélation d’image volumique (DVC), complétée par une série d'algorithmes de traitement d'image originaux, développés spécifiquement pour analyser les microstructures 3D, mesurer les déformations à travers l'épaisseur du tube, détecter et caractériser quantitativement le réseau de microfissures créées par le chargement mécanique. De plus, les microstructures réelles, décrites par les images de haute résolution issues des tests in situ, sont utilisées dans les simulations numériques multi-échelle. Les champs de contrainte à l’échelle microstructurale sont calculés en régime élastique par une technique utilisant la transformée de Fourier rapide (FFT). Ils permettent de mieux comprendre l'initiation des fissures et d’interpréter les observations expérimentales par une comparaison directe. Ces approches expérimentales et numériques sont appliquées à trois tubes présentant différents angles de tressage (30 °, 45 ° et 60 °). L’influence de l'angle de tressage sur l'initiation et l'évolution de l’endommagement à cœur des composites est ainsi mise en évidence / Because of their outstanding physical and chemical properties at high temperature, in comparison with metals, silicon carbide (SiC) composite materials are studied as possible nuclear fuel cladding materials either for future advanced fission/fusion reactors, or more recently, for the currently existing light water reactors. 2D-braided SiC/SiC composite tubes, manufactured by chemical vapor infiltration (CVI), exhibit an anisotropic, hardly deformable (~1%) mechanical behavior. Understanding the relations between the microstructure, the damage mechanisms and the macroscopic behavior is essential to optimize the structural design of this material for the considered applications. One important manufacturing parameter is the braiding angle, i.e. the angle between the fiber tows and the tube axis. The objective of this work is to provide a comprehensive understanding of the damage-microstructure relations, in particular of the effects of the braiding angle on the damage mechanisms. For this purpose, an investigation combining experimental observations at macro and micro-scale and numerical simulations is developed. The composite tubes are first studied through in situ tensile testing under X-ray computed tomography. Experiments were carried out on the PSICHE beamline at synchrotron SOLEIL using a pink polychromatic beam. The recorded 3D images are processed using the digital volume correlation (DVC) technique, extended by a series of advanced image processing algorithms specifically developed in order to analyze the 3D microstructures, to measure the deformations through the tube thickness, and to detect and quantitatively characterize the network of micro-cracks created by the mechanical loading. In addition, numerical simulations are performed on the real microstructures as observed in the high-resolution images recorded during the in situ tests. Stress fields are calculated at the microstructural scale in the elastic regime using a numerical tool based on the Fast Fourier Transform (FFT). They help to better understand crack initiation and interpret the experimental observations within one-to-one comparisons. Both the experimental and numerical approaches are applied to three tubes with different braiding angles (30°, 45° and 60°). The effect of the braiding angle on the initiation and evolution of damage in the bulk of the composite materials can thus be highlighted

No description available.

The nonequispaced fast Fourier transform (NFFT) allows the fast approximate evaluation of trigonometric polynomials with frequencies supported on full box-shaped grids at arbitrary sampling nodes. Due to the curse of dimensionality, the total number of frequencies and thus, the total arithmetic complexity can already be very large for small refinements at medium dimensions. In this paper, we present an approach for the fast approximate evaluation of trigonometric polynomials with frequencies supported on an arbitrary subset of the full grid at arbitrary sampling nodes, which is based on Taylor expansion and rank-1 lattice methods. For the special case of symmetric hyperbolic cross index sets in frequency domain, we present error estimates and numerical results.

We describe an implementation of a multi-threaded NFFT (nonequispaced fast Fourier transform) software library and present the used parallelization approaches. Besides the NFFT kernel, the NFFT on the two-sphere and the fast summation based on NFFT are also parallelized. Thereby, the parallelization is based on OpenMP and the multi-threaded FFTW library. Furthermore, benchmarks for various cases are performed. The results show that an efficiency higher than 0.50 and up to 0.79 can still be achieved at 12 threads.

In this paper we describe a parallel algorithm for calculating nonequispaced fast Fourier transforms on massively parallel distributed memory architectures. These algorithms are implemented in an open source software library called PNFFT. Furthermore, we derive a parallel fast algorithm for the computation of the Coulomb potentials and forces in a charged particle system, which is based on the parallel nonequispaced fast Fourier transform. To prove the high scalability of our algorithms we provide performance results on a BlueGene/P system using up to 65536 cores.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The power consumption reduction in the fast Fourier transform (FFT) is important because applications in battery-powered embedded systems grows daily. Thus this work focuses on the application of techniques to reduce power in specific projects of FFT algorithms. The goal is to achieve an architectural exploration in the FFT core, the decimation in time butterfly radix-2 and the efficient implementation of arithmetic operators in the internal structure of this butterfly. The techniques applied to the butterfly are aimed at reducing power consumption through architectural exploration and data encryption. Five different butterfly topologies are shown, one of those, proposed in this work uses three real multipliers, and is based on the previous storage of the product of real and imaginary values of the twiddle factors. The advantage of this topology is the possibility of using 4:2 adder compressors, which performs the sum of four operands simultaneously with reduced critical path. These adder compressors have XOR gates in the critical path, is proposed in this paper a new XOR gate circuit, which is based on the use of pass transistors logic. This new XOR gate circuit has been applied to adder compressors 3:2 and 4:2, which are applied to adders blocks of the butterflies. Digital circuits have been developed in hardware description language and some in the electrical schematic level. Results of area, power consumption and cell count in the logic synthesis in 180nm at 100MHz and 20MHz with switching activity analysis for 10,000 random input vectors were obtained for this work. The electrical level simulations in an environment of mixed digital and analog signals were also performed to the evaluation of the compressors with new topology of XOR gate. Analyses show that 3:2 adder compressor has lower power consumption using the new XOR gate circuit. However, the same conclusion was not achieve in relation to the 4:2 adder compressor which has a lower power consumption using the CMOS XOR gate. Butterfly structures evaluated uses a significant amount of arithmetic operators in their internal structures, so was used different design strategies for implementation. Initially was used the arithmetic operators of automatic synthesis tool (Cadence). After, used dedicated arithmetic operators (adder compressors with the new XOR gate circuit, RNS adders and array multipliers). The results show that butterflies have lower power consumption with the use of adder compressors in their internal structures. / A redução no consumo de potência na transformada rápida de Fourier (FFT) é importante pois sua aplicação cresce em sistemas embarcados movidos à bateria. Sendo assim este trabalho tem como foco a aplicação de técnicas de redução de potência para projetos específicos de algoritmos da FFT. O objetivo é realizar uma exploração arquitetural no elemento central de cálculo da FFT, borboleta na base 2 com decimação no tempo, bem como a aplicação de operadores aritméticos eficientes na estrutura interna desta borboleta. As técnicas aplicadas à borboleta têm por objetivo a redução do consumo de potência através de exploração arquitetural e codificação de dados. São apresentadas cinco diferentes topologias de borboleta, sendo uma destas, proposta no âmbito deste trabalho utilizando três multiplicadores reais é baseada no armazenamento prévio do produto dos valores real e imaginário dos coeficientes. A vantagem desta topologia é a possibilidade do uso de somadores compressores 4:2, que realiza a soma simultânea de quatro operandos, com reduzido caminho crítico. Como estes somadores compressores apresentam portas XOR no caminho crítico, é proposta neste trabalho uma nova porta XOR, que é baseada no uso de transistores de passagem. Esta nova porta lógica XOR foi aplicada em somadores compressores 3:2 e 4:2, que são aplicados nos blocos somadores das borboletas. Os circuitos digitais foram desenvolvidos em linguagem de descrição de hardware e alguns em esquemáticos de nível elétrico. Resultados de área, potência e contagem de células na síntese lógica em 180nm a 100MHz e 20MHz com análise de atividade de chaveamento para 10.000 vetores aleatórios de entrada foram obtidos e simulações no nível elétrico em um ambiente de sinais digitais e analógicos misto também foram realizadas para a avaliação dos compressores com a nova topologia de porta XOR. As análises mostram que os somadores compressores 3:2 apresentam menor consumo de potência com o uso da nova porta XOR. Entretanto, o mesmo não se observa em relação ao compressor 4:2 que apresenta um menor consumo de potência utilizando a porta XOR CMOS. Como as estruturas de borboleta avaliadas utilizam uma quantidade significativa de operadores aritméticos nas suas estruturas internas, foram utilizadas diferentes estratégias de projeto para as suas implementações. Inicialmente foram utilizados os operadores aritméticos da ferramenta de síntese automática (Cadence). Após, foram utilizados operadores aritméticos dedicados (somadores compressores com a nova porta XOR, somadores RNS e multiplicadores array). Os resultados mostram que as borboletas apresentam menores consumos de potência com o uso dos somadores compressores em suas estruturas.

Made available in DSpace on 2014-07-29T15:08:19Z (GMT). No. of bitstreams: 1 dissertacao RamonCampos UFG 2012.pdf: 5667385 bytes, checksum: 1ff8645bd9d1b27aa406264298e405ef (MD5) Previous issue date: 2012-07-09 / This study aimed to development of a computational tool for electromyographic signal (EMG) analysis by signal processing techniques to determine muscular fatigue. With Ethics Committee of Federal University of Goiás approve were recorded from the dominant biceps brachii of 10 volunteers, that did not ever had muscular disease. The protocol consisted on get the maximal voluntary isometric contraction (MVIC) from the volunteer seated, floor contact with the feet, and forearm in 90 degree, doing three maximal voluntary contraction against a rigid and fixed surface, by five seconds, with a five resting minutes between each acquisition. The MVIC values were obtained by arithmetical mean from the three greater values of each contraction. In statistical analysis the volunteer sustained a load of 60% MVIC for 30 seconds, or while they supported. For dynamical analysis was used a electrogoniometer tied in forearm to measure the angle and a 60% MVIC load for 30 seconds measured, achieved angle of 70° until 130°, and return to 70°. Each flexion was did in 1,5 seconds, or while volunteer support. To analyze the signal in time domain were used Root main square (RMS) values and Continuous wavelet transform (CWT). To analyze in frequency domain were adopted the values of mean and median from Fast Fourier Transform (FFT), Welch spectral estimator, auto regressive moving average (ARMA) filter, and analytic wavelet transform (AWT). Linear regressions were obtained using a window of 250 ms for all techniques. Slopes with positive values, in time domain, and slopes with negative values, in frequency domain, indicate muscular fatigue. Using high scales of wavelet transform shows great results while compared with default techniques, like RMS and FFT. ANOVA one way were adopted as statistical method of analysis, with P < 0,05. Only in dynamic contraction, on frequency domain, had P value < 0,05. Tukey test were applied to identify which techniques had variance great than 5%. Is suggested as future works development of a wireless system to acquire EMG signals, improvement in the software to motor unit action potentials (MUAP) detection, prosthesis control, and synchronization with others systems of data collection. / Este trabalho propõe o desenvolvimento de uma ferramenta computacional para realizar a análise do sinal eletromiográfico (EMG) por meio de técnicas de processamento de sinais a fim de detectar fadiga muscular. Com aprovação do Comitê de Ética da Universidade Federal de Goiás, foram captados os sinais eletromiográfico do bíceps braquial do braço dominante de 10 voluntários, que não apresentavam histórico de problemas musculares. O protocolo consistiu na obtenção do valor de contração isométrica voluntária máxima (CIVM) com o voluntário sentado, pés em contato com o chão e o antebraço em ângulo de 90° em relação ao tronco, realizando três repetições de contração máxima, contra uma superfície fixa e rígida, durante 5 segundos, intercaladas por um período de 5 minutos em repouso. O valor da CIVM, representando 100% da força máxima exercida, foi determinado por meio da média aritmética dos maiores valores de cada amostra. Para análise de contração estática, o voluntário realizou uma nova contração com carga de 60% da CIVM durante 30 segundos, ou até onde suportasse. Na análise de contração dinâmica, foi utilizado um eletrogoniômetro para medição do ângulo do antebraço que, ao carregar uma carga com 60% da CIVM, realizou manobra de flexão, alcançando ângulo de 70°, e manobra de extensão, atingindo ângulo de 130° do antebraço em relação ao tronco. Cada manobra (flexão e extensão) foi realizada em 1,5 segundos, durante um período de 30 segundos ou enquanto suportasse, totalizando no máximo de 10 flexões e 10 extensões. Foram adotadas para análise do sinal EMG no domínio do tempo as técnicas de cálculo do valor quadrático médio (RMS) e transformada wavelet contínua (TWC). Para análise no domínio da frequência foram adotados os valores médios e medianos obtidos pelas técnicas de transformada rápida de Fourier (FFT), o estimador espectral de Welch, o filtro autorregressivo de média móvel (ARMA) e as transformadas wavelets analíticas (TWA). Utilizando uma janela de 250 ms foram obtidos os gráficos contendo a regressão linear de todas as técnicas. A inclinação positiva da reta de regressão, para o domínio do tempo, e inclinação negativa, para o domínio da frequência, indica o processo de fadiga muscular. A utilização da transformada wavelet, em grandes escalas, apresenta valor mais significativo de indícios de fadiga muscular quando comparada às técnicas padrões RMS e FFT. O método estatístico utilizado foi a ANOVA de um fator, com o P < 0,05. Apenas na contração dinâmica no domínio da frequência obteve um P < 0,05. Aplicada a análise post hoc do teste de Tukey foram identificadas, das técnicas comparadas duas a duas, quais apresentaram um grau de variância maior que 5%. Ainda no trabalho é sugerido o desenvolvimento de equipamento de coleta de sinais EMG sem fio, o aperfeiçoamento da ferramenta desenvolvida para detecção de potenciais de ativação de unidade motora (MUAP), o controle de próteses de reabilitação, e a sincronização com outros sistemas de coleta de dados.