We consider fast computation methods for simulation of dynamics of a collection of particles dispersed in an unbounded Stokesian suspension. Stokesian suspensions are of great practical interest in the manufacturing and processing of various commercial products. The most popular dynamic simulation method for these kind of suspensions was developed by Brady and Bossis (Brady and Bossis [1988]). This method uses a truncated multipole expansion to represent the fluid traction on particle surfaces. The hydrodynamic interactions in Stoke-sian suspension are long ranged in nature, resulting in strong coupled motion of all particles. For an N particle system, this method imposes an O(N3) computational cost, thus posing limitations to the number of particles that may be simulated. More recent methods (Sierou and Brady [2001], Scintilla, Darve and Shaqfeh [2005]) have attempted to solve this problem using Particle Mesh Ewald summation techniques by distributing the moments on a grid and using Fast Fourier Transform algorithms, resulting in an O(N log N) computational cost. We review these methods and propose a version that we believe is some-what superior. In the course of this study, we have identified and corrected errors in previous studies that maybe of some importance in determining the bulk properties of suspensions. Finally, we show the utility of our method in determining certain properties of suspensions and compare them to existing analytical results for the same.

A prestudy indicated superior accuracy and convergence properties of apseudo-spectral method compared to a spline-based method implemented byCòrdoba et al. in 2005 when solving the α-patches problem. In this thesis wefurther investigate the numerical properties of the pseudo-spectral method and makeit more robust by implementing the Nonequispaced Fast Fourier Transform. Wepresent a more detailed overview and analysis of the pseudo-spectral method and theα-patches problem in general and conclude that the pseudo-spectral method issuperior in regards to accuracy in periodic settings.

Fluid simulating is one of the most difficult problems in computer graphics. On the other hand, water appears in our life very frequently. This thesis focuses on water simulating. We have two main methods to do this in the thesis: the first is wave based water simulating; Sine wave summing based and Fast Fourier Transform based methods are all belong to this part. The other one is physics based water simulating. We make it based on Navier-Stokes Equation and it is the most realistic animation of water. It can deal with the boundary and spray which other method cannot express. Then we put our emphasis on implement by the physics method using Navier-Stokes Equation.

O trabalho ressalta a importância do tema Qualidade da Energia (QE) e apresenta alguns dos diversos distúrbios responsáveis pelo seu comprometimento. Tais distúrbios, quando presentes em um dado sistema elétrico, podem causar sérios danos tanto aos equipamentos de medição e controle pertencentes ao fornecedor de energia, como também aos equipamentos mais sensíveis pertencentes aos usuários deste sistema. Os fenômenos mais freqüentes no estudo da QE foram destacados, bem como suas definições. Conhecidos estes fenômenos, implementou-se um algoritmo computacional, utilizando como ferramenta a transformada rápida de Fourier janelada (Windowed Fast Fourier Transform - WFFT) - TRFJ, para identificar e classificar estas perturbações em um dado sistema elétrico de distribuição. Para que o resultado fosse o mais próximo possível de uma situação real, utilizou-se para análise, um sistema elétrico real de distribuição da CPFL (Companhia Paulista de Força e Luz). Sobre o referido sistema elétrico foram simulados casos de afundamentos, elevações e oscilações de tensão, criando assim, um banco de dados para, posteriormente, podermos testar e validar o algoritmo computacional implementado, na identificação destes fenômenos. Este algoritmo permite variarmos tanto o tamanho da janela, quanto a freqüência amostral do sinal. Neste estudo em particular, utilizamos tamanhos de janelas de 1 ciclo e 1/2 ciclo, e freqüência amostral do sinal, de 7,68 kHz (inicialmente utilizada para obtenção do banco de dados), e 0,769 kHz, aproximadamente. Como resultados, obtivemos que o tamanho da janela de dados para esta implementação, não apresentou diferenças significativas na análise, quando comparados com os dados iniciais. Entretanto, observa-se um comportamento contrário com a variação da taxa amostral, ou seja, quanto menor a freqüência amostral empregada, maior a perda de informações importantes em relação ao sinal inicial. / The present work at lines the importance of Power Quality (PQ) and it presents some of the many disturbances related to it and its implications. Such disturbances, as presented in an electrical system, can cause serious damages in the measurements, in the control of power utility equipments, as well as in sensitive equipments. The most frequent phenomena in the study of PQ had been emphasized, as well as its definitions. Once these phenomena are known, a computational algorithm was implemented, using the Windowed Fast Fourier Transform - WFFT as a tool to identify and classify these disturbances, considering electrical distribution system. In order to have the best situation for the test, a real electrical distribution system from CPFL (Companhia Paulista de Força e Luz) utility was simulated. Some cases of voltage sag, voltage swell and oscillatory transient were simulated, creating a data base to test and validate the computational algorithm implemented. This algorithm allows changing the window length as the sample rate. For the proposed study, 1 cycle and 1/2 cycle as window length was analyzed with sample rate of 7,68 kHz (initially used for obtaining the data base), and 0,769 kHz. It was observed that the window length studied did not influence significantly the proposed analysis concerning PQ. However, concerning the sample rate, it was observed a deterioration of the analysis with the 0,769 kHz rate.

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.

Les techniques avancées pour l’approximation de rang faible des matrices sont des outils de réduction de dimension fondamentaux pour un grand nombre de domaines du calcul scientifique. Les approches hiérarchiques comme les matrices H2, en particulier la méthode multipôle rapide (FMM), bénéficient de la structure de rang faible par bloc de certaines matrices pour réduire le coût de calcul de problèmes d’interactions à n-corps en O(n) opérations au lieu de O(n2). Afin de mieux traiter des noyaux d’interaction complexes de plusieurs natures, des formulations FMM dites ”kernel-independent” ont récemment vu le jour, telles que les FMM basées sur l’interpolation polynomiale. Cependant elles deviennent très coûteuses pour les noyaux tensoriels à fortes dimensions, c’est pourquoi nous avons développé une nouvelle formulation FMM efficace basée sur l’interpolation polynomiale, appelée Uniform FMM. Cette méthode a été implémentée dans la bibliothèque parallèle ScalFMM et repose sur une grille d’interpolation régulière et la transformée de Fourier rapide (FFT). Ses performances et sa précision ont été comparées à celles de la FMM par interpolation de Chebyshev. Des simulations numériques sur des cas tests artificiels ont montré que la perte de précision induite par le schéma d’interpolation était largement compensées par le gain de performance apporté par la FFT. Dans un premier temps, nous avons étendu les FMM basées sur grille de Chebyshev et sur grille régulière au calcul des champs élastiques isotropes mis en jeu dans des simulations de Dynamique des Dislocations (DD). Dans un second temps, nous avons utilisé notre nouvelle FMM pour accélérer une factorisation SVD de rang r par projection aléatoire et ainsi permettre de générer efficacement des champs Gaussiens aléatoires sur de grandes grilles hétérogènes. Pour finir, nous avons développé un algorithme de réduction de dimension basé sur la projection aléatoire dense afin d’étudier de nouvelles façons de caractériser la biodiversité, à savoir d’un point de vue géométrique. / Advanced techniques for the low-rank approximation of matrices are crucial dimension reduction tools in many domains of modern scientific computing. Hierarchical approaches like H2-matrices, in particular the Fast Multipole Method (FMM), benefit from the block low-rank structure of certain matrices to reduce the cost of computing n-body problems to O(n) operations instead of O(n2). In order to better deal with kernels of various kinds, kernel independent FMM formulations have recently arisen such as polynomial interpolation based FMM. However, they are hardly tractable to high dimensional tensorial kernels, therefore we designed a new highly efficient interpolation based FMM, called the Uniform FMM, and implemented it in the parallel library ScalFMM. The method relies on an equispaced interpolation grid and the Fast Fourier Transform (FFT). Performance and accuracy were compared with the Chebyshev interpolation based FMM. Numerical experiments on artificial benchmarks showed that the loss of accuracy induced by the interpolation scheme was largely compensated by the FFT optimization. First of all, we extended both interpolation based FMM to the computation of the isotropic elastic fields involved in Dislocation Dynamics (DD) simulations. Second of all, we used our new FMM algorithm to accelerate a rank-r Randomized SVD and thus efficiently generate multivariate Gaussian random variables on large heterogeneous grids in O(n) operations. Finally, we designed a new efficient dimensionality reduction algorithm based on dense random projection in order to investigate new ways of characterizing the biodiversity, namely from a geometric point of view.

Detection of a human emotion from human speech is always a challenging task. Factors like intonation, pitch, and loudness of signal vary from different human voice. So, it's important to know the exact pitch, intonation and loudness of a speech for making it a challenging task for detection. Some voices exhibit high background noise which will affect the amplitude or pitch of the signal. So, knowing the detailed properties of a speech to detect emotion is mandatory. Detection of emotion in humans from speech signals is a recent research field. One of the scenarios where this field has been applied is in situations where the human integrity and security are at risk In this project we are proposing a set of features based on the decomposition signals from discrete wavelet transform to characterize different types of negative emotions such as anger, happy, sad, and desperation. The features are measured in three different conditions: (1) the original speech signals, (2) the signals that are contaminated with noise or are affected by the presence of a phone channel, and (3) the signals that are obtained after processing using an algorithm for Speech Enhancement Transform. According to the results, when the speech enhancement is applied, the detection of emotion in speech is increased and compared to results obtained when the speech signal is highly contaminated with noise. Our objective is to use Artificial neural network because the brain is the most efficient and best machine to recognize speech. The brain is built with some neural network. At the same time, Artificial neural networks are clearly advanced with respect to several features, such as their nonlinearity and high classification capability. If we use Artificial neural networks to evolve the machine or computer that it can detect the emotion. Here we are using feedforward neural network which is suitable for classification process and using sigmoid function as activation function. The detection of human emotion from speech is achieved by training the neural network with features extracted from the speech. To achieve this, we need proper features from the speech. So, we must remove background noise in the speech. We can remove background noise by using filters. wavelet transform is the filtering technique used to remove the background noise and enhance the required features in the speech.

V této práci je navrhnut energeticky úsporný procesor typu TTA (Transport Triggered Architecture) pro výpočet rychlé Fourierovy transformace (FFT). Návrh procesoru byl vytvořen na míru použitému algoritmu pomocí speciáoních funkčních jednotek. Algoritmus byl realizován jako posloupnost instrukcí tak, že většina výpočtu probíhá ve smyčce obrahující pouze jedionu paralelní instrukci. Tato instrukce je umístěna do instrukčního bufferu, odkud je potom volána místo instrukční paměti. Díky tomu se dá docílit nižší spotřeby, neboť volání z instrukčního bufferu je efektivnější než volání z instrukční paměti. Program byl zkompilován na časovém modelu procesoru a časová simulace potvrdila správnost návrhu. Součástí práce jsou rovněž pomocné programy v Pythonu, které slouží ke generaci referenčních výsledků a automatické simulaci a porovnání výsledků simulace s referencí.

This dissertation thesis concerns with Analysis of Influence of Collagen Organization on Mechanical Properties of Arteries and it is divided into three main parts. Motivation for this dissertation thesis was in a study reviewing effect of material model upon resulting stresses in AAA. The effect was calculated in 70 patient-specific geometries of AAA, which exceeds the number of geometries in other scientific papers by one order. Within this study, two material models were used, i.e. real one and 100× stiffer, and obtained stresses were mutually compared. It was quantified that peak stress difference can be higher than 20 % in 10% of patients and therefore the real material model should be preferred over the artificial one although operation with this model is more demanding. The second part of this thesis deals with an identification of structural parameters (orientation and dispersion of collagen fibres) of porcine aortic tissue by using adjusted Fast Fourier Transform based algorithm. The extracted structural parameters were inserted into two-layer structure-motivated constitutive model Martufi-Gasser. This model was validated and its predictive capabilities were also tested with fine results. The most important information obtained from the digital image processing of ~9000 micrographs is existence of only one family of dispersed collagen fibres which breaks the current dogma present in many scientific papers about two families of collagen fibres. The third part concerns with a proposal of an automated phase-correlation based algorithm for obtaining collagen fibre direction from polarized light microscopy images. The proposed algorithm was verified and validated and it yields histograms of collagen fibre directions with overall number of measured points larger than it would be possible to get from any manual measurement. The limitation of the original proposed algorithm is in 90° period of polarized light intensity, thus the method results in angles in the range of 0°–90. Therefore the end of the thesis is dedicated resolving this problem and obtaining real angles in a span of 0°–180°. To this end, the microscope set-up was changed and the algorithm was adjusted accordingly. The original and the adjusted algorithms are collagen-specific, fast and an operator independent. Despite all the author´s effort put into collagen fibre waviness quantification directly from the histograms, the waviness has not been quantified yet in this way and it remains at the stage of research.

This thesis is a part of the k-Wave project, which is a toolbox for the simulation and reconstruction of acoustic wave felds and one of its main contributions is the planning of focused ultrasound surgeries (HIFU). One simulation can take tens of hours and about 60% of the simulation time is taken by the calculation of the 3D Fast Fourier transforms. Up until now the 3D FFT has been calculated purely by the FFTW library and its 1D decomposition, whose major limitation is the maximum number of employable cores. Therefore we introduce a new approach, called the 2D hybrid decomposition of the 3D FFT (HybridFFT), where we combine both MPI processes and OpenMP threads to reach as best performance as possible. On a low number of cores, on the order of a few hundreds, we are about as fast or slightly faster than FFTW and pure MPI 2D decomposition libraries (PFFT and P3DFFT). One of the best results was achieved on a 512^3FFT using 512 cores, where our hybrid version run 31ms, FFTW run 39ms and PFFT run 44ms. The most significant performance advantage should be seen when employing around 8-16 thousand cores, however we haven't had an access to a machine with such resources. Almost a linear scalability has been proven for up to 2048 employed cores.