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Application of the spectral method to the simulation of the phase-field model for martensitic transformation
Sejková, Klára ; Tůma, Karel (advisor) ; Kružík, Martin (referee)
For some alloys martensitic transformation is responsible for the so-called shape memory effect and pseudoelasticity. These properties are used in a wide range of industry applications. Each of these materials is transformed to the shape it was manufactured in when heated to its critical temperature (austenite phase) no matter how seriously it was deformed at lower temperatures (martensite phase). Looking at the microstructure, one can observe significant change of crystalographic lattice depending on temperature and deformation. This the- sis focuses on modelling the evolution of microstructure during deformation for materials in the martensite phase. In this case, the creation of multiple variants of martensite is observed, divided by interfaces where a part of energy is stored. This behaviour can be described by the phase-field model. The numerical im- plementation of this model using the standard finite element method requires large computational costs. The aim of this thesis is to implement this model in MATLAB using a spectral method based on the fast Fourier transform, which is suitable for solving problems on a periodic domain. It is interesting to com- pare the computation using spectral method on a conventional PC with the computation written in FEniCS computed on a cluster. However, the...
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Parallelization of Ultrasound Simulations Using 2D Decomposition
Nikl, Vojtěch ; Dvořák, Václav (referee) ; Jaroš, Jiří (advisor)
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.
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The effect of sampling period error on frequency analysis
Pietrowicz, Daniel ; Marada, Tomáš (referee) ; Zuth, Daniel (advisor)
This thesis will be focused on signal measurement in connection with digitization and analysis inaccuracy of sampling peroid effect. Brief narration of frequency analysis and description of Matlab and his capabilities with this issue. Then creation procedure for simulation model of analog signal and his fault digitization via sampling period. Systematic comparation of this effect on inaccuracy of sampling period on frequency analysis.
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Analysis of Influence of Collagen Organization on Mechanical Properties of Arteries
Novák, Kamil ; Daniel, Matej (referee) ; Vimmr, Jan (referee) ; Burša, Jiří (advisor)
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.
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Radar Signal Processor in FPGA
Přívara, Jan ; Musil, Petr (referee) ; Maršík, Lukáš (advisor)
This work describes design and implementation of radar processor in FPGA. The theoretical part is focused on Doppler radar, principles of radar signal processing methods and target platform Xilinx Zynq. The next part describes design of radar processor including its individual components and the solution is implemented. FPGA components are written in VHDL language. In the end, the implementation is evaluated and possible continuation of this work is stated.
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Implementation of Fast Fourier Transformation on Transport Triggered Architecture
Žádník, Jakub ; Slovák, Jiří (referee) ; Maršálek, Roman (advisor)
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.
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The fast Fourier transform and its applications to European spread option pricing
Bladyko, Daniil ; Stádník, Bohumil (advisor) ; Fleischmann, Luboš (referee)
This master thesis should provide reader with an overview of the European spread options evaluation using the fast Fourier transform numerical method. The first and second part of the thesis deal with the theoretical foundations of Fourier analysis and existing approaches of spread option valuation under two and three-factors frameworks (namely GBM - geometric Brown motion and SV - stochastic volatility). The third part describes extention of Hurd-Zhou (2010) valuation method by tool for call and put spread options pricing in case of negative or zero strikes. Extension will be compared with Monte Carlo simulation results from a variety of perspectives, including computing complexity and implementation requirements. Dempster-Hong model, Hurd-Zhou model and Monte Carlo simulation are implemented and tested in R (programming language).
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Computing the aggregate claims distribution
Dlouhá, Veronika ; Pešta, Michal (advisor) ; Cipra, Tomáš (referee)
In this bachelor thesis I study the distribution of aggregate claims. First I introduce the topic and present main models. Then, I show some distributions used for modeling number and amound of claims with estimates of their parameters. Next I get to compound distribution and its basic charakteristics. In other parts of the thesis I study the probability of aggregate claims using Panjer recursion and fast Fourier transform and apply the thoery to examples. Finally I mention some methods to approximate aggregate claims using known distribution.
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Stereo equalizer with spectrum analyzer
Náhlík, Ondřej ; Šotner, Roman (referee) ; Kratochvíl, Tomáš (advisor)
This bachelor’s work is focused on design of ten band analog stereo equalizer, which is solved by using an active band-pass filters of 2nd order. Simulated output signal isn‘t rippled more than ± 1 dB at zero amplification and can be amplified at maximum ca. ± 8 dB. Prototype of equalizer is then built and it’s characteristics are measured. The circuit of an integrated power amplifier working in the class AB is solved in the next part of this work. Amplifier is then built and it’s characteristics are measured. In the last part of this work, there is described function of a spectral analyzer which is then designed, built and programmed. The analyzer uses the Fast Fourier transform (FFT) and resulting spectrum is displayed on a display.
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Spectral Analysis of EEG Signal
Miklenda, Petr ; Orság, Filip (referee) ; Kupková, Karolína (advisor)
This bachelor thesis is focused at the EEG signal analysis using the Fast Fourier Transform. The theoretical part consist of EEG signal description, its creation and selected method for signal analysis. The practical part presents program for recording data from EEG headset and displaying the Fourier spectrum.
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