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Newton and numerical mathematics
Obrátil, Štěpán ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor)
Topic of this bachelor thesis are Newton's methods for numerical solutions of various problems. Especially the problems of solving nonlinear equations and systems of nonlinear equations, as well as numerical integration are explained. The Newton's method for solving nonlinear equations is presented, as well as its many modifications and its generalisation for systems of nonlinear equations. Usefulness of methods is demonstrated on various examples. In the end, Newton-Cotes quadrature formulae for numerical integration are presented.
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Design and analysis of membrane roof of a stadium.
Lang, Rostislav ; Kytýr,, Jií (referee) ; Němec, Ivan (advisor)
This diploma thesis deals with problem of design and calculation of membrane structure of stadium roof. This is a complex engineering problem, which includes many partial problems: finding of initial form of membrane, statically and architecturally suitable arrangement of catenaries, economical solution of boundary conditions (foundations). All components affect each other and cannot be dealt without mutual coordination. It always greatly depends on the experience and intuition of engineer who design such structure. Task which cannot be resolved according to the theory of the first order. Equilibrium forces on the deformed structure, which in many projected structures gives satisfactory results, did not correspond to reality. It is therefore necessary to consider equilibrium of forces on the deformed structure according to the theory of large deformations. Diploma thesis was entered with regard to the intention of the companies Ing. Software Dlubal s.r.o. and FEM consulting s.r.o., working together to develop software RFEM. These companies plan to complement this program system with a module MEMBRANE for searching of initial shapes of membrane structures. This work is a contribution to the creation of this module.
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Image analysis for correction of electron microscopes
Smital, Petr ; Schwarz, Daniel (referee) ; Kolář, Radim (advisor)
This thesis describes the physical nature of corrections of an electron microscope and mathematical methods of image processing required for their complete automation. The corrections include different types of focusing, astigmatism correction, electron beam centring, and image stabilisation. The mathematical methods described in this thesis include various methods of measuring focus and astigmatism, with and without using the Fourier transform, edge detection, histogram operations, and image registration, i.e. detection of spatial transformations in images. This thesis includes detailed descriptions of the mathematical methods, their evaluation using an “offline” application, descriptions of the algorithms of their implementation into an actual electron microscope and results of their testing on the actual electron microscope, in the form of a video footage grabbed from its control computer’s screen.
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Acceleration of numerical computation of heat conduction in solids in inverse tasks
Ondruch, Tomáš ; Komínek, Jan (referee) ; Pohanka, Michal (advisor)
The master's thesis deals with possible ways of accelerating numerical computations, which are present in problems related to heat conduction in solids. The thesis summarizes basic characteristics of heat transfer phenomena with emphasis on heat conduction. Theoretical principles of control volume method are utilized to convert a direct heat conduction problem into a sparse linear system. Relevant fundamentals from the field of inverse heat conduction problems are presented with reference to intensive computations of direct problems of such kind. Numerical methods which are well-suited to find a solution of direct heat conduction problems are described. Remarks on practical implementation of time-efficient computations are made in relation with a two-dimensional heat conduction model. The results are compared and discussed with respect to obtained computational time for several tested methods.
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Finite Integrals Numerical Computations
Mikulka, Jiří ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
The application of the finite integral of multiple variable functions is penetrating into more and more industries and science disciplines. The demands placed on solutions to these problems (such as high accuracy or high speed) are often quite contradictory. Therefore, it is not always possible to apply analytical approaches to these problems; numerical methods provide a suitable alternative. However, the ever-growing complexity of these problems places too high a demand on many of these numerical methods, and so neither of these methods are useful for solving such problems. The goal of this thesis is to design and implement a new numerical method that provides highly accurate and very fast computation of finite integrals of multiple variable functions. This new method combines pre-existing approaches in the field of numerical mathematics.
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Vehicle Kinematics and Dynamics Simulations
Zháňal, Lubor ; Bauer, František (referee) ; Píštěk, Václav (referee) ; Kaplan, Zdeněk (advisor)
This paper focuses on the kinematic and dynamic numerical simulation of mechanisms by applying a numerical method, and a complex simulation programme built on it, developed by the author. Described are mathematical principles of the numerical method used and also the programming progression of the important parts of the application and its optimization. The final part includes comparative measuring of the accuracy and performance.
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Physically-based Modeling and Simulation
Dvořák, Radim ; Racek, Stanislav (referee) ; Šujanský,, Milan (referee) ; Zbořil, František (advisor)
Disertační práce se zabývá modelováním znečištění ovzduší, jeho transportních a disperzních procesů ve spodní části atmosféry a zejména numerickými metodami, které slouží k řešení těchto modelů. Modelování znečištění ovzduší je velmi důležité pro předpověď kontaminace a pomáhá porozumět samotnému procesu a eliminaci následků. Hlavním tématem práce jsou metody pro řešení modelů popsaných parciálními diferenciálními rovnicemi, přesněji advekčně-difúzní rovnicí. Polovina práce je zaměřena na známou metodu přímek a je zde ukázáno, že tato metoda je vhodná k řešení určitých konkrétních problémů. Dále bylo navrženo a otestováno řešení paralelizace metody přímek, jež ukazuje, že metoda má velký potenciál pro akceleraci na současných grafických kartách a tím pádem i zvětšení přesnosti výpočtu. Druhá polovina práce se zabývá poměrně mladou metodou ELLAM a její aplikací pro řešení atmosférických advekčně-difúzních rovnic. Byla otestována konkrétní forma metody ELLAM společně s navrženými adaptacemi. Z výsledků je zřejmé, že v mnoha případech ELLAM překonává současné používané metody.
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Noise associated with the rail wheel
Mareš, Adam ; Řehák, Kamil (referee) ; Rec, Matouš (advisor)
The issue of noise associated with rail transport, focusing primarily on noise from the wheel – rail contact, is examined mainly in connection with rail transport, but also concerns tram transport in cities and, to a lesser extent, funicular railways. The noise of rail transport is one of the reasons why it is perceived negatively by the public, even though it offers many advantages over other modes of transport, such as environmental friendliness, travel comfort, travel speed and more. This is one of the reasons why it is necessary to focus on noise in rail transport and to understand, research and further develop and improve the whole issue as well, both in the area of passive and active noise control measures. For this reason, the aim of this work is to provide a comprehensive overview of the issue. The work therefore deals with the issue of noise in a comprehensive way, from the theoretical definition of noise, through noise sources and their distribution to noise measurement and the use of numerical methods for its evaluation and determination of appropriate preventive and anti-noise measures.
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