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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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Physics Simulator for SandBox Type Games
Kotulič, Patrik ; Peringer, Petr (referee) ; Hrubý, Martin (advisor)
This thesis focuses on the creation of a physics simulator of rigid body mechanics. The reader is familiarized with the principles used in current simulators of rigid body mechanics. The thesis then deals with numerical integration of the equations of motion, collision detection and collision resolution. The simulator is presented on a series of experiments. The resulting application can be used as a video game or as a tool for experimentation.
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Integration of microstructure informed enrichment base functions
Ladecký, Martin ; Zeman,, Jan (referee) ; Eliáš, Jan (advisor)
This thesis deals with problems related to the numerical integration of rapidly oscillatory functions. Analyze classical methods of numerical integration and compare them with method published by David Levin\cite{levin82}. Levin's method is applied in solving Laplace differential equation that describes deflection of membrane. To solve potential problem is used hybrid finite element method with Trefftz bases functions.
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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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Partial Differential Equations Parallel Solutions
Čambor, Michal ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
This thesis deals with the concepts of numerical integrator using floating point arithmetic for solving partial differential equations. The integrator uses Euler method and Taylor series. Thesis shows parallel and serial approach to computing with exponents and significands. There is also a comparison between modern parallel systems and the proposed concepts.
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Electric Circuits Simulations in a Specialized Parallel System
Janko, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.
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Multiple Integrals
Valešová, Nikola ; Veigend, Petr (referee) ; Šátek, Václav (advisor)
The problem of definite integral and differential equation computation is still a significant part of many scientific branches and the solution of integral calculus tasks can be found in many industrial fields too. During the computation of such tasks, the accuracy and high-speed requirements are often confronted. These requirements are crucial during the process of the suitable method choice. The aim of this thesis is to propose, describe, implement and test a new numerical method, which combines the solution of definite integrals by transforming them into differential equations solved by the Taylor series with the traditional methods, which use the Newton-Cotes formulas. As a result, a new application has been developed, that provides fast results of definite two-dimensional integrals and reaches at least the precision of MATLAB. The major accomplishment of this thesis is the development of a new numerical method and its comparison to other established ways of computation.
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Specialized Parallel System and Elementar Processors
Nevřala, Pavel ; Kunovský, Jiří (referee) ; Šátek, Václav (advisor)
The present thesis deals with the conceptual design of the elementary processor for computation of fixed point. This study will examine and analyze the cooperation of processors in the calculation of linear systems of differential equations with a focus on Euler's method, Runge-Kutta method and Taylor series. The thesis is divided into two major parts. The first part contains the processor design according to the type of communication processor internal components and the type of communication between processors in the calculation. The second part describes the design and implementation of a specialized multi-variant parallel system and a compararison between them.
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Parallel/Serial ALU Interconecting System
Sekaninová, Michaela ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This thesis deals with creation of parallel/serial ALU interconecting system. The content of the work is to introduce the issue of interconecting systems and numerical solutions of di fferential equations using Taylor series method. The practical aim of the thesis is to design and implement interconecting system performing calculations of di fferential equations. The system connects integrators automatically by given problem.
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Space structure of industry building object
Pelikán, Adam ; Švaříčková,, Ivana (referee) ; Šimůnek, Petr (advisor)
The subject of this project is the structure of the storage hall which is made of reinforced concrete. It is designed as precast frame (span of 18m), founded on pocket footings. The roof deck (non-rigid) consists of ribbed slabs. The cladding is made of sandwich panels (reinforced concrete and isolation) layed on foundation beam. The design is focused on the single typical frame. Roof girder, column and pocket footing are designed. Designed life of the structure is 50 years.
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