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MV netwok design for 75 new houses in Damborice
Makuta, Peter ; Novák, Vojtěch (referee) ; Ptáček, Michal (advisor)
Content of this thesis is medium voltage network design for seventy five houses in Damborice. At the beginning author discuss about history of transmission network and distribution network. Next topic is about steady state of network. In theoretic part are different solving methods of linear and non-linear simultaneous equations discussed. Author describes four methods – method of node voltages, elimination of balance node, Gauss-Seidel and Newton method. The electric properties of both the overhead transmission lines and cable lines and their variety are part of this work too. There is purpose, forms and parameters of transformers described. Simplicity of author’s design should reduce the usage of many electrical elements visible to residents.
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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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Flow in channels with open water level
Palička, Miroslav ; Štigler, Jaroslav (referee) ; Haluza, Miloslav (advisor)
This bacherol thesis deals with steady water flow, in open channels with different cross-sections. The main aim was mathematical derivation of relations for the most favorable water level, graphic representation of those relations and numerical confirmation of results. Practical use and evaluation of results are summarized in conclusion.
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Analysis of possibilities of solution of buckling of a screw-shaped beam
Pokorný, Jan ; Fuis, Vladimír (referee) ; Burša, Jiří (advisor)
Bachelor’s thesis deals with the effect of the pretwist of a column on the increase in buckling load and also focuses on a column with rectangular cross section. This problem is divided into two main parts. The first one is represented by the column with a large thread pitch, the second one by a small thread pitch. The results are obtained by a numerical approach using MATLAB software. The verification is carried out via finite element software. The outcome of this thesis is plotting the ratio of the critical loads of the twisted and prismatic columns against the ratio of the side lengths of the rectangular cross section. The results are shown for both types of considered columns.
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Conic optimization: theory and applications
Dortová, Zuzana ; Kopa, Miloš (advisor) ; Branda, Martin (referee)
1 This work discusses the roles of second-order cone programming, these tasks are a special class semidefinitního programming. The work summarized basic de- finitions, properties and claims known about these tasks. Special attention is paid to methods of solving SOCP problems. In the last part of the paper are formu- lated in some special tasks of mathematical programming (linear programming, quadratic programming, ...) as special cases of SOCP problems.
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The calculation of magnetic field distribution in nonlinear anisotropic media using the finite element method
Kunický, Zdeněk
Title: The calculation of magnetic field distribution in nonlinear anisotropic media Author: Zdeněk Kunický Department: Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: RNDr. Tomáš Vejchodský, Ph.D., Mathematical Institute of the Academy of Sciences of the Czech Republic Supervisor's e-mail address: vejchod@math.cas.cz Abstract: In the present work we study the modelling of stationary magnetic fields in nonlinear anisotropic media by FEM. The magnetic characteristics of such materials are thouroughly examined and eventually applied to the construction of a full 2D model of an anisotropic steel sheet. Some improvements in the construction in comparision with the ones previously published were achieved. We point out that the standard formulations and the subsequent theorems for the boundary value problems do not in fact correspond with the physical situation. Instead, we propose new formulations that reflect real physical properties of matter. General existence and uniqueness theorems for the obtained boundary value problems are proved as well as the convergence theo- rems for the discrete solutions. The conventional and full 2D model of an anisotropic steel sheet are compared in two transformer core models using the adaptive Newton- Raphson...
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Flow in channels with open water level
Palička, Miroslav ; Štigler, Jaroslav (referee) ; Haluza, Miloslav (advisor)
This bacherol thesis deals with steady water flow, in open channels with different cross-sections. The main aim was mathematical derivation of relations for the most favorable water level, graphic representation of those relations and numerical confirmation of results. Practical use and evaluation of results are summarized in conclusion.
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The calculation of magnetic field distribution in nonlinear anisotropic media using the finite element method
Kunický, Zdeněk
Title: The calculation of magnetic field distribution in nonlinear anisotropic media Author: Zdeněk Kunický Department: Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University in Prague Supervisor: RNDr. Tomáš Vejchodský, Ph.D., Mathematical Institute of the Academy of Sciences of the Czech Republic Supervisor's e-mail address: vejchod@math.cas.cz Abstract: In the present work we study the modelling of stationary magnetic fields in nonlinear anisotropic media by FEM. The magnetic characteristics of such materials are thouroughly examined and eventually applied to the construction of a full 2D model of an anisotropic steel sheet. Some improvements in the construction in comparision with the ones previously published were achieved. We point out that the standard formulations and the subsequent theorems for the boundary value problems do not in fact correspond with the physical situation. Instead, we propose new formulations that reflect real physical properties of matter. General existence and uniqueness theorems for the obtained boundary value problems are proved as well as the convergence theo- rems for the discrete solutions. The conventional and full 2D model of an anisotropic steel sheet are compared in two transformer core models using the adaptive Newton- Raphson...
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A tool for evaluation of different methods for solving nonlinear equations
Do Manh, Tuan ; Mikula, Tomáš (advisor) ; Horáček, Jaroslav (referee)
The objective of this work is to create a tool for solving nonlinear equations using numeric methods. It uses both slow working methods, such as bisection method or regula falsi method, and fast working methods, such as Newton's method. The Newton's method, while fast, can be very problematic in certain scenarios. It does not always converse to the root of the equation. That is why in this work, I try to implement modified methods, which attempt to deal with the imperfections of the Newton's method. The program is suppose to be a good tool for comparing and evaluating the efficiency of each methods in different situations.
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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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