|
|
Comparison of various methods for nonlinear analysis of structures from the point of view of speed, accuracy and robustness.
Bravenec, Ladislav ; Křiváková, Jarmila (referee) ; Němec, Ivan (advisor)
The aim of the thesis is to compare the iterative methods which program RFEM 5 uses the non-linear calculations of structures, namely the analysis of large deformations and post critical analysis. Comparison should serve as a basis for which calculation method is the most accurate, fastest and most reliable in terms of getting results. Time-consuming will be judged according to the calculation of the solution and the time needed to compute one iterativ. Robustness we will compare the reliability of methods in in normal use. Accuracy of the calculation will be determined by comparing the maximum deformation structures. Comparison will be made with examples from practice.
|
|
|
Steady state and short-circuit conditions within E.ON 110 kV power network at parallel operation of nodal areas of Čebín substation and Sokolnice substation
Múdry, Peter ; Rampl, Martin (referee) ; Blažek, Vladimír (advisor)
In the distribution network 110 kV of E.ON Company there are the nodal areas of Čebin substation and Sokolnice substation which are operated separately at the present time. There is one 400/110 kV transformer for each nodal area. In case of fault on one of these transformers or on busbar in which the set transformer is working, it comes to an outage of electric supply in the set nodal area. This problem has to be solved with help of the parallel operation of nodal areas of Čebín substation and Sokolnice substation. The main and also the practical task of this work is to design the bridge connection appropriate for parallel operation of nodal areas (supply transformers 400/110 kV). With help of a computing program there were made calculations of steady state and short-circuit conditions in distribution network 110 kV for separated and parallel operation of nodal areas. Voltage conditions, load of transformers (400/110 kV and 110/vn kV) and conditions on 110 kV lines are evaluated and controlled as the result of steady state calculations. Based on short-circuit conditions there is controlled the short-circuit resistance of the substations. Finally there are compared advantages and disadvantages of separated and parallel operations of nodal areas. If necessary, technical arrangements required for introduction of parallel operation of nodal areas of Čebín substation and Sokolnice substation will be designed. The theoretical part of the work deals with calculation of steady state with help of iterative methods, namely Newton´s and Gauss-Seidel methods. There are further described the method of calculating short-circuit currents, characteristic values and time behaviours of short-circuit current.
|
|
| |
|
|
Methods for enforcing non-negativity of solution in Krylov regularization
Hoang, Phuong Thao ; Hnětynková, Iveta (advisor) ; Pozza, Stefano (referee)
The purpose of this thesis is to study how to overcome difficulties one typically encounters when solving non-negative inverse problems by standard Krylov subspace methods. We first give a theoretical background to the non-negative inverse problems. Then we concentrate on selected modifications of Krylov subspace methods known to improve the solution significantly. We describe their properties, provide their implementation and propose an improvement for one of them. After that, numerical experiments are presented giving a comparison of the methods and analyzing the influence of the present parameters on the behavior of the solvers. It is clearly demonstrated, that the methods imposing nonnegativity perform better than the unconstrained methods. Moreover, our improvement leads in some cases to a certain reduction of the number of iterations and consequently to savings of the computational time while preserving a good quality of the approximation.
|
|
|
Least-squares problems with sparse-dense matrices
Riegerová, Ilona ; Tůma, Miroslav (advisor) ; Tichý, Petr (referee)
Problém nejmenších čtverc· (dále jen LS problém) je aproximační úloha řešení soustav lineárních algebraických rovnic, které jsou z nějakého d·vodu za- tíženy chybami. Existence a jednoznačnost řešení a metody řešení jsou známé pro r·zné typy matic, kterými tyto soustavy reprezentujeme. Typicky jsou ma- tice řídké a obrovských dimenzí, ale velmi často dostáváme z praxe i úlohy s maticemi o proměnlivé hustotě nenulových prvk·. Těmi se myslí řídké matice s jedním nebo více hustými řádky. Zde rozebíráme metody řešení tohoto LS pro- blému. Obvykle jsou založeny na rozdělení úlohy na hustou a řídkou část, které řeší odděleně. Tak pro řídkou část m·že přestat platit předpoklad plné sloupcové hodnosti, který je potřebný pro většinu metod. Proto se zde speciálně zabýváme postupy, které tento problém řeší. 1
|
|
|
Methods for the solution of nonlinear equations
Havelková, Eva ; Kučera, Václav (advisor) ; Tichý, Petr (referee)
The aim of this bachelor thesis is to present an overview of elementary numerical methods for solving nonlinear algebraic equations in one variable. Firstly, related concepts from numerical mathematics and mathematical analysis are explained. The main part of the thesis provides a detailed description of chosen iterative methods as well as the proofs of their orders of convergence. The methods covered are namely the bisection method, fixed-point iteration, regula falsi method, Newton's method, secant method and methods that are based on quadratic interpolation. The practical part of the thesis presents results of numerical experiments that were carried out with Matlab software on various types of nonlinear equations. These results are compared with the theory introduced in the preceding parts. The contribution of this thesis is to provide a comprehensive overview and comparison of the characteristics of basic methods for solving nonlinear equations based on a variety of literature. Powered by TCPDF (www.tcpdf.org)
|
|
| |
|
|
Comparison of various methods for nonlinear analysis of structures from the point of view of speed, accuracy and robustness.
Bravenec, Ladislav ; Křiváková, Jarmila (referee) ; Němec, Ivan (advisor)
The aim of the thesis is to compare the iterative methods which program RFEM 5 uses the non-linear calculations of structures, namely the analysis of large deformations and post critical analysis. Comparison should serve as a basis for which calculation method is the most accurate, fastest and most reliable in terms of getting results. Time-consuming will be judged according to the calculation of the solution and the time needed to compute one iterativ. Robustness we will compare the reliability of methods in in normal use. Accuracy of the calculation will be determined by comparing the maximum deformation structures. Comparison will be made with examples from practice.
|
|
|
Steady state and short-circuit conditions within E.ON 110 kV power network at parallel operation of nodal areas of Čebín substation and Sokolnice substation
Múdry, Peter ; Rampl, Martin (referee) ; Blažek, Vladimír (advisor)
In the distribution network 110 kV of E.ON Company there are the nodal areas of Čebin substation and Sokolnice substation which are operated separately at the present time. There is one 400/110 kV transformer for each nodal area. In case of fault on one of these transformers or on busbar in which the set transformer is working, it comes to an outage of electric supply in the set nodal area. This problem has to be solved with help of the parallel operation of nodal areas of Čebín substation and Sokolnice substation. The main and also the practical task of this work is to design the bridge connection appropriate for parallel operation of nodal areas (supply transformers 400/110 kV). With help of a computing program there were made calculations of steady state and short-circuit conditions in distribution network 110 kV for separated and parallel operation of nodal areas. Voltage conditions, load of transformers (400/110 kV and 110/vn kV) and conditions on 110 kV lines are evaluated and controlled as the result of steady state calculations. Based on short-circuit conditions there is controlled the short-circuit resistance of the substations. Finally there are compared advantages and disadvantages of separated and parallel operations of nodal areas. If necessary, technical arrangements required for introduction of parallel operation of nodal areas of Čebín substation and Sokolnice substation will be designed. The theoretical part of the work deals with calculation of steady state with help of iterative methods, namely Newton´s and Gauss-Seidel methods. There are further described the method of calculating short-circuit currents, characteristic values and time behaviours of short-circuit current.
|
|
|
Mnohoúrovňové modelování geomateriálů a iterační řešiče
Blaheta, Radim ; Byczanski, Petr ; Harasim, Petr
The knowledge of microstructure in combination with properties of the constituents and mathematical modelling can be used for investigation of the properties of geomaterials at application scale. We investigate problems with both deterministic knowledge of microstructure, derived from X-ray CT scans, and stochastic one. The stochastic generation is also used for a systematic study of robustness of iterative solvers, particularly for Schwarz methods for PDE problems discretized by mixed FEM.
|
guest ::
