Browsing by Subject "convergence"

Now showing 1 - 20 of 22

Access status: Open Access ,
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
(2007) Malec, Marian; Sapa, Lucjan
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in $\mathbf{R}^{1+n}$. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Access status: Open Access ,
Efektywna pojemność komór magazynowych gazu w pokładowych złożach soli kamiennej
(Wydawnictwa AGH, 2010) Ślizowski, Jarosław; Serbin, Karolina; Wiśniewska, Monika
This paper presents the perspectives for gas storage in the Zechstein salt deposits in the Fore-Sudetic Monocline (nine areas) and in the Łeba elevation region (four areas). The parameters taken into account were: the thickness of the deposit, affecting the cavern volume and the depth of the deposit that affects the minimum and maximum storage pressures, hence volume of the gas that could be stored in the cavern. It has been found that large initial storage capacities, that can be obtained from deposits located deeper, decrease rapidly due to the convergence. The most favorable conditions for location of the storage caverns at the Fore-Sudetic Monocline occur in the Bytom Odrzański region. At the Leba elevation, the most favorable conditions occur in the Kosakowo region, where construction of the storage facility has been started. To summarize the results, the estimated storage capacities of the individual caverns located in the selected regions and the storage capacities per 1 km$^{2}$ of deposits surface are presented in the paper.
Access status: Open Access ,
Efficient time-delay system optimization with auto-configured metaheuristics
(2024) Senkerik, Roman; Guzowski, Hubert; Janku, Peter; Kadavy, Tomas; Kominkova Oplatkova, Zuzana; Matusu, Radek; Pluhacek, Michal; Pekar, Libor; Viktorin, Adam; Byrski, Aleksander; Smołka, Maciej
Wydział Informatyki
This paper presents an experimental study that compares the performance of four selected metaheuristic algorithms for optimizing a time delay system model. Time delay system models are complex and challenging to optimize due to their inherent characteristics, such as non-linearity, multi-modality, and constraints. The study includes an explanation of the choice and core functionality of the selected algorithms, which are both baseline and state-of-the-art variants of self-organizing migrating algorithm (SOMA), state-of-the-art variant from the Success-History-based Adaptive Differential Evolution family of algorithms, with emphasis on diverse search (DISH algorithm), and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm. The hyperparameters of the metaheuristic algorithms were set using the iRace automatic algorithm configuration framework. The paper emphasizes the importance of metaheuristic algorithms in control engineering for time-delay systems to develop more effective and efficient control strategies and precise model identifications. The experimental results highlight the effectiveness of the state-of-the-art algorithms with specific adaptive mechanisms like population organization process, diverse search and adaptation mechanisms ensuring a gradual transition from exploration to exploitation. Overall, this study contributes to understanding the challenges and advantages of using metaheuristic algorithms in control engineering for time delay systems. The results provide valuable insights into the performance of modern metaheuristic algorithms and can help guide the selection of appropriate adaptive mechanisms of metaheuristics.
Access status: Restricted ,
Koncepcja systemu informacji przestrzennej dla oceny stanu zagrożenia górotworu solnego
(Data obrony: 2014-10-14) Dynda, Michał; Dubiel, Łukasz
Wydział Geodezji Górniczej i Inżynierii Środowiska
Access status: Restricted ,
Koncepcja systemu informacji przestrzennej dla oceny stanu zagrożenia górotworu solnego
(Data obrony: 2014-10-14) Dubiel, Łukasz; Dynda, Michał
Wydział Geodezji Górniczej i Inżynierii Środowiska
Access status: Restricted ,
Lemat Urysohna i twierdzenie Tietzego
(Data obrony: 2010-07-06) Ginter, Aleksandra
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metoda prostych dla różniczkowo-funkcyjnych równań parabolicznych
(Data obrony: 2017-07-18) Kądziela, Agnieszka
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metoda różnicowa typu Mickensa dla uogolnionego równania Burgersa-Haxleya
(Data obrony: 2016-04-27) Góratowska, Klaudia
Wydział Matematyki Stosowanej
Access status: Restricted ,
Metody różnicowe typu Cranka-Nicolsona
(Data obrony: 2015-03-03) Lewińska, Paulina
Wydział Matematyki Stosowanej
Access status: Open Access ,
Naprężenia, odkształcenia i konwergencje na różnych głębokościach kopalń soli, studium modelowe dla chodnika w górotworze solnym
(Wydawnictwa AGH, 2009) Maj, Agnieszka
The paper presents the influence of depth on stresses and strains around the gallery in salt rock mass. The method of taking the values of initial stresses corresponding to the state of stress in salt rock mass for analyses is described. The distributions of stress, strain and convergence of gallery are calculated for elastic-viscous medium using Finite Element Method. The results of this paper may be used for recognition of the stress conditions in salt rock mass and estimation of viscous properties of rock mass on the basis of the convergence measurements at various depths.
Access status: Open Access ,
New efficient time integrators for non-linear parabolic problems
(2006) Bujanda, Blanka; Jorge, Juan Carlos
In this work a new numerical method is constructed for time-integrating multidimensional parabolic semilinear problems in a very efficient way. The method reaches the fourth order in time and it can be combined with standard spatial discretizations of any order to obtain unconditinally convergent numerical algorithms. The main theoretical results which guarantee this property are explained here, as well as the method characteristics which guarantee a very strong reduction of computational cost in comparison with classical discretization methods.
Access status: Open Access ,
On the convergence of workings and the purpose of working observations in salt mines
(Wydawnictwa AGH, 2012) Kortas, Grzegorz
W pracy przedstawiono definicje konwergencji jako strumienia pola wektorowego przemieszczenia. Określono wzory na konwergencję wyrobisk w kształcie prymitywów geometrycznych oraz wyodrębniono i scharakteryzowano fazy rozwoju konwergencji w czasie. Omówiono podstawowe zasady zaciskania wyrobisk, wiążące główne konwergencje w komorze prostopadłościennej z jej wymiarami i konwergencją objętościową. Dotychczasowy stan wiedzy wykorzystano do sformułowania celów prowadzenia pomiarów konwergencji w podziemnych kopalniach soli. Opis faz konwergencji i studium konwergencji w prostopadłościennej komorze mają walory poznawcze, a wyłonione cele obserwacji mogą być wykorzystane przy projektowaniu obserwacji konwergencji i interpretacji ich wyników.
Access status: Restricted ,
Oszacowania rozwiązań równań różniczkowo-funkcyjnych i różnicowo-funkcyjnych
(Data obrony: 2011-10-21) Czaja, Piotr
Wydział Matematyki Stosowanej
Access status: Restricted ,
Otwarto-zamknięte ogólne metody liniowe dla równań różniczkowych zwyczajnych
(Data obrony: 2018-07-18) Pierzchała, Paulina
Wydział Matematyki Stosowanej
Access status: Open Access ,
Pseudospectral method for semilinear partial functional differential equations
(Wydawnictwa AGH, 2010) Czernous, Wojciech
We present a convergence result for two spectral methods applied to an initial boundary value problem with functional dependence of Volterra type. Explicit condition of Courant-Friedrichs-Levy type is assumed on time step τ and the number $N$ of collocation points. Stability statements and error estimates are written using continuous norms in weighted Jacobi spaces.
Access status: Restricted ,
Różne sposoby definiowania topologii oraz ich zastosowania
(Data obrony: 2014-10-30) Bugno, Ewelina
Wydział Matematyki Stosowanej
Access status: Restricted ,
Słaba i mocna zbieżność miar
(Data obrony: 2010-07-05) Wilk, Łukasz
Wydział Matematyki Stosowanej
Access status: Open Access ,
Tectonic strain in salt rock mass based on measurements
(Wydawnictwa AGH, 2023) Szczerbowski, Zbigniew ; Niedbalski, Zbigniew; Bednarek, Łukasz
The measurement method with the application of an extensometer for the detection of the manifestation of tectonic strain is presented in this paper. The instrument is operated in underground construction for engineering purposes, and the authors applied it in a deeply placed underground old mine gallery in the Bochnia Salt Mine, just at the tectonic boundary of the Outer Carpathians which is commonly considered to be a tectonically active zone. The presented study is characterized by two basic features. The first is the placement of the measurements deep in an old mine which is an environment free of atmospheric factors disturbing the detection of a tectonic signal. The second is a combination of routine measurements carried out for engineering purposes and research measurements enabling the extension of the observation of displacements in the space outside underground workings, inside the rock mass that has been penetrated by extensometer probes. The extensometric measurements have been made using three 7-meter long sections. The results showed the differentiation in the displacement rates of points placed in the side walls: in the southern profile, the annual displacements are approximately 1.5 mm and in the northern one – approximately 1 mm. The combined result corresponds to the amount of the annual convergence value which has been determined by the classical surveys in the excavation where extensometric measurements have been made. What is more, the ongoing displacements in the southern side wall involve the entire part of the rock mass which is penetrated by an extensometric probe, but the displacements in the northern side are only observed in the first 2 m of the penetrated part of the rock mass. This differentiation is interpreted by the authors as being the result of tectonic strain acting from the south exerted by the Carpathians.
Access status: Open Access ,
Wpływ parametrów ośrodka sprężysto-lepkiego na konwergencję powierzchniową prostokątnego chodnika na podstawie badań modelowych
(Wydawnictwa AGH, 2008) Maj, Agnieszka
Dependence of relative areal convergence and its rate on slenderness of rectangular gallery and Young modulus was presented in this paper. FEM and Cosmos/M were used to compute of displacements in elastic-viscous medium. Parabolic relation between slenderness and convergence was obtained as well as hyperbolic relation between Young's modulus and convergence. Minimum values of functions were reached for slenderness lambda = 1 and values of these functions were the same for slenderness lambda and 1\lambda. Influence of Poisson's ratio in range from 0,2 to 0,4 was smaller. Absolute value of areal convergence and its rate decreased with increase of Poisson ratio. Results of research have been shown on figures.
Access status: Open Access ,
Zaciskanie konturu typowej komory prostopadłościennej w Kopalni Soli Kłodawa
(Wydawnictwa AGH, 2009) Marcola-Sadowska, Jolanta; Bieniasz, Józef; Wojnar, Waldemar
For over 30 years Chemkop has researched convergence survey in Polish salt mines. In 1998 in one of typical salt chamber in Kłodawa installed unique measuring points system for convergence observation of vertical cross-section on 630 m depth. For 11 years measured multiple horizontal, vertical and oblique bases and levelled bench-marks. This measurements allowed determine relative velocity of area convergence about 1 per mille annually.