Home > Search Results: Šarmanová, Martina
Search:
 
Search Tips :: Simple Search
Search collections:
Sort by: Display results: Output format:
National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Mathematical modeling of vibrational dynamics in electron scattering from molecule.
 Šarmanová, Martina ; Čížek, Martin (advisor) ; Pultarová, Ivana (referee)
In this work, we study low-energy electron-molecule collisions. To understand these processes, it is necessary to explain the phenomena appearing in so called 2D electron energy-loss spectra. These spectra are very different for different molecules, which we still cannot explain satisfactorily. Therefore we would like to gain deeper understand- ing through mathematical modeling of the problem. The collision of an electron with a molecule can be mathematically formulated in the language of partial integro-differential equations. The discretization converts the problem to a system of linear algebraic equa- tions with a complex symmetric matrix. The matrix of this system is also sparse and for this reason we believe that the use of iterative methods to solve the resulting system is a suitable choice. However, as we were convinced when testing the convergence rate of the Krylov subspace methods for the model with two degrees of freedom (which we dealt with in the bachelor thesis), iterative methods suffer from slow convergence. This motivated us to try using preconditioning which is considered to be crucial for the relia- bility of iterative techniques across the literature. Our main goal in this work was to find a suitable preconditioning technique for Krylov subspace methods, which would ensure their faster...
Detailed record
Iterative calculation of vibrational dynamics in electron scattering from molecule
 Šarmanová, Martina ; Čížek, Martin (advisor) ; Tůma, Miroslav (referee)
The main focus of present thesis is the numerical solution of systems of linear algebraic equations arising from the physical model of a collision of an electron with a molecule. The first third of the thesis introduces the basic concepts used in the treatment of molecular vibrations. The description of the Jahn-Teller model of the vibronic dynamics of the in- termediate molecular anion in the form of the system of stationary Schrödinger equations is also included. Then, we show how this system of integro-differential equations can be transformed into a system of linear algebraic equations represented by a symmetric matix. In the second chapter, nine numerical methods (both direct and iterative), which have been chosen considering the character of the present problem, are discussed in detail. The explanation of the main idea of preconditioning of the problem concludes the theoretical part of the thesis. The last third of the thesis is dedicated to the numerical experiments. The main aim of the epxeriments was to compare the abovementioned methods with the emphasis on the usability within the scope of electron-molecule collision simulations. 1
Detailed record

Interested in being notified about new results for this query?
Subscribe to the RSS feed.
Digital Repository :: Search :: Submit :: Personalize :: Help
Powered by Invenio v1.1.2
Maintained by admin.invenio@techlib.cz
This site is also available in the following languages:
Česky  English