Space-Time Adaptive Methods for Beam Dynamics Simulations.
Technische Universität, Darmstadt
[Ph.D. Thesis], (2009)
Sascha Schnepp, Space-Time Adaptive Methods for Beam Dynamics Simulations, PhD thesis -
Available under Creative Commons Attribution Non-commercial No Derivatives, 2.5.
Download (5MB) | Preview
|Item Type:||Ph.D. Thesis|
|Title:||Space-Time Adaptive Methods for Beam Dynamics Simulations|
This work establishes techniques for adjusting the local spatial resolution of selected numerical methods in a time-adaptive manner. Such techniques are developed within the framework of the Finite Integration Technique (FIT), a hybrid Finite Integration-Finite Volume (FI-FV) Scheme and the Discontinuous Galerkin Method (DGM). While the FIT and the DGM are established methods for the numerical solution of electromagnetic field problems, the FI-FV scheme has been developed in the context of this work. The semi-discrete, i.e., discrete in space and continuous in time, as well as the fully discretized formulations of all considered methods are presented. For both formulations of each method, an analysis of the dispersive and dissipative behavior on fixed computational grids is carried out. As a result, asymptotic orders of the dispersion and dissipation errors are established. Techniques for the determination and modification of the discrete electromagnetic field quantities in locally refined regions are presented for each of the numerical methods. For the FIT and the FI-FV Scheme, adaptations based on linear and third order spline interpolations are presented. The adaptation techniques for the DGM are based on projection operators, which are shown to minimize the adaptation error. The numerical stability of the developed adaptive methods is proven. The developed algorithms are applied to the self-consistent simulation of charged particle dynamics and electrodynamics. The results of the first design study simulating the complete first section of the Free-Electron Laser in Hamburg (FLASH), taking space charge and structure interactions into account, are presented.
|Place of Publication:||Darmstadt|
|Uncontrolled Keywords:||Raum-Zeit Adaptive Simulationen, Adaptive Gitter Verfeinerung, Finite Integration Technique, FIT, Finite Volume Method, FV, Discontinuous Galerkin Method, DG, Maxwellsche Gleichungen, Maxwell, Selbst-konsistente Simulationen geladener Teilchen, Dispersion, Konsistenz, Stabilität, Konvergenz|
|Classification DDC:||500 Naturwissenschaften und Mathematik > 500 Naturwissenschaften
500 Naturwissenschaften und Mathematik > 530 Physik
500 Naturwissenschaften und Mathematik > 510 Mathematik
|Divisions:||18 Department of Electrical Engineering and Information Technology > Institute for Computational Electromagnetics
18 Department of Electrical Engineering and Information Technology
|Date Deposited:||26 May 2009 10:14|
|Last Modified:||07 Dec 2012 11:55|
|Referees:||Weiland, Prof. Dr.- Thomas and Dyczij-Edlinger, Prof. Dr. Romanus|
|Refereed:||23 April 2009|