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Space-Time Adaptive Methods for Beam Dynamics Simulations

Schnepp, Sascha (2009):
Space-Time Adaptive Methods for Beam Dynamics Simulations.
Darmstadt, Technische Universität, TU Darmstadt, [Online-Edition: urn:nbn:de:tuda-tuprints-13757],
[Ph.D. Thesis]

Abstract

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.

Item Type: Ph.D. Thesis
Erschienen: 2009
Creators: Schnepp, Sascha
Title: Space-Time Adaptive Methods for Beam Dynamics Simulations
Language: English
Abstract:

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
Publisher: Technische Universität
Uncontrolled Keywords: Space-Time Adaptive Simulations, Adaptive Mesh Refinement, Finite Integration Technique, FIT, Finite Volume Method, FV, Discontinuous Galerkin Method, DG, Maxwells Equations, Self-Consistent Charged Particle Simulations, Low-Dispersion Methods, Consistency, Stability, Convergence
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory (from 01.01.2019 renamed Institute for Accelerator Science and Electromagnetic Fields)
Date Deposited: 26 May 2009 10:14
Official URL: urn:nbn:de:tuda-tuprints-13757
License: Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0
Referees: Weiland, Prof. Dr.- Thomas and Dyczij-Edlinger, Prof. Dr. Romanus
Refereed / Verteidigung / mdl. Prüfung: 23 April 2009
Alternative keywords:
Alternative keywordsLanguage
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, KonvergenzGerman
Alternative Abstract:
Alternative abstract Language
In der vorliegenden Arbeit werden Techniken zur zeitadaptiven Anpassung der lokalen räumlichen Auflösung für die Methode der Finiten Integration (FIT), die Discontinuous Galerkin Methode (DGM) und eine Hybridmethode, welche die FIT mit der Methode der Finiten Volumen kombiniert (FI-FV), eingeführt. Die FIT und die DGM sind etablierte Methoden zur numerischen Berechnung elektromagnetischer Feldprobleme. Die FI-FV Hybridmethode wurde im Rahmen dieser Arbeit entwickelt. Die semi-diskreten, also räumlich diskret jedoch kontinuierlich in der Zeit, und die voll diskreten Formulierungen der untersuchten Methoden werden abgeleitet. Für jeweils beide Formulierungen wird eine Untersuchung der Dispersions- und Dissipationseigenschaften auf statischen Rechengittern durchgeführt. Als ein Ergebnis dieser Analysen werden asymptotische Ordnungen des Dispersions- und Dissipationsfehlers angegeben. Anschließend werden für jede der numerischen Methoden, Techniken zur Bestimmung und Modifizierung der diskreten elektromagnetischen Größen in lokal verfeinerten Gebieten dargelegt. Die Adaptionstechniken für die FIT und die FI-FV Methode basieren auf linearen oder Splineinterpolationen dritter Ordnung. Im Rahmen der DGM werden Projektionsoperatoren verwendet, und es wird gezeigt, dass deren Anwendung zu minimalen Adaptionsfehlern führt. Die numerische Stabilität der entwickelten adaptiven Methoden wird bewiesen. Die entwickelten Algorithmen finden Anwendung bei der selbstkonsistenten Simulation der Dynamik geladener Teilchen und elektromagnetischer Felder. Die Ergebnisse der ersten Designstudie des vollständigen ersten Abschnitts des Freie-Elektronen Laser in Hamburg (FLASH), unter Berücksichtigung von Raumladungs- und Strukturwechselwirkungen, werden vorgestellt.German
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