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Numerical Methods for the Estimation of the Impact of Geometric Uncertainties on the Performance of Electromagnetic Devices

Corno, Jacopo (2017):
Numerical Methods for the Estimation of the Impact of Geometric Uncertainties on the Performance of Electromagnetic Devices.
Darmstadt, Technische Universität, [Online-Edition: http://tuprints.ulb.tu-darmstadt.de/7038],
[Ph.D. Thesis]

Abstract

This work addresses the application of Isogeometric Analysis to the simulation of particle accelerator cavities and other electromagnetic devices whose performance is mainly determined by their geometry. By exploiting the properties of B-Spline and Non-Uniform B-Spline basis functions, the Isogeometric approximation allows for the correct discretisation of the spaces arising from Maxwell's equations and for the exact representation of the computational domain. This choice leads to substantial improvements in both the overall accuracy and computational effort.

The suggested framework is applied to the evaluation of the sensitivity of these devices with respect to geometrical changes using Uncertainty Quantification methods and to shape optimisation processes. The particular choice of basis functions simplifies the construction of the geometry deformations significantly.

Finally, substructuring methods are proposed to further reduce the computational cost due to matrix assembly and to allow for hybrid coupling of Isogeometric Analysis and more classical Finite Element Methods. Considerations regarding the stability of such methods are addressed.

The methods are illustrated by simple numerical tests and real world device simulations with particular emphasis on particle accelerator cavities.

Item Type: Ph.D. Thesis
Erschienen: 2017
Creators: Corno, Jacopo
Title: Numerical Methods for the Estimation of the Impact of Geometric Uncertainties on the Performance of Electromagnetic Devices
Language: English
Abstract:

This work addresses the application of Isogeometric Analysis to the simulation of particle accelerator cavities and other electromagnetic devices whose performance is mainly determined by their geometry. By exploiting the properties of B-Spline and Non-Uniform B-Spline basis functions, the Isogeometric approximation allows for the correct discretisation of the spaces arising from Maxwell's equations and for the exact representation of the computational domain. This choice leads to substantial improvements in both the overall accuracy and computational effort.

The suggested framework is applied to the evaluation of the sensitivity of these devices with respect to geometrical changes using Uncertainty Quantification methods and to shape optimisation processes. The particular choice of basis functions simplifies the construction of the geometry deformations significantly.

Finally, substructuring methods are proposed to further reduce the computational cost due to matrix assembly and to allow for hybrid coupling of Isogeometric Analysis and more classical Finite Element Methods. Considerations regarding the stability of such methods are addressed.

The methods are illustrated by simple numerical tests and real world device simulations with particular emphasis on particle accelerator cavities.

Place of Publication: Darmstadt
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)
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) > Computational Engineering (from 01.01.2019 renamed Computational Electromagnetics)
Date Deposited: 17 Dec 2017 20:55
Official URL: http://tuprints.ulb.tu-darmstadt.de/7038
URN: urn:nbn:de:tuda-tuprints-70389
Referees: Sebastian, Prof. Dr. Schöps and Carlo, Prof. Dr. de Falco
Refereed / Verteidigung / mdl. Prüfung: 26 September 2017
Alternative Abstract:
Alternative abstract Language
Diese Arbeit befasst sich mit der Anwendung der isogeometrischen Analyse auf die Simulation von Beschleunigerkavitäten und anderen elektomagnetischen Geräten, deren Leistung hauptsächlich mit ihrer Geometrie zusammenhängt. Durch die inhärenten Strukturen der B-Spline-Basis ermöglicht der isogeometrische Ansatz eine konforme Diskretisierung der Funktionenräume, die aus den Maxwellgleichungen hervorgehen, sowie eine exakte Darstellung des Rechengebietes. Die Wahl des isogeometrischen Ansatzes führt zu nicht zu vernachlässigenden Verbesserungen von Genauigkeit und Rechenaufwand. Mit Hilfe des Ansatzes wird, zusammen mit Methoden der Unsicherheitsquantifizierung und Formoptimierung, auch die Empfindlichkeit der Geräte bezüglich Änderungen der Geometrie untersucht. Hierbei wird die Berücksichtigung von Deformationen durch die Wahl der speziellen Basisfunktionen vereinfacht. Letztendlich wird erläutert, wie durch Zerlegungsmethoden der Rechenaufwand beim Assemblieren der Matrizen weiter reduziert werden kann, und eine Kopplung von isogeometrischer und klassischer Numerik wird, zusammen mit Anmerkungen zur Stabilität einer solchen Hybridmethode, erläutert. Die vorgestellten Techniken werden an einfachen numerischen Testbeispielen und industriellen Geräten illustriert, wobei der Fokus auf Beschleunigerkavitäten gerichtet ist.German
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