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Numerical Approximation of the Magnetoquasistatic Model with Uncertainties and its Application to Magnet Design

Römer, Ulrich (2015):
Numerical Approximation of the Magnetoquasistatic Model with Uncertainties and its Application to Magnet Design.
Darmstadt, Technische Universität,
[Ph.D. Thesis]

Abstract

This work addresses the magnetoquasistatic approximation of Maxwell’s equations with uncertainties in material data, shape and current sources, originating, e.g., from manufacturing imperfections. Well-established numerical schemes for the deterministic model are recalled. A parametric/stochastic model is established on the partial differential equation level and its differentiability is analyzed. Sensitivity analysis techniques are at the core of the uncertainty propagation methods discussed afterwards. Schemes for propagating both probabilistic and nonprobabilistic uncertain inputs as well as techniques for dimension reduction are addressed and compared. The findings are illustrated by simple numerical and real world examples with emphasis on accelerator magnet design using open source, in-house and commercial software.

Item Type: Ph.D. Thesis
Erschienen: 2015
Creators: Römer, Ulrich
Title: Numerical Approximation of the Magnetoquasistatic Model with Uncertainties and its Application to Magnet Design
Language: English
Abstract:

This work addresses the magnetoquasistatic approximation of Maxwell’s equations with uncertainties in material data, shape and current sources, originating, e.g., from manufacturing imperfections. Well-established numerical schemes for the deterministic model are recalled. A parametric/stochastic model is established on the partial differential equation level and its differentiability is analyzed. Sensitivity analysis techniques are at the core of the uncertainty propagation methods discussed afterwards. Schemes for propagating both probabilistic and nonprobabilistic uncertain inputs as well as techniques for dimension reduction are addressed and compared. The findings are illustrated by simple numerical and real world examples with emphasis on accelerator magnet design using open source, in-house and commercial software.
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)
Date Deposited: 04 Oct 2015 19:55
Official URL: http://tuprints.ulb.tu-darmstadt.de/4950
URN: urn:nbn:de:tuda-tuprints-49504
Referees: Weiland, Prof. Dr. Thomas ; Ulbrich, Prof. Dr. Stefan ; Sebastian, Prof. Dr. Schöps
Refereed / Verteidigung / mdl. Prüfung: 13 February 2015
Alternative Abstract:
Alternative abstract Language

Gegenstand dieser Arbeit ist die magnetoquasistatische Approximation der Maxwell-Gleichungen unter Einbeziehung von, bspw. fertigungsbedingten, Unsicherheiten in Materialdaten, der Geometrie und der Stromanregung. Zunächst werden etablierte numerische Verfahren für das deterministische Modell vorgestellt. Anschließend wird ein parametrisch/stochastisches Modell, basierend auf partiellen Differentialgleichungen hergeleitet und analysiert. Der zentrale Bestandteil dieser Arbeit sind Verfahren zur Sensitivitätsanalyse und darauf basierende Methoden zur Quantifizierung von Unsicherheiten. Dabei werden stochastische und deterministische Eingangsparameter sowie Verfahren zur Dimensionsreduktion diskutiert und verglichen. Die Resultate werden anhand von einfachen numerischen Benchmarks, sowie von realistischen Beispielen aus dem Magnetdesign unter Verwendung von Open-Source, eigener und kommerzieller Software illustriert.

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