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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.
Technische Universität Darmstadt
Ph.D. Thesis, Primary publication

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Item Type: Ph.D. Thesis
Type of entry: Primary publication
Title: Numerical Approximation of the Magnetoquasistatic Model with Uncertainties and its Application to Magnet Design
Language: English
Referees: Weiland, Prof. Dr. Thomas ; Ulbrich, Prof. Dr. Stefan ; Sebastian, Prof. Dr. Schöps
Date: 2015
Place of Publication: Darmstadt
Date of oral examination: 13 February 2015
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.

Alternative Abstract:
Alternative AbstractLanguage

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.

German
URN: urn:nbn:de:tuda-tuprints-49504
Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
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: 02 Oct 2015 11:05
Last Modified: 09 Jul 2020 01:05
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/4950
PPN: 365286060
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