Numerical Approximation of the Magnetoquasistatic Model with Uncertainties

Applications in Magnet Design

  • Ulrich Römer

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Ulrich Römer
    Pages 1-3
  3. Ulrich Römer
    Pages 65-90
  4. Ulrich Römer
    Pages 91-104
  5. Ulrich Römer
    Pages 105-106
  6. Back Matter
    Pages 107-114

About this book


This book presents a comprehensive mathematical approach for solving stochastic magnetic field problems. It discusses variability in material properties and geometry, with an emphasis on the preservation of structural physical and mathematical properties. It especially addresses uncertainties in the computer simulation of magnetic fields originating from the manufacturing process. Uncertainties are quantified by approximating a stochastic reformulation of the governing partial differential equation, demonstrating how statistics of physical quantities of interest, such as Fourier harmonics in accelerator magnets, can be used to achieve robust designs. The book covers a number of key methods and results such as: a stochastic model of the geometry and material properties of magnetic devices based on measurement data; a detailed description of numerical algorithms based on sensitivities or on a higher-order collocation; an analysis of convergence and efficiency; and the application of the developed model and algorithms to uncertainty quantification in the complex magnet systems used in particle accelerators.



Nonlinear Magnetoquasistatic Problem Magnetoquasistatic Approximation Uncertain Material Properties Uncertainty Propagation Generalized Polynomial Chaos Magnetic Material Coefficient Interface Sensitivity Higher Order Whitney Forms Stochastic Modeling Material Uncertainty Uncertainties in Magnet Design

Authors and affiliations

  • Ulrich Römer
    • 1
  1. 1.Technische Universität DarmstadtInstitut für Theorie Elektromagnetischer FelderDarmstadtGermany

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-41293-1
  • Online ISBN 978-3-319-41294-8
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site
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Energy, Utilities & Environment