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Parametric Model, Continuity and First Order Sensitivity Analysis

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Numerical Approximation of the Magnetoquasistatic Model with Uncertainties

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Abstract

The subject of this chapter is a detailed description of a parametric magnetoquasistatic model, generalizing the deterministic setting of Chap. 3. To this end we choose a continuous setting, i.e., parametrization is discussed on the differential equation level. Moreover, in a first step we allow for a general, possibly infinite dimensional parametrization, before discussing its finite dimensional approximation later on. Continuity and differentiability results will be established for different kind of inputs. In particular the sensitivity analysis presented in Sects. 4.4, 4.5 will be a key tool for propagating uncertainties in Chaps. 5 and 6.

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Notes

  1. 1.

    A more detailed description of coil- and iron-dominated magnets will be given in Chap. 6.

  2. 2.

    In mechanics \(\mathbf {x}\) is referred to as Eulerian variable, whereas \(\mathbf {X}\) denotes the Lagrangian variable.

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  1. Institut für Theorie Elektromagnetischer Felder, Technische Universität Darmstadt, Darmstadt, Germany

    Ulrich Römer

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  1. Ulrich Römer
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Correspondence to Ulrich Römer .

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Römer, U. (2016). Parametric Model, Continuity and First Order Sensitivity Analysis. In: Numerical Approximation of the Magnetoquasistatic Model with Uncertainties. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41294-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-41294-8_4

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