Adjoint Error Estimation for a Pseudo-Spectral Approach to Stochastic Field-Circuit Coupled Problems

Corresponding Author

Ulrich Römer

[email protected]

Institut für Theorie Elektromagnetischer Felder, Technische Universitaet Darmstadt, Schlossgartenstr. 8, D-64289 Darmstadt, Germany

Graduate School of Computational Engineering, Technische Universitaet Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany

phone +49 6151 16 5903, fax +49 6151 16 4611Search for more papers by this author

Sebastian Schöps,

Sebastian Schöps

Institut für Theorie Elektromagnetischer Felder, Technische Universitaet Darmstadt, Schlossgartenstr. 8, D-64289 Darmstadt, Germany

Graduate School of Computational Engineering, Technische Universitaet Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany

Search for more papers by this author

Ulrich Römer,

Corresponding Author

Ulrich Römer

[email protected]

Institut für Theorie Elektromagnetischer Felder, Technische Universitaet Darmstadt, Schlossgartenstr. 8, D-64289 Darmstadt, Germany

Graduate School of Computational Engineering, Technische Universitaet Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany

phone +49 6151 16 5903, fax +49 6151 16 4611Search for more papers by this author

Sebastian Schöps,

Sebastian Schöps

Institut für Theorie Elektromagnetischer Felder, Technische Universitaet Darmstadt, Schlossgartenstr. 8, D-64289 Darmstadt, Germany

Graduate School of Computational Engineering, Technische Universitaet Darmstadt, Dolivostr. 15, D-64293 Darmstadt, Germany

Search for more papers by this author

First published: 21 October 2015

https://doi.org/10.1002/pamm.201510345

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Abstract

This work is concerned with the numerical approximation of random differential-algebraic equations (DAE), arising from electric field-circuit coupled problems. Using the adjoint DAE, the stochastic collation error is analyzed. The error can be evaluated using a collocation method of the same polynomial degree for the adjoint DAE. In particular, there is no need for constructing a solution of higher polynomial degree. The accuracy of the estimator is illustrated by a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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