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Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation

Eppler, Karsten and Harbrecht, Helmut and Schlenkrich, Sebastian and Walther, Andrea. (2019) Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation. Journal of Mathematical Study, 52 (3). pp. 227-243.

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Abstract

Shape optimization based on analytical shape derivatives is meanwhile a well-established tool in engineering applications. For an appropriate discretization of the underlying problem, the technique of algorithmic differentiation can also be used to provide a discrete analogue of the analytic shape derivative. The present article is concerned with the comparison of both types of gradient calculation and their effects on a gradient-based optimization method with respect to accuracy and performance, since so far only a few attempts have been made to compare these approaches. For this purpose, the article discusses both techniques and analyses the obtained numerical results for a generic test case from electromagnetic shaping. Since good agreement of both methods is found, algorithmic differentiation seems to be worthwhile to be used also for more demanding shape optimization problems.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Global Science Press
ISSN:1006-6837
e-ISSN:2617-8702
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
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Last Modified:23 Oct 2019 08:34
Deposited On:23 Oct 2019 08:34

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