Volume 52, Issue 3
Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation

Karsten Eppler, Helmut Harbrecht, Sebastian Schlenkrich & Andrea Walther

J. Math. Study, 52 (2019), pp. 227-243.

Published online: 2019-09

[An open-access article; the PDF is free to any online user.]

Preview Full PDF 159 2749
Export citation
  • 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.

  • Keywords

Exterior electromagnetic shaping, shape optimization, boundary element method, automatic differentiation.

  • AMS Subject Headings

49M25, 49Q10, 78M15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

karsten.eppler@tu-dresden.de (Karsten Eppler)

helmut.harbrecht@unibas.ch (Helmut Harbrecht)

sebastian.schlenkrich@d-fine.de (Sebastian Schlenkrich)

andrea.walther@unipaderborn.de (Andrea Walther)

  • BibTex
  • RIS
  • TXT
Copy to clipboard
The citation has been copied to your clipboard