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.]

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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.

  • 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
@Article{JMS-52-227, author = {Eppler , Karsten and Harbrecht , Helmut and Schlenkrich , Sebastian and Walther , Andrea }, title = {Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {3}, pages = {227--243}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n3.19.01}, url = {http://global-sci.org/intro/article_detail/jms/13296.html} }
TY - JOUR T1 - Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation AU - Eppler , Karsten AU - Harbrecht , Helmut AU - Schlenkrich , Sebastian AU - Walther , Andrea JO - Journal of Mathematical Study VL - 3 SP - 227 EP - 243 PY - 2019 DA - 2019/09 SN - 52 DO - http://doi.org/10.4208/jms.v52n3.19.01 UR - https://global-sci.org/intro/article_detail/jms/13296.html KW - Exterior electromagnetic shaping, shape optimization, boundary element method, automatic differentiation. AB -

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.

Karsten Eppler, Helmut Harbrecht, Sebastian Schlenkrich & Andrea Walther. (2019). Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation. Journal of Mathematical Study. 52 (3). 227-243. doi:10.4208/jms.v52n3.19.01
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