Year: 2019
Author: Karsten Eppler, Helmut Harbrecht, Sebastian Schlenkrich, Andrea Walther
Journal of Mathematical Study, Vol. 52 (2019), Iss. 3 : pp. 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v52n3.19.01
Journal of Mathematical Study, Vol. 52 (2019), Iss. 3 : pp. 227–243
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Exterior electromagnetic shaping shape optimization boundary element method automatic differentiation.