@Article{JMS-52-3,
author = {Karsten, Eppler and Helmut, Harbrecht and Sebastian, Schlenkrich 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 = {<p style="text-align: justify;">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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v52n3.19.01},
url = {https://global-sci.com/article/87731/computation-of-shape-derivatives-in-electromagnetic-shaping-by-algorithmic-differentiation}
}