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 - <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>