Computation of Shape Derivatives in Electromagnetic Shaping by Algorithmic Differentiation (Journal of Mathematical Study, 2019)
Shape optimization based on analytical shape derivatives is meanwhile awell-established tool in engineering applications. For an appropriate discretization ofthe underlying problem, the technique of algorithmic differentiation can also be usedto provide a discrete analogue of the analytic shape derivative. The present article isconcerned with the comparison of both types of gradient calculation and their effectson 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 thispurpose, the article discusses both techniques and analyses the obtained numericalresults for a generic test case from electromagnetic shaping. Since good agreement ofboth methods is found, algorithmic differentiation seems to be worthwhile to be usedalso for more demanding shape optimization problems.