Efficient PDE Constrained Shape Optimization Based on Steklov-Poincaré-Type Metrics

@article{Schulz2015EfficientPC,
  title={Efficient PDE Constrained Shape Optimization Based on Steklov-Poincar{\'e}-Type Metrics},
  author={Volker Schulz and Martin Siebenborn and Kathrin Welker},
  journal={SIAM J. Optim.},
  year={2015},
  volume={26},
  pages={2800-2819}
}
Recent progress in PDE constrained optimization on shape manifolds is based on the Hadamard form of shape derivatives, i.e., in the form of integrals at the boundary of the shape under investigation, as well as on intrinsic shape metrics. From a numerical point of view, domain integral forms of shape derivatives seem promising, which rather require an outer metric on the domain surrounding the shape boundary. This paper tries to harmonize both points of view by employing a Steklov-Poincar\'e… 

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