An a posteriori error estimator for shape optimization: application to EIT

Author (s): Giacomini, M.; Pantz, O.; Trabelsi, K.
Journal: Journal of Physics: Conference Series

Volume: 657
Date: 2015

Abstract:
In this paper we account for the numerical error introduced by the Finite Element approximation of the shape gradient to construct a guaranteed shape optimization method. We present a goal-oriented strategy inspired by the complementary energy principle to construct a constant-free, fully-computable a posteriori error estimator and to derive a certified upper bound of the error in the shape gradient. The resulting Adaptive Boundary Variation Algorithm (ABVA) is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion for the optimization loop. Some preliminary numerical results for the inverse identification problem of Electrical Impedance Tomography are presented.

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Bibtex:

@article{MG-GPT-15,
  author={M Giacomini and O Pantz and K Trabelsi},
  title={An a posteriori error estimator for shape optimization: application to {EIT}},
  journal={Journal of Physics: Conference Series},
  volume={657},
  number={1},
  pages={012004},
  url={http://stacks.iop.org/1742-6596/657/i=1/a=012004},
  year={2015},
}