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.
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},
}