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}, }