Certified Descent Algorithm for shape optimization driven by fully-computable a posteriori error estimators

Author (s): Giacomini, M.; Pantz, O. and Trabelsi, K.
Journal: ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

Volume: 23, Issue 3
Pages: 977 – 1001
Date: 2017

Abstract:
In this paper we introduce a novel certified shape optimization strategy – named Certified Descent Algorithm (CDA) – to account for the numerical error introduced by the Finite Element approximation of the shape gradient. We present a goal-oriented procedure to derive a certified upper bound of the error in the shape gradient and we construct a fully-computable, constant-free a posteriori error estimator inspired by the complementary energy principle. The resulting CDA is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion. After validating the error estimator, some numerical simulations of the resulting certified shape optimization strategy are presented for the well-known inverse identification problem of Electrical Impedance Tomography.

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Bibtex:

@article{2017-COCV-GPT,
	Author = {Giacomini, Matteo and Pantz, Olivier and Trabelsi, Karim},
	Title = {{Certified Descent Algorithm for shape optimization driven by fully-computable 
		a posteriori error estimators}},
	Fjournal = {ESAIM: Control, Optimisation and Calculus of Variations},
	Journal = {ESAIM:COCV},
	Volume = {23},
	Number = {3},
	Pages = {977--1001},
	Year = {2017},
	DOI = {10.1051/cocv/2016021},
	url= {https://doi.org/10.1051/cocv/2016021},
}