An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations

Author (s): Giacomini, M.
Journal: Journal of Scientific Computing

Volume: 75
Pages: 560 – 595
Date: 2018

Abstract:
The certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It relies on the computation of an upper bound of the error introduced by the finite element approximation of the shape gradient. In this paper, we present a goal-oriented error estimator which depends solely on local quantities and is fully-computable. By means of the equilibrated fluxes approach, we construct a unified strategy valid for both conforming finite element approximations and discontinuous Galerkin discretizations. The new variant of the CDA is tested on the inverse identification problem of electrical impedance tomography: both its ability to identify a genuine descent direction at each iteration and its reliable stopping criterion are confirmed.

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Bibtex:

@Article{2017-JSC-G,
author="Giacomini, Matteo",
title="An Equilibrated Fluxes Approach to the Certified Descent Algorithm for Shape Optimization 
	Using Conforming Finite Element and Discontinuous Galerkin Discretizations",
journal="Journal of Scientific Computing",
year="2018",
month="Apr",
day="01",
volume="75",
number="1",
pages="560--595",
issn="1573-7691",
doi="10.1007/s10915-017-0545-1",
url="https://doi.org/10.1007/s10915-017-0545-1"
}