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

5th International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Giacomini, M.^1,2 ; Pantz, O.^1 ; Trabelsi, K.^2

CMAP Ecole Polytechnique, (M. Giacomini and O. Pantz Are Members of the DEFI Project at INRIA Saclay Ile-de-France), Route de Saclay, Palaiseau

91128, France^1

DRI Institut Polytechnique des Sciences Avancées, 7-9 rue M. Grandcoing, Ivry-sur-Seine

94200, France^2

关键词: Boundary variations;    Complementary energy principles;    Descent directions;    Electrical impedance tomography;    Finite element approximations;    Inverse identification;    Posteriori error estimator;    Upper-bound of the error;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/657/1/012004/pdf
DOI  :  10.1088/1742-6596/657/1/012004

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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.