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

[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.

[发布机构] 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

[效力级别] 计算机科学 [学科分类] 计算机科学（综合）

[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