New regularization method for calibrated POD Reduced-Order Models

B. Abou El Majd (1) , L. Cordier (2)

1 LIAD Laboratory, FSAC, Hassan II University, Morocco
2 PPrime [Poitiers] - Institut Pprime [UPR 3346]

Reduced-order models based on Proper Orthogonal Decomposition are known to suffer from a lack of accuracy due to the truncation effect introduced by keeping only the most energetic modes. In this paper, we propose a new regularized calibration method aiming at minimizing a weighted average of normalized error, and a term measuring the change of the coefficients from their value obtained by Galerkin projection. We also determine the optimal value of the regularization parameter by analogy of the L-curve method. This paper is a sequel of [8] in which we compared various methods of calibration and introduced a Tikhonov-based regularization method. The proposed approach is assessed for a two dimensional wake flow around a cylinder, characteristic of the configurations of interest.

Mots clés: POD Reduced-Order Model; Regularization; Singular Value Decomposition; L-curve; Optimization AMS Subject Classification: 78M34; 78M50; 76F20; 91A10

Domaines: Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]; Mécanique [physics]

B. Abou El Majd, L. Cordier. New regularization method for calibrated POD Reduced-Order Models. Mathematical Modelling and Analysis, 2016, 21 (1), pp.47-62. ⟨10.3846/13926292.2016.1132486⟩. ⟨hal-01262583v2⟩