Toward guaranteed PGD-reduced models

Pierre Ladevèze (1) , Ludovic Chamoin (1)

1 LMT - Laboratoire de Mécanique et Technologie

In this paper, a verification approach is introduced to build guaranteed PGD-reduced models for linear elliptic or parabolic problems depending on parameters. It is based on the concept of constitutive relation error and provides for strict bounds on both global error and error on outputs of interest defined with respect to the reference multi-parameter model. It also enables to assess contributions of various error sources, which helps driving adaptive strategies. Consequently, virtual charts associated with quantities of interest and computed from PGD models can satisfy a prescribed accuracy. Numerical experiments on transient thermal conduction illustrate the proposed verification approach and its performances.

Mots clés: Model Reduction; Verification; Error Estimation; Proper Generalized Decomposition; Separated Representation; Constitutive Relation Error

Domaines: Sciences de l'ingénieur [physics]

Pierre Ladevèze, Ludovic Chamoin. Toward guaranteed PGD-reduced models. G. Zavarise and D.P. Boso. Bytes and Science, CIMNE, Barcelona, 2012, 978-84-940243-2-0. ⟨hal-01579916⟩