PGD driven by the Constitutive Relation Error - Minimal CRE/PGD
Résumé
Many science and engineering problems still remain intractable because of their numerical complexity. Due to a huge number of degrees of freedom required, those models cannot be tackled with classical brute force methods. Therefore, alternative numerical approaches are required, such as model reduction methods. A promising model order reduction method is the Proper Generalized Decomposition (PGD) that does not require any knowledge on the solution.
Even though PGD is usually very effective, a major question is to derive verification tools for controlling the calculation process. Specific error indicators have been build for PGD reduced models. A first robust approach for PGD verification, using the concept of Constitutive Relation Error (CRE), leads to guaranteed and relevant error evaluation. However in this error estimator, the required dual field is computed after the PGD procedure and then cannot influence the solution.
This poster presents a new PGD strategy derived from the CRE concept and showing very interesting properties. Based on minimizing the CRE under admissibility conditions, the PGD solution is computed and controlled on the fly during the PGD procedure thanks to the CRE estimate. Compared to other PGD strategies on an highly nonseparable test case, minimizing the CRE improves the accuracy of the solution thanks to an effective error estimator. We show that this strategy reduces the computational cost associated since its accurate reduction error estimator enables to know when to stop the progressive algorithm.
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