Certification of PGD reduced-order models with separated spatial variables
For researchers and engineers using PGD reduced-order models for plate and shell geometries, this provides a certification method to ensure approximation reliability, though it is an incremental extension of existing error estimation techniques.
This work introduces a guaranteed global error estimate for PGD-based reduced-order models with separated spatial variables, applied to diffusion problems in plate-like domains. The error bounds are derived from the Constitutive Relation Error method, and an adaptive strategy controls discretization error and PGD modes, with numerical examples demonstrating reliability and efficiency.
Model order reduction techniques have become an attractive approach for obtaining fast approximations of multidimensional problems. Besides computational efficiency, ensuring the reliability of the resulting approximations is of primary importance. This work focuses on the certification of PGD-based reduced-order models based on the separation of spatial variables, which are particularly well suited to plate and shell geometries. Considering diffusion problems defined in plate-like domains, we introduce a guaranteed global error estimate associated with the PGD approximation. To this end, the error bounds are derived from the Constitutive Relation Error (CRE) method. The main difficulty of this approach lies in the construction of equilibrated fluxes, for which a dedicated procedure is proposed. Based on the resulting estimator, an adaptive strategy is developed to control both the discretization error and the number of PGD modes. This certification procedure is further extended to the error control in quantities of interest. We provide several numerical examples illustrating the reliability and efficiency of our procedure.