Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models - Application to transient elastodynamics in space-time domainReport as inadecuate




Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models - Application to transient elastodynamics in space-time domain - Download this document for free, or read online. Document in PDF available to download.

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures Villeurbanne 2 LAMPA-ECPS - Laboratoire Arts et Métiers ParisTech - Ecoulements Complexes Photonique et Surfaces 3 IUF - Institut Universitaire de France 4 GeM - Institut de Recherche en Génie Civil et Mécanique

Abstract : It is now well established that separated representations built with the help of proper generalized decomposition PGD can drastically reduce computational costs associated with solution of a wide variety of problems.
However, it is still an open question to know if separated representations can be efficiently used to approximate solutions of hyperbolic evolution problems in space-time domain.
In this paper, we numerically address this issue and concentrate on transient elastodynamic models.
For such models, the operator associated with the space-time problem is non-symmetric and low-rank approximations are classically computed by minimizing the space-time residual in a natural L2 sense, yet leading to non optimal approximations in usual solution norms.
Therefore, a new algorithm has been recently introduced by one of the authors and allows to find a quasi-optimal low-rank approximation a priori with respect to a target norm.
We presently extend this new algorithm to multi-field models.
The proposed algorithm is applied to elastodynamics formulated over space-time domain with the Time Discontinuous Galerkin method in displacement and velocity.
Numerical examples demonstrate convergence of the proposed algorithm and comparisons are made with classical a posteriori and a priori approaches.


Keywords : Elastodynamics Separation of variables Proper orthogonal decomposition POD Proper generalized decomposition PGD Minimal residual Multi-field





Author: Lucas Boucinha - Amine Ammar - Anthony Gravouil - Anthony Nouy -

Source: https://hal.archives-ouvertes.fr/



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