Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models – Application to transient elastodynamics in space-time domain
dc.contributor.author
hal.structure.identifier | BOUCINHA, Lucas
|
dc.contributor.author
hal.structure.identifier | AMMAR, Amine
|
dc.contributor.author
hal.structure.identifier | GRAVOUIL, Anthony
|
dc.contributor.author
hal.structure.identifier | NOUY, Anthony
|
dc.date.accessioned | 2014 |
dc.date.available | 2014 |
dc.date.issued | 2014 |
dc.date.submitted | 2014 |
dc.identifier.issn | 0045-7825 |
dc.identifier.uri | http://hdl.handle.net/10985/8456 |
dc.description.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. |
dc.description.sponsorship | Agence Nationale de la Recherche Française (ANR-10-COSI-0006) |
dc.language.iso | en_US |
dc.publisher | Elsevier |
dc.rights | Post-print |
dc.subject | Elastodynamics |
dc.subject | Separation of variables |
dc.subject | Proper orthogonal decomposition (POD) |
dc.subject | Proper generalized decomposition (PGD) |
dc.subject | Minimal residual |
dc.subject | Multi-field |
dc.title | Ideal minimal residual-based proper generalized decomposition for non-symmetric multi-field models – Application to transient elastodynamics in space-time domain |
ensam.hal.submit | verify |
dc.identifier.doi | 10.1016/j.cma.2014.01.019 |
dc.typdoc | Article dans une revue avec comité de lecture |
dc.localisation | Centre de Angers |
dc.subject.hal | Sciences de l'ingénieur: Mécanique |
ensam.audience | Internationale |
ensam.page | 56-76 |
ensam.journal | Computer Methods in Applied Mechanics and Engineering |
ensam.volume | 273 |
hal.identifier | hal-01060940 |
hal.version | 1 |
hal.submission.permitted | updateMetadata |
hal.status | accept |