A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM
Parametric simulations of thermomechanical metal forming processes still remain computational costly and difficult due to inherent strong non-linearities. To this end, Reduced Order Models (ROMs) are introduced to decrease the computational time in large scale models and provide near-optimal solutio...
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doaj-7c560fa59edb4da2bb2fe7c4c3b6d55f2021-08-05T13:51:05ZengEDP SciencesMATEC Web of Conferences2261-236X2020-01-013180104310.1051/matecconf/202031801043matecconf_icmmen20_01043A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEMFriderikos OrestisOlive Marc0Baranger Emmanuel1Sagris Dimitrios2David Constantine N.3Université Paris-Saclay, ENS Paris-Saclay, CNRS, LMT Laboratoire de Mécanique et TechnologieUniversité Paris-Saclay, ENS Paris-Saclay, CNRS, LMT Laboratoire de Mécanique et TechnologieMechanical Engineering Department, Laboratory of Manufacturing Technology & Machine Tools, International Hellenic UniversityMechanical Engineering Department, Laboratory of Manufacturing Technology & Machine Tools, International Hellenic UniversityParametric simulations of thermomechanical metal forming processes still remain computational costly and difficult due to inherent strong non-linearities. To this end, Reduced Order Models (ROMs) are introduced to decrease the computational time in large scale models and provide near-optimal solutions in acceptable times. ROMs based on the Proper Orthogonal Decomposition (POD) are usually capable of accurately reproducing the dynamics of high-fidelity FEM simulations and offer the potential for near real-time analysis. However, ROMs are not robust with respect to parameter changes and must often be rebuilt for each parameter variation. This work aims to interpolate ROM POD basis associated with a limited number of training points on Grassmann manifolds, so as to obtain a robust ROM corresponding to a target parameter. A novel Space-Time (ST) POD basis interpolation, where the reduced spatial and time basis are separately interpolated on Grassmann manifolds, is proposed. Good correlations of the ROM ST models with respect to their associated high-fidelity FEM counterpart simulations are found. Hence, application of the ROM adaptation method for near real-time metal forming simulations using off-line computed ROM POD databases can be possible.https://www.matec-conferences.org/articles/matecconf/pdf/2020/14/matecconf_icmmen20_01043.pdf |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Friderikos Orestis Olive Marc Baranger Emmanuel Sagris Dimitrios David Constantine N. |
spellingShingle |
Friderikos Orestis Olive Marc Baranger Emmanuel Sagris Dimitrios David Constantine N. A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM MATEC Web of Conferences |
author_facet |
Friderikos Orestis Olive Marc Baranger Emmanuel Sagris Dimitrios David Constantine N. |
author_sort |
Friderikos Orestis |
title |
A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM |
title_short |
A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM |
title_full |
A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM |
title_fullStr |
A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM |
title_full_unstemmed |
A Space-Time POD Basis Interpolation on Grassmann Manifolds for Parametric Simulations of Rigid-Viscoplastic FEM |
title_sort |
space-time pod basis interpolation on grassmann manifolds for parametric simulations of rigid-viscoplastic fem |
publisher |
EDP Sciences |
series |
MATEC Web of Conferences |
issn |
2261-236X |
publishDate |
2020-01-01 |
description |
Parametric simulations of thermomechanical metal forming processes still remain computational costly and difficult due to inherent strong non-linearities. To this end, Reduced Order Models (ROMs) are introduced to decrease the computational time in large scale models and provide near-optimal solutions in acceptable times. ROMs based on the Proper Orthogonal Decomposition (POD) are usually capable of accurately reproducing the dynamics of high-fidelity FEM simulations and offer the potential for near real-time analysis. However, ROMs are not robust with respect to parameter changes and must often be rebuilt for each parameter variation. This work aims to interpolate ROM POD basis associated with a limited number of training points on Grassmann manifolds, so as to obtain a robust ROM corresponding to a target parameter. A novel Space-Time (ST) POD basis interpolation, where the reduced spatial and time basis are separately interpolated on Grassmann manifolds, is proposed. Good correlations of the ROM ST models with respect to their associated high-fidelity FEM counterpart simulations are found. Hence, application of the ROM adaptation method for near real-time metal forming simulations using off-line computed ROM POD databases can be possible. |
url |
https://www.matec-conferences.org/articles/matecconf/pdf/2020/14/matecconf_icmmen20_01043.pdf |
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