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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Main Authors: Friderikos Orestis, Olive Marc, Baranger Emmanuel, Sagris Dimitrios, David Constantine N.
Format: Article
Language:English
Published: EDP Sciences 2020-01-01
Series:MATEC Web of Conferences
Online Access:https://www.matec-conferences.org/articles/matecconf/pdf/2020/14/matecconf_icmmen20_01043.pdf
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spelling 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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