Article (Scientific journals)
A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
Hale, Jack; Schenone, Elisa; Baroli, Davide et al.
2021In Computer Methods in Applied Mechanics and Engineering, 380, p. 113723
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(c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).


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Keywords :
hyper-reduction; reduced order modelling; model order reduction; non-linear PDEs; hyperelasticity; FKPP
Abstract :
[en] At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material.
Disciplines :
Mathematics
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Hale, Jack  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Schenone, Elisa
Baroli, Davide ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Beex, Lars ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Bordas, Stéphane ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
External co-authors :
yes
Language :
English
Title :
A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
Publication date :
01 July 2021
Journal title :
Computer Methods in Applied Mechanics and Engineering
ISSN :
1879-2138
Publisher :
Elsevier, Amsterdam, Netherlands
Volume :
380
Pages :
113723
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
European Projects :
FP7 - 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
FnR Project :
FNR6693582 - Advanced Computational Methods For The Simulation Of Cutting In Surgery, 2013 (01/01/2014-31/12/2015) - Jack Samuel Hale
Funders :
CE - Commission Européenne [BE]
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