Reference : A hyper-reduction method using adaptivity to cut the assembly costs of reduced order ...
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http://hdl.handle.net/10993/36557
A hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
English
Hale, Jack mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Schenone, Elisa []
Baroli, Davide mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Beex, Lars mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
2018
Submitted preprint
No
[en] hyper-reduction ; reduced order modelling ; model order reduction ; non-linear PDEs ; hyperelasticity ; FKPP
[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.
Researchers
http://hdl.handle.net/10993/36557
https://doi.org/10.6084/m9.figshare.5753292
FP7 ; 279578 - REALTCUT - Towards real time multiscale simulation of cutting in non-linear materials with applications to surgical simulation and computer guided surgery
FnR ; FNR6693582 > Jack Samuel Hale > ACCeSS > Advanced Computational Methods for the Simulation of Cutting in Surgery > 01/01/2014 > 31/12/2015 > 2013

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