A non-intrusive proper generalized decomposition scheme with application in biomechanics

Author (s): Zou, X.; Conti, M.; Díez, P. and Auricchio, F.
Journal: International Journal for Numerical Methods in Engineering

Volume: 113
Pages: 230 – 251
Date: 2018

Proper generalized decomposition (PGD) is often used for multi-query and fast-response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multi-parametric partial differential equations. Most implementations of PGD are intrusive extensions based on in-house developed finite element (FE) solvers. In this work, we propose a non-intrusive PGD scheme using off-the-shelf FE codes (such as certified commercial software) as an external solver. The scheme is implemented and monitored by in-house flow-control codes. A typical implementation is provided with downloadable codes. Moreover, a novel parametric separation strategy for the PGD resolution is presented. The parametric space is split into two- or three-dimensional subspaces, to allow PGD technique solving problems with constrained parametric spaces, achieving higher convergence ratio. Numerical examples are provided. In particular, a practical example in biomechanics is included, with potential application to patient-specific simulation.



@article {NME:NME5610,
author = {Zou, X. and Conti, M. and Díez, P. and Auricchio, F.},
title = {A nonintrusive proper generalized decomposition scheme with application in biomechanics},
journal = {International Journal for Numerical Methods in Engineering},
issn = {1097-0207},
url = {http://dx.doi.org/10.1002/nme.5610},
doi = {10.1002/nme.5610},
pages = {n/a--n/a},
keywords = {model order reduction, nonintrusive, proper generalized decomposition},
note = {nme.5610},