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

Abstract

This is the peer reviewed version of the following article: Zou, X., Conti, M., Diez, P., Auricchio, F. A non-intrusive proper generalized decomposition scheme with application in biomechanics. "International journal for numerical methods in engineering", 7 Setembre 2017., which has been published in final form at http://dx.doi.org/10.1002/nme.5610. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Proper generalized decomposition (PGD) is often used for multiquery and fast-response simulations. It is a powerful tool alleviating the curse of dimensionality affecting multiparametric partial differential equations. Most implementations of PGD are intrusive extensions based on in-house developed FE solvers. In this work, we propose a nonintrusive 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.Peer ReviewedPostprint (author's final draft