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

Abstract

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.