A Multigrid PGD-based Algorithm for Volumetric Displacement Fields Measurements

The use of a finite elements-based Digital Volume Correlation (FE-DVC) leads to lower measurement uncertainties in comparison to subset-based approaches. However, the associated computing time may become prohibitive when dealing with high-resolution measurements. To overcome this limitation, a Proper Generalised Decomposition solver was recently applied to 2D digital image correlation. In this paper, this method is extended to measure volumetric displacements from 3D digital images. In addition, a multigrid Proper Generalised Decomposition algorithm is developed, which allows to use different discretisations in each term of the decomposition. Associated to a coarse graining of the digital images, this allows to avoid local minima, especially in presence of large displacements. Synthetic and practical cases are analysed with the present approach, and measurement uncertainties are compared with standard FE-DVC. Results show that such an approach reduces the computational cost (when compared to FE-DVC) whilst maintaining lower measurement uncertainties than standard subset-based DVC.