Polynomial interpolation schemes for internal derivative distributions on structured grids
Applied Numerical Mathematics
A multigrid tutorial: second edition
A multigrid tutorial: second edition
Principles of computerized tomographic imaging
Principles of computerized tomographic imaging
Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts,Theory and Applications
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In this study a robust strategy for 3D-Volume Digital Image Correlation DIC is presented, apt to provide accurate kinematic measurements within a loaded sample on the basis of three-dimensional digital images by X-ray computed micro-tomography. In the framework of a Galerkin, finite element discretization of the displacement field, the inverse problem of estimating 3D motion inside the bulk material is solved recursively on a hierarchical family of grids, linked by suitable restriction and prolongation operators. Such structured grids are defined over an image pyramid, which is generated starting from the raw tomographic reconstructions by a reiterated application of average filters and sub-sampling operators. To achieve robust estimates of the underlying displacement fields, multi-grid cycles are performed ascending and descending along the pyramid in a selected sequence. At each scale, the least-square matching function for DIC is enriched by means of a penalty term in the spirit of Tychonoff regularization, including as a priori information the estimate achieved at the previous grid and transferred to the current scale. For each grid only one Newton iteration can be considered, implying important time savings. Results are presented concerning a laboratory X-ray micro-tomography experiment on a polymeric foam sample, subjected to loading by an apparatus ad-hoc realized.