Multi-level Micro-Finite Element Analysis for Human Bone Structures

Topic

Using microarchitectural bone imaging, it is possible to assess both
the apparent density and the trabecular microstructure of intact bones
in a single measurement. In combination with microstructural finite
element (microFE) analysis this could provide a powerful tool to
improve strength assessment and individual fracture risk prediction.
However, the resulting microFE models are very large and require
dedicated solution techniques. So, in this paper we investigate the
efficient solution of the resulting large systems of linear equations
by the conjugate gradient algorithm with smoothed aggregation
multilevel preconditioning. We introduce a variant of smoothed
aggregation preconditioning in which the matrix of the finest level is
stored in an element-by-element fashion. In this way, a large fraction
of the overall storage requirement is saved. The implementation is
based on the Trilinos framework and, in particular, on the multilevel
solver package ML. We report on numerical results showing that our
approach leads to a fully parallel finite element solver.