A scalable memory efficient multigrid solver for micro-finite element analyses based on CT images

Micro-structural finite element (μFE) analysis based on high-resolution computed tomography represents the current gold standard to predict bone stiffness and strength. Recent progress in solver technology makes possible simulations on large supercomputers that involve billions of degrees of freedom.In this paper we present an improved solver that has a significantly smaller memory footprint compared to the currently used solvers. This new approach fully exploits the information that is contained in the underlying CT image itself. It admits to execute all steps in the underlying multigrid-preconditioned conjugate gradient algorithm in matrix-free form.The reduced memory footprint allows to solve bigger bone models on a given hardware. It is an important step forward to the clinical usage of μFE simulations.The new solver is fully parallel. We show almost perfect scalability up to 8000 cores of a Cray XT-5 supercomputer.

► Micro-structural finite element analysis is the state of the art in predicting bone stiffness and strength.
► Voxel-based approach avoids building element-to-node table and stiffness matrix.
► Conjugate gradient algorithm with matrix-free geometric multigrid preconditioner.
► Problem size of 17 bio degrees of freedom exceeds the previous maximum by 1 order of magnitude.