A scalable multi‐level preconditioner for matrix‐free µ‐finite element analysis of human bone structures

Abstract

Abstract. The recent advances in microarchitectural bone imaging are disclosing the possibility to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. Coupling these imaging possibilities with microstructural finite element (µFE) analysis offers a powerful tool to improve bone stiffness and strength assessment for individual fracture risk prediction.Many elements are needed to accurately represent the intricate microarchitectural structure of bone; hence, the resulting µFE models possess a very large number of degrees of freedom. In order to be solved quickly and reliably on state-of-the-art parallel computers, the µFE analyses require advanced solution techniques. In this paper, we investigate the solution of the resulting systems of linear equations by the conjugate gradient algorithm, preconditioned by aggregation-based multigrid methods. We introduce a variant of the preconditioner that does not need assembling the system matrix but uses element-by-element techniques to build the multilevel hierarchy. The preconditioner exploits the voxel approach that is common in bone structure analysis, it has modest memory requirements, while being at the same time robust and scalable.Using the proposed methods, we have solved in less than 10 minutes a model of trabecular bone composed of 247'734'272 elements, leading to a matrix with 1'178'736'360 rows, using only 1024 CRAY XT3 processors. The ability to solve, for the first time, large biomedical problems with over 1 billion degrees of freedom on a routine basis will help us improve our understanding of the influence of densitometric, morphological and loading factors in the etiology of osteoporotic fractures such as commonly experienced at the hip, the spine and the wrist.

Parallel Performance Evaluation of MIC(0) Preconditioning Algorithm for Voxel μFE Simulation

“…[1,2]). Furthermore, the isotropic linear elasticity model considered here is a brick in the development of a generalized toolkit for µFE simulation of the bone micro-structure.…”

Alya: Computational Solid Mechanics for Supercomputers

“…However, if preconditioner optimization studies for large scale computing were tackled shortly after [49], and barring a few exceptions (e.g., Ref. [35] focusing on XFEM), they have almost always been focused on conventional FE codes (and often for one unique application) without consideration of all the previously listed evolutions [17,33,60,79]. In the particular case of FE for Solid Mechanics, many computer codes were written to solve one specific application and are not flexible enough to adapt the newest schemes and technological improvements.…”

Extreme scalability challenges in micro‐finite element simulations of human bone

“…Recently, we have devised a matrix-free variant of PCG that does not require building the system matrix but still is able to construct an aggregationbased AMG preconditioner [1]. The method is implemented in the software package ParFE 2 which is parallelized using MPI 3 and is based on the publicdomain object-oriented software framework Trilinos [5].…”