A scalable multi-level preconditioner for matrix-free µ-finite element analysis of human bone structures
Open access
Date
2011Type
- Report
ETH Bibliography
yes
Altmetrics
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. Show more
Permanent link
https://doi.org/10.3929/ethz-a-006784136Publication status
publishedJournal / series
Technical Report / ETH Zurich, Department of Computer ScienceVolume
Publisher
ETH, Department of Computer ScienceSubject
Matrix-Free Preconditioning; KNOCHEN, SKELETT, OSTEOLOGIE (ANATOMIE UND PHYSIOLOGIE); OBJEKTMODELLIERUNG (COMPUTERGRAFIK); Algebraic Multigrid; OBJECT MODELLING (COMPUTER GRAPHICS); BONES, SKELETON, OSTEOLOGY (ANATOMY AND PHYSIOLOGY); Micro Finite Element Analysis; FINITE-ELEMENTE-METHODE (NUMERISCHE MATHEMATIK); FINITE ELEMENT METHOD (NUMERICAL MATHEMATICS); Aggregation MethodsOrganisational unit
02150 - Dep. Informatik / Dep. of Computer Science
Notes
Technical Reports D-INFK.More
Show all metadata
ETH Bibliography
yes
Altmetrics