 
Summary: APPLICATIONS OF ALGEBRAIC MULTIGRID TO LARGESCALE FINITE ELEMENT
ANALYSIS OF WHOLE BONE MICROMECHANICS ON THE IBM SP
MARK F. ADAMS 1 , HARUN H. BAYRAKTAR 2,3,5 , AND TONY M. KEAVENY 2,3,4
PANAYIOTIS PAPADOPOULOS 3,5
Abstract. Accurate microfinite element analyses of whole bone require the solution of large sets of algebraic equations.
Multigrid has proven to be an e#ective approach to the design of highly scalable linear solvers for solid mechanics problems.
We present some of the first applications of scalable linear solvers, on massively parallel computers, to whole vertebral body
structural analysis. We analyze the performance of our algebraic multigrid (AMG) methods on problems with over 237 million
degrees of freedom on IBM SP parallel computers. We demonstrate excellent parallel scalability, both in the algorithms and
the implementations, and analyze the nodal performance of the important AMG kernels on the IBM Power3 and Power4
architectures.
Key words. multigrid, trabecular bone, human vertebral body, finite element method, massively parallel computing.
1. Introduction. This paper presents applications of optimal linear solver methods to largescale tra
becular bone finite element (FE) modeling problems on massively parallel computers. Trabecular bone is the
primary loadbearing biological structure in the human spine as well as at the end of long bones such as the
femur. It has a very complicated structure with typical porosity values exceeding 80% in most anatomic sites.
A common method to study the structural properties of trabecular bone is to use specimenspecific high
resolution finite element models obtained from 3D microcomputed tomography (microCT) images (Figure
1.1). This process converts image voxels into a finite element mesh of hexahedral elements. These voxel
meshes have the advantage of being able to capture complex geometries intrinsically but require many ele
