Application of Algebraic Multigrid to Large Scale Bone Modeling Problems

Mark F. Adams

Computational Sciences,
Computer Sciences and Mathematics
Sandia National Laboratories
MS 9217 Livermore, CA 94551


Abstract

Trabecular bone is the primary load bearing biological tissue in the spine and in the hip, and has a very complicated structure with over 80% porosity. A common method to determine the structural properties of trabecular bone is to use 3D digital images obtained from micro computed tomography to construct a finite element (FE) mesh of voxel elements. These voxel meshes have the advantage of being able to capture complex geometries but require many elements to accurately model the mechanics. For example, a convergent linear analysis of one human vertebral body requires over 23 million elements. This talk will discuss some of the first applications using highly scalable FE methods with highly scalable linear solver algorithms in whole vertebral body structural analysis. We analyze the performance of our parallel FE code Athena (built on a serial research FE code FEAP) and our implementation of a smoothed aggregation multigrid method, in the linear solver package Prometheus, on problems with over 100 million degrees of freedom on IBM SP parallel computers.