c © 2006 PIPS Comparative analysis of PCG solvers for voxel FEM systems

Abstract. The presented comparative analysis concerns two iterative solvers for large-scale linear systems related to µFEM simulation of human bones. The benchmark problems represent the strongly heterogeneous structure of real bone specimens. The voxel data are obtained by a high resolution computer tomography. Non-conforming Rannacher-Turek finite elements are used for discretization of the considered elliptic problem. It is well known that the preconditioned conjugate gradient method is the best tool for efficient solution of large-scale symmetric systems with sparse positive definite matrices. Here, the performance of two preconditioners is studied, namely the modified incomplete Cholesky factorization MIC(0) and the algebraic multigrid. The comparative analysis is mostly based on the computing times to run the sequential codes. The number of iterations for both preconditioners are also discussed. Numerical tests of a novel parallel MIC(0) code are given at the end. The obtained parallel speed-ups and efficiencies well illustrate the scope of efficient applications for real-life large-scale problems