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1 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

1 2007

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Preconditioning of voxel FEM elliptic systems

Margenov S., Vutov Y.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2007

Vol. 11, No 1-2

117-128

The presented comparative analysis concerns two iterative solvers for large-scale linear systems related to žFEM simulation of human bones. The considered scalar elliptic problems represent the strongly heterogeneous structure of real bone specimens. The voxel data are obtained with high resolution computer tomography. Non-conforming Rannacher-Turek finite elements are used to discretize of the considered elliptic problem. The preconditioned conjugate gradient method is known to be 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 modified incomplete Cholesky factorization, MIC(0), and algebraic multigrid. The comparative analysis is mostly based on the computing times to run the sequential codes. The number of iterations for both preconditioners is also discussed. Finally, numerical tests of a novel parallel MIC(0) code are presented. The obtained parallel speed-ups and efficiencies illustrate the scope of efficient applications for real-life large-scale problems.