Numerical performance of preconditioning techniques for the solution of complex sparse linear systems

Preconditioning techniques based on ILU decomposition, on Frobenius norm minimization and on factorized sparse approximate inverse are considered. These algorithms are applied with conjugate gradient-type methods, namely Bi-CGSTAB, QMR and TFQMR for the solution of complex, large, sparse linear systems. The results of numerical experiments in scalar environment with matrices arising from transport in porous media, quantum chemistry, structural dynamics and electromagnetism are analysed. The preconditioner that appears most significant in parallel environment (based on factorized sparse approximate inverse) is then employed on a Cray T3E supercomputer. The experimental results show the satisfactory parallel performance of the proposed algorithm.