ACCURACY AND EFFECTIVENESS OF PRECONDITIONED CONJUGATE-GRADIENT ALGORITHMS FOR LARGE AND ILL-CONDITIONED PROBLEMS

Different implementations of the preconditioned conjugate gradient method are presented for solving large and very ill-conditioned algebraic systems of equations resulting from the finite element method. A special implementation based on mixed precision calculations proved to be robust in performance and reliable in accuracy as well as storage effective. Additionally, a new type of iterative refinement scheme is introduced to improve the accuracy of direct methods based on conjugate gradient iterations; it is found to be a significant improvement on the standard iterative refinement approach.