PRECONDITIONING OF THE CONJUGATE GRADIENT METHOD BASED ON AGGREGATION ALGORITHM

Abstract eng:
Efficient solvers for large systems of algebraic equations are still in the center of attention because time devoted to the solution of such systems is the main part of computational time. This contribution deals with preconditioning of the conjugate gradient method by the aggregation method. The preconditioning described is useful especially for very ill-conditioned problems which lead to thousands of iterations. Unknowns are aggregated to non-overlapped aggregates and a smoothing procedure is used for generation of the overlap. Correction operators are defined and used for computation of the new residual in the conjugate gradient method. Several plate problems are solved and results are summarized at the end of this paper.

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