The International Conference on Computational Mathematics
ICCM-2004


Abstracts


Computational algebra

A new variant of incomplete factorization method to solve three dimensional elliptical difference equations with nonsymmetrical coefficient matrices

Ginkin V.P., O.M.Naumenko

SSC RF Institute for Power and Physics Engineering (Obninsk)

A new variant of NIF incomplete factorization method to solve three dimensional elliptical difference equations with nonsymmetrical coefficient matrices has been developed. Results are presented of testing the method numerically for convergence, the combined incomplete factorization method CIF interleaving NIF and HF [1] methods at the same time changing the direction of calculation. In this case high efficiency of the convergence acceleration is shown by numerical experiments to be reached in comparison with each individual schemes considered. As is seen from considered examples in symmetrical case the CIF procedure has a less number of iterations than the conjugate gradient method with an incomplete factorization preconditioner (the CGPIF procedure [2]). In nonsymmetrical case the rate of convergence is increasing with an absolute value of nonsymmetrical terms of equations.

References

[1] Ginkin V.P. Method of h-factorization to solve 2d-elliptical equations. In book Computational methods of a linear algebra, Novosibirsk, 1977, p.123-132.

[2] Ginkin V.P., Kulik A.V., Naumenko O.M. An efficient preconditioning procedure in the conjugate gradient method for 3D HEX-Z geometry. Proceedings of the forth international conference on supercomputing in nuclear computations (SNA 2000), Tokyo, Japan, 2000.

Note. Abstracts are published in author's edition


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