Kaporin–Kon’shin’s method of parallel implementation of block preconditioners for asymmetric matrices in problems of filtration of a multicomponent mixture in a porous medium / K. Yu. Bogachev, Ya. V. Zhabitskii. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 46-52 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 44-50].

The ILU class preconditioners (ILU(0), ILU(1), ILUT) employed for iterative algorithms for nonsymmetrical linear sparse matrix systems are considered. Test matrices used in this study are originated from discretization of systems of partial differential equations describing multicomponent fluid flow in porous media. Novel parallel algorithm for block ILU factorization is suggested. This algorithm demonstrates a good convergence and significant speed-up in comparison with sequential algorithms. New integrated approach was tested on the wide range of matrices resulted from real hydrodynamic simulations of oil fields of Western Siberia and demonstrated significant reduction in computational time.

Key words: parallel block ILU factorization, sparse matrices, iterative algorithm, preconditioner.