FILU: An efficient incomplete LU preconditioner. Preconditioned iterative methods provide some of the most efficient approaches for solving general, large sparse linear systems arising in many scientific and engineering applications. It is well-known that the convergence rate of an iterative solver depends strongly on the quality of the preconditioner used. Incomplete LU factorization is one of the most popular preconditioning techniques for unsymmetric linear systems. We present a fill-in incomplete LU (FILU) preconditioner which includes two drop tolerance parameters, a fill-in threshold parameter, a strip tolerance parameter, a relaxation parameter, and a set of row norms. The first drop tolerance parameter is used for dropping only new entries, which extends the original matrix pattern. The second drop tolerance parameter is used for dropping entries from a preconditioned row. The fill-in threshold parameter is used to limit the number of nonzero entries in a preconditioned row. The strip tolerance parameter is used for dropping small entries from the original row before preconditioning. The relaxation parameter is a coefficient for subtracting a sum of all dropped entries from the diagonal entry of the corresponding row. Finally, we develop special row norms different for the $L$ and $U$ parts of a preconditioned row. This extended set of dropping criteria with a special row norm allows us to obtain a preconditioner with a good balance between the quality of LU factorization and the extension ratio of the original pattern. In combination with scalings and reorderings this preconditioner shows good results for problems arising in hydrocarbon reservoir simulation. The performance of the preconditioner is illustrated by numerical experiments on a set of test linear systems and compared with that of several freely available software packages.
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- Pravilnikov, V.Y.; Diyankov, O.V.; Kotegov, S.S.; Koshelev, S.V.; Krasnogorov, I.V.; Kuznetsova, N.N.: FILU: An efficient incomplete LU preconditioner (2007)