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—In this paper, we study a class of modified incomplete Cholesky factorization preconditioners LL, with two control parame- ters including dropping rules. Before computing preconditioners, the modified incomplete Cholesky factorization algorithm allows to decide the sparsity of incomplete factorization preconditioners by two fill- in control parameters: (1) p, the number of the largest number p of nonzero entries in each row; (2) dropping tolerance. With RCM re- ordering scheme as a crucial operation for incomplete factorization preconditioners, our numerical results show that both the number of PCOCG and PCG iterations and the total computing time are re- duced evidently for appropriate fill-in control parameters. Numerical tests on harmonic analysis for 2D and 3D scattering problems show the efficiency of our method.

MODIFIED INCOMPLETE CHOLESKY FACTORIZATION FOR SOLVING ELECTROMAGNETIC SCATTERING PROBLEMS