TY - JOUR
T1 - A multilevel dual reordering strategy for robust incomplete LU factorization of indefinite matrices
AU - Zhang, Jun
PY - 2000/10
Y1 - 2000/10
N2 - A dual reordering strategy based on both threshold and graph reorderings is introduced to construct robust incomplete LU (ILU) factorization of indefinite matrices. The ILU matrix is constructed as a preconditioner for the original matrix to be used in a preconditioned iterative scheme. The matrix is first divided into two parts according to a threshold parameter to control diagonal dominance. The first part with large diagonal dominance is reordered using a graph-based strategy, followed by an ILU factorization. A partial ILU factorization is applied to the second part to yield an approximate Schur complement matrix. The whole process is repeated on the Schur complement matrix and continues for a few times to yield a multilevel ILU factorization. Analyses are conducted to show how the Schur complement approach removes small diagonal elements of indefinite matrices and how the stability of the LU factor affects the quality of the preconditioner. Numerical results are used to compare the new preconditioning strategy with two popular ILU preconditioning techniques and a multilevel block ILU threshold preconditioner.
AB - A dual reordering strategy based on both threshold and graph reorderings is introduced to construct robust incomplete LU (ILU) factorization of indefinite matrices. The ILU matrix is constructed as a preconditioner for the original matrix to be used in a preconditioned iterative scheme. The matrix is first divided into two parts according to a threshold parameter to control diagonal dominance. The first part with large diagonal dominance is reordered using a graph-based strategy, followed by an ILU factorization. A partial ILU factorization is applied to the second part to yield an approximate Schur complement matrix. The whole process is repeated on the Schur complement matrix and continues for a few times to yield a multilevel ILU factorization. Analyses are conducted to show how the Schur complement approach removes small diagonal elements of indefinite matrices and how the stability of the LU factor affects the quality of the preconditioner. Numerical results are used to compare the new preconditioning strategy with two popular ILU preconditioning techniques and a multilevel block ILU threshold preconditioner.
KW - Incomplete LU factorization
KW - Multilevel incomplete LU preconditioner
KW - Reordering strategies
KW - Sparse matrices
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U2 - 10.1137/S0895479899354251
DO - 10.1137/S0895479899354251
M3 - Article
AN - SCOPUS:0035219260
SN - 0895-4798
VL - 22
SP - 925
EP - 947
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 3
ER -