TY - JOUR
T1 - BILUTM
T2 - A domain-based multilevel block ILUT preconditioner for general sparse matrices
AU - Saad, Yousef
AU - Zhang, Jun
PY - 1999
Y1 - 1999
N2 - This paper describes a domain-based multilevel block ILU preconditioner (BILUTM) for solving general sparse linear systems. This preconditioner combines a high accuracy incomplete LU factorization with an algebraic multilevel recursive reduction. Thus, in the first level the matrix is permuted into a block form using (block) independent set ordering and an ILUT factorization for the reordered matrix is performed. The reduced system is the approximate Schur complement associated with the partitioning, and it is obtained implicitly as a by-product of the partial ILUT factorization with respect to the complement of the independent set. The incomplete factorization process is repeated with the reduced systems recursively. The last reduced system is factored approximately using ILUT again. The successive reduced systems are not stored. This implementation is efficient in controlling the fill-in elements during the multilevel block ILU factorization, especially when large size blocks are used in domain decomposition-type implementations. Numerical experiments are used to show the robustness and efficiency of the proposed technique for solving some difficult problems.
AB - This paper describes a domain-based multilevel block ILU preconditioner (BILUTM) for solving general sparse linear systems. This preconditioner combines a high accuracy incomplete LU factorization with an algebraic multilevel recursive reduction. Thus, in the first level the matrix is permuted into a block form using (block) independent set ordering and an ILUT factorization for the reordered matrix is performed. The reduced system is the approximate Schur complement associated with the partitioning, and it is obtained implicitly as a by-product of the partial ILUT factorization with respect to the complement of the independent set. The incomplete factorization process is repeated with the reduced systems recursively. The last reduced system is factored approximately using ILUT again. The successive reduced systems are not stored. This implementation is efficient in controlling the fill-in elements during the multilevel block ILU factorization, especially when large size blocks are used in domain decomposition-type implementations. Numerical experiments are used to show the robustness and efficiency of the proposed technique for solving some difficult problems.
KW - ILUT
KW - Incomplete LU factorization
KW - Krylov subspace methods
KW - Multielimination ILU factorization
KW - Multilevel ILU preconditioner
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U2 - 10.1137/S0895479898341268
DO - 10.1137/S0895479898341268
M3 - Article
AN - SCOPUS:0033233446
SN - 0895-4798
VL - 21
SP - 279
EP - 299
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
IS - 1
ER -