Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Parallel Iterative Methods in Modern Physical Applications
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Robust Parallel ILU Preconditioning Techniques for Solving Large Sparse Matrices
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
The Korean Journal of Computational & Applied Mathematics
Applied Numerical Mathematics
A fully parallel block independent set algorithm for distributed sparse matrices
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
Multilevel block ILU preconditioner for sparse nonsymmetric M-matrices
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Using the parallel algebraic recursive multilevel solver in modern physical applications
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems
Applied Numerical Mathematics
Parallel Multilevel Sparse Approximate Inverse Preconditioners in Large Sparse Matrix Computations
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Distributed block independent set algorithms and parallel multilevel ILU preconditioners
Journal of Parallel and Distributed Computing
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Parallel FEM Software for CFD Problems
Informatica
Exploiting domain knowledge to optimize parallel computational mechanics codes
Proceedings of the 27th international ACM conference on International conference on supercomputing
VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems
Journal of Computational and Applied Mathematics
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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.