A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
Nested grids ILU-decomposition (NGILU)
Proceedings of the 6th international congress on Computational and applied mathematics
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
Approximate Inverse Techniques for Block-Partitioned Matrices
SIAM Journal on Scientific Computing
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
SIAM Journal on Scientific Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Finding Exact and Approximate Block Structures for ILU Preconditioning
SIAM Journal on Scientific Computing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Robust and Efficient ILU that Incorporates the Growth of the Inverse Triangular Factors
SIAM Journal on Scientific Computing
Variations on algebraic recursive multilevel solvers (ARMS) for the solution of CFD problems
Applied Numerical Mathematics
An overview of SuperLU: Algorithms, implementation, and user interface
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Multilevel ILU With Reorderings for Diagonal Dominance
SIAM Journal on Scientific Computing
Multilevel Preconditioners Constructed From Inverse-Based ILUs
SIAM Journal on Scientific Computing
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
A domain-decomposing parallel sparse linear system solver
Journal of Computational and Applied Mathematics
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Sparse matrices arising from the solution of systems of partial differential equations often exhibit a perfect block structure, meaning that the nonzero blocks in the sparsity pattern are fully dense (and typically small), e.g., when several unknown quantities are associated with the same grid point. Similar block orderings can be sometimes unravelled also on general unstructured matrices, by ordering consecutively rows and columns with a similar sparsity pattern, and treating some zero entries of the reordered matrix as nonzero elements, with a little sacrifice of memory. We show how we can take advantage of these frequently occurring structures in the design of the multilevel incomplete LU factorization preconditioner ARMS (Saad and Suchomel, 2002 [14]) and maximize computational efficiency.