Journal of Computational and Applied Mathematics
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
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
Distributed block independent set algorithms and parallel multilevel ILU preconditioners
Journal of Parallel and Distributed Computing
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Journal of Computational Physics
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems
Journal of Computational and Applied Mathematics
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We introduce block versions of the multielimination incomplete LU (ILUM) factorization preconditioning technique for solving general sparse unstructured linear systems. These preconditioners have a multilevel structure and, for certain types of problems, may exhibit properties that are typically enjoyed by multigrid methods. Several heuristic strategies for forming blocks of independent sets are introduced and their relative merits are discussed. The advantages of block ILUM over point ILUM include increased robustness and efficiency. We compare several versions of the block ILUM, point ILUM, and the dual-threshold-based ILUT preconditioners. In particular, tests with some convection-diffusion problems show that it may be possible to obtain convergence that is nearly independent of the Reynolds number as well as of the grid size.