Parallel Threshold-based ILU Factorization

Factorization algorithms based on threshold incomplete LU factorization have been found to be quite effective in preconditioning iterative system solvers. However, because these factorizations allow the fill elements to be created dynamically, they have been considered to be unsuitable for distributed-memory parallel computers. We present a highly parallel formulation of the ILUT(m, t) threshold-based incomplete factorization algorithm. ILUT employs a dual dropping strategy that is able to control the computational requirements during the factorization as well as during the application of the preconditioner. Our parallel ILUT algorithm utilizes parallel multilevel k-way partitioning and parallel independent set computation algorithms to effectively parallelize both the factorization as well as the application of the preconditioner.

[1]  D. P. Young,et al.  Application of sparse matrix solvers as effective preconditioners , 1989 .

[2]  Vipin Kumar,et al.  Parallel Multilevel k-way Partitioning Scheme for Irregular Graphs , 1996, Proceedings of the 1996 ACM/IEEE Conference on Supercomputing.

[3]  Mark T. Jones,et al.  Scalable Iterative Solution of Sparse Linear Systems , 1994, Parallel Comput..

[4]  Yousef Saad,et al.  Distributed ILU(0) and SOR Preconditioners for Unstructured Sparse Linear Systems , 1998 .

[5]  Vipin Kumar,et al.  Parallel Threshold-based ILU Factorization , 1997, SC.

[6]  Vipin Kumar,et al.  Highly Scalable Parallel Algorithms for Sparse Matrix Factorization , 1997, IEEE Trans. Parallel Distributed Syst..

[7]  O. Axelsson.  Iterative solution methods , 1995 .

[8]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[9]  Yousef Saad,et al.  ILUT: A dual threshold incomplete LU factorization , 1994, Numer. Linear Algebra Appl..

[10]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[11]  E. D'Azevedo,et al.  Towards a cost-effective ILU preconditioner with high level fill , 1992 .

[12]  A. Sameh,et al.  A parallel hybrid sparse linear system solver , 1990 .

[13]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[14]  C.R. Johnson,et al.  The effects of inhomogeneities and anisotropies on electrocardiographic fields: a three-dimensional finite element study , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.