Distributed block independent set algorithms and parallel multilevel ILU preconditioners

Authors:
Chi Shen;Jun Zhang;Kai Wang
Affiliations:
Department of Computer Science, Laboratory for High Performance Scientific Computing and Computer Simulation, University of Kentucky, 773 Anderson Hall, Lexington, KY 40506-0046, USA;Department of Computer Science, Laboratory for High Performance Scientific Computing and Computer Simulation, University of Kentucky, 773 Anderson Hall, Lexington, KY 40506-0046, USA;Department of Computer Science, Laboratory for High Performance Scientific Computing and Computer Simulation, University of Kentucky, 773 Anderson Hall, Lexington, KY 40506-0046, USA
Venue:
Journal of Parallel and Distributed Computing
Year:
2005

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Abstract

We present a class of parallel preconditioning strategies utilizing multilevel block incomplete LU (ILU) factorization techniques to solve large sparse linear systems. The preconditioners are constructed by exploiting the concept of block independent sets (BISs). Two algorithms for constructing BISs of a sparse matrix in a distributed environment are proposed. We compare a few implementations of the parallel multilevel ILU preconditioners with different BIS construction strategies and different Schur complement preconditioning strategies. We also use some diagonal thresholding and perturbation strategies for the BIS construction and for the last level Schur complement ILU factorization. Numerical experiments indicate that our domain-based parallel multilevel block ILU preconditioners are robust and efficient.