Author(s) :
Matthias Bollhoefer
,
Yousef Saad
The paper is published :
SIAM Journal on Scientific Computing 27 (5), 1627-1650, 2006
MSC 2000
- 65F05 Direct methods for linear systems and matrix inversion
-
65F10 Iterative methods for linear systems
-
65F50 Sparse matrices
-
65Y05 Parallel computation
Abstract :
This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few of strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the Incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. As a consequence a few strategies are developed whose goal is to achieve this feature. A number of ``templates'' for enabling implementations of these factorizations are presented. Numerical experiments show that the resulting ILUs offer a good compromise between robustness and efficiency.
Keywords :
incomplete LU-decompositions, ILU, preconditioning, multilevel ILU, approximate inverse, algebraic multilevel method, iterative solver