Iterative methods for solving sparse linear systems with a parallel preconditioner

Abstract

The incomplete LU factorization is one of the more effective preconditioner of the conjugate gradient-type methods in connection with the solution of large, sparse systems of linear equations. In this paper, the results obtained with the use of the level scheduling method are shown. In view of the sparsity, it is possible to reorder the rows and columns of the coefficient matrix in order to obtain a block triangular system (lower and upper) so that groups of unknowns can be solved in parallel. The size of the test problems ranges from 500 to 4500. The speedup obtained is up to 2. 5 for the solution of both the symmetric and nonsymmetric systems on a CRAY Y-MP8/432 (with 4 processors).

Keywords:

• Linear systems
• iterative projection methods
• parallel algorithms
• supercomputers

C.R. CATEGORIES::

• G.1.3.