|Title:|| A PARALLELIZABLE
PRECONDITIONER FOR THE SOLUTION OF SPARSE LINEAR SYSTEMS.
|Authors:|| Y. Shapira, A. Sidi and M. Israeli
An algebraic condition ensuring stability of the ILU (1,1) decomposition of sparse matrices is given. A stability and convergence theory for some multi-dimensional recursions that are relevant to the ILU preconditioning method for the solution of sparse linear systems is presented. Relying on this theory, a parallelizable truncated ILU (PTILU) preconditioning method is developed. Numerical experiments show that for grids of size up to 160 \times 160, with 8 \times 8 subdomains, the amount of arithmetic operations of PTILU is very similar to that of standard ILU, no more than 3 times larger when implemented as a modification of Row-Sum ILU (RSILU) and no more that twice larger when implemented as a modification of Alternating Direction Implicit (ADI) methods. In addition, PTILU is applicable as a smoother in multigrid methods.
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