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Parallel block preconditioning based on SSOR and MILU
Author(s) -
Washio Takumi,
Hayami Ken
Publication year - 1994
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680010603
Subject(s) - preconditioner , block (permutation group theory) , linear system , coefficient matrix , discretization , mathematics , parallel computing , convergence (economics) , iterative method , rate of convergence , matrix (chemical analysis) , computational science , algorithm , computer science , mathematical analysis , geometry , eigenvalues and eigenvectors , chemistry , key (lock) , physics , computer security , quantum mechanics , economics , economic growth , chromatography
Two kinds of parallel preconditioners for the solution of large sparse linear systems which arise from the 2‐D 5‐point finite difference discretization of a convection‐diffusion equation are introduced. The preconditioners are based on the SSOR or MILU preconditioners and can be implemented on parallel computers with distributed memories. One is the block preconditioner, in which the interface components of the coefficient matrix between blocks are ignored to attain parallelism in the forward‐backward substitutions. The other is the modified block preconditioner, in which the block preconditioner is modified by taking the interface components into account. The effect of these preconditioners on the convergence of preconditioned iterative methods and timing results on the parallel computer (Cenju) are presented.