On a Parallel Version of a Second-Order Incomplete Triangular Factorization Method

Abstract

We consider a parallel version of the stabilized second-order incomplete triangular factorization–conjugate gradient method in which the reordering of the coefficient matrix that corresponds to the ordering based on splitting into subdomains with separators is used. The incomplete triangular factorization is constructed using the truncation of the fill-in chosen “by value” at the internal nodes of the subdomains and “by value” and ‘by positions” on the separators. The reliability of the method under consideration is theoretically proved. The reliability and convergence rate of the parallel method are numerically analyzed. The developed algorithms are implemented using a Message Passing Interface (MPI); the computational results are presented for benchmark problems with matrices from the collection of the University of Florida.