About one parallel version of the $2^{\text{nd}}$ order incomplete triangular factorization

One parallel version of the stabilized $2^{\text{nd}}$ order incomplete triangular factorization is considered as preconditioner for the conjugate gradient method. This parallel version is based on the reordering of the matrix used of certain domain decomposition type splitting with separators. The incomplete factorization is organized using the truncation of fill-in “by value” within the subdomains and “by position” and “by value” at the separators. Non-failure operation of the considered method is theoretically proved, non-failure operation and convergence speed of the parallel method are numerically investigated. For an MPI implementation of the iterative linear solver, numerical results are given obtained for matrices from the University of Florida collection.