Combination of numerical and structural approaches in the parallel first-order incomplete triangular decomposition preconditioning method

A parallel version of the method of incomplete triangular Cholesky decomposition of the first order of conjugate gradients is considered, which uses a reordering of the coefficient matrix corresponding to a reordering of grid nodes consistent with the partition of the calculation domain. The construction of an incomplete triangular decomposition is carried out with cutting off by value at the internal nodes of subdomains and by value and position on the separators during coarse-grained parallelization. . Sufficient conditions for failure-free performance of the conjugate gradient method with this preconditioner are obtained. Methods of using MPI and MPI+OpenMP technology in constructing and inverting a preconditioner are considered. The time taken to solve problems by the method under consideration using MPI and the hybrid MPI+OpenMP technology is compared using the example of the model problem and a number of problems from the SuiteSparse collection. The convergence rate of this method is compared with the convergence rate of other known methods using the example of solving test problems.