Iterative solver for systems of linear equations with a sparse stiffness matrix on clusters

In this paper, a package of programs for solving systems of linear equations with a sparse matrix for computers with distributed memory is proposed. The package is based on an iterative algorithm for solving the initial system of equations with a preconditioner constructed using an algebraic domain decomposition. Such an approach makes it possible to simultaneously multiply the preconditioner and the stiffness matrix by a vector on a cluster. Also, to improve the efficiency of computation, the functionalities PARDISO and Sparse BLAS of the Intel®MKL library are used on each process. In addition to processes parallelization, the package uses OpenMP parallelization on each of these processes, as well as Intel®MKL internal functional parallelization.