Parallel algebraic solvers library Krylov

Article describes functional capabilities and software implementation peculiarities of parallel algorithms library Krylov, which is oriented on the solution of large systems of linear algebraic equations with sparse symmetric and unsymmetric matrices (positive definite and semi-definite) obtained from discrete approximations of multidimensional boundary value problems for partial differential equations on unstructured meshes. The library includes two-level iterative methods in Krylov subspaces; preconditioning of the latter is based on the balanced decomposition of the computational domain with variable sizes of subdomain overlapping and different boundary conditions on interfacing boundaries. Program implementations use typical compressed sparse matrix data formats. Results of numerical experiments are presented which demonstrate the efficiency of parallelization for typical ill-conditioned problems.