Parallel methods for SLAE solution on the systems with distributed memory in Krylov library

The paper presents an approach to creation of black-box parallel iterative solver, which is used in Krylov library for solving systems of linear algebraic equations (SLAEs) with large sparse matrices in CSR format arising from discretization of multidimensional boundary value problems. A variant of one-dimensional algebraic decomposition method is offered. The algorithm is based on breadth-first search of SLAE’s adjacency graph that allows to reduce the matrix to block-tridiagonal form. The algebraic solver is based on additive Schwarz method which naturally suits distributed memory computer systems. The generalized minimal residual method is used to solve the SLAEs arising from relations on subdomains’ boundaries. Auxiliary subdomain systems are solved with Intel MKL’s multithreaded direct solver PARDISO. Implemented algorithms were tested on the numerical solution of the series of computational mathematics problems, such as problems of hydrodynamics, diffusion-convection equations, problems of electromagnetism and others. Adduced numerical experiments results show the effectiveness of the presented algorithms for multiprocessor computational systems with distributed memory.