XAMG: A library for solving linear systems with multiple right-hand side vectors

This paper presents the XAMG library for solving large sparse systems of linear algebraic equations with multiple right-hand side vectors. The specializes but is not limited to solution obtained from discretization elliptic differential equations. A corresponding set numerical methods includes Krylov subspace, multigrid, Jacobi, Gauss-Seidel, and Chebyshev iterative methods. parallelization implemented MPI+POSIX shared memory hybrid programming model, which introduces a three-level hierarchical decomposition using per-level synchronization communication primitives. code contains number optimizations, including multilevel data segmentation, compression indices, mixed-precision floating-point calculations, vector status flags, others. uses program well-known hypre construct multigrid matrix hierarchy. XAMG's own implementation solve phase provides up twofold speedup compared tests performed. Additionally, extended functionality