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