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.

中文翻译：

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XAMG：一个用于求解具有多个右侧向量的线性系统的库

本文介绍了XAMG库，用于求解带有多个右侧向量的线性方程组的大型稀疏系统。该库专门研究但不限于从椭圆型微分方程离散化获得的线性系统的解。一组相应的数值方法包括Krylov子空间，代数多重网格，Jacobi，Gauss-Seidel和Chebyshev迭代方法。并行化是通过MPI + POSIX共享内存混合编程模型实现的，该模型使用相应的每级同步和通信原语引入了三级分层分解。该代码包含许多优化，包括多级数据分段，索引压缩，混合精度浮点计算，向量状态标志等。XAMG库使用众所周知的hypre库的程序代码来构造多网格矩阵层次结构。XAMG在迭代方法的求解阶段自己实现，与进行测试的hypre相比，提速高达两倍。另外，XAMG提供扩展功能来求解具有多个右侧向量的系统。