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

TL;DR

XAMG is a high-performance library for solving large sparse linear systems with multiple right-hand sides, offering significant speedups and extended functionality over existing solutions like hypre.

Contribution

The paper introduces XAMG, a new library that enhances solving efficiency for systems with multiple right-hand sides using advanced parallelization and optimization techniques.

Findings

XAMG achieves up to twofold speedup over hypre.

The library effectively handles multiple right-hand side vectors.

Optimizations improve performance in solving large sparse systems.

Abstract

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.