Development of Krylov and AMG linear solvers for large-scale sparse matrices on GPUs

SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods

Hybrid CPU-GPU algorithms for Algebraic Multigrid methods (AMG) to efficiently utilize both CPU and GPU resources are presented. In particular, hybrid AMG framework focusing on minimal utilization of GPU memory with performance on par with GPU-only implementations is developed. The hybrid AMG framework can be tuned to operate at a significantly lower GPU-memory, consequently, enables to solve large algebraic systems. Combining the hybrid AMG framework as a preconditioner with Krylov Subspace solvers like Conjugate Gradient, BiCG methods provides a solver stack to solve a large class of problem…

面向迭代线性求解器的基于多GPU聚合的AMG预处理器

Multi-GPU aggregation-based AMG preconditioner for iterative linear solvers

本研究提出并开源了一种基于混合MPI-CUDA环境、依托BootCMatchG库AMG预处理器的多GPU Krylov型稀疏线性求解器，通过优化通信开销兼顾单GPU效率，求解性能较Nvidia AmgX最高提升2倍。

JAX-AMG：一个用于JAX的GPU加速可微分稀疏线性求解器库

JAX-AMG: A GPU-Accelerated Differentiable Sparse Linear Solver Library for JAX

提出JAX-AMG，通过封装Nvidia AmgX求解器套件，为JAX生态提供GPU加速的代数多重网格求解器，支持自动微分、分布式多GPU执行，适用于PDE约束优化和反问题。

Two-Stage Gauss--Seidel Preconditioners and Smoothers for Krylov Solvers on a GPU cluster

Gauss-Seidel (GS) relaxation is often employed as a preconditioner for a Krylov solver or as a smoother for Algebraic Multigrid (AMG). However, the requisite sparse triangular solve is difficult to parallelize on many-core architectures such as graphics processing units (GPUs). In the present study, the performance of the traditional GS relaxation based on a triangular solve is compared with two-stage variants, replacing the direct triangular solve with a fixed number of inner Jacobi-Richardson (JR) iterations. When a small number of inner iterations is sufficient to maintain the Krylov conver…

Compressed Basis GMRES on High Performance GPUs

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in all current computer architectures, motivating the recent investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This paper introduces a new communication-reduction strategy for the (Krylov) GMRES solver that advocates f…

低马赫数Navier-Stokes压力求解器的ILU平滑器

ILU Smoothers for Low Mach Navier-Stokes Pressure Solvers

针对GPU上ILU平滑器直接三角求解慢的问题，提出通过行缩放降低非正规性并用Richardson迭代替代，显著提升了大规模并行GPU上压力求解器的计算速度和并行扩展性。