CRII: SHF: ACI: Performance-in-Depth Sparse Solvers for Heterogeneous Parallel Platforms.

稀疏数值计算是许多科学和工程模拟的核心。然而，稀疏方法中复杂的不规则性限制了许多科学软件的性能。该项目集成了数学重新表述、算法重新设计和性能工程，以开发适用于异构型并行平台的高性能稀疏解算器。这项研究的结果是创新的工具和方法，推动了大规模科学模拟领域的发展。此外，该项目在培养研究生进行跨学科研究方面具有更广泛的影响。该项目对稀疏解算器中的性能瓶颈进行了深入的调查，并重新制定了它们的标准变体，以提供端到端的性能。开发跨层解决方案是为了改善数据局部性，减少通信，并增加稀疏线性求解器中的内在并行性。这些解决方案包括多级算法重构和性能调整，以显著提高稀疏计算的可扩展性和性能，同时保持其数值精度、收敛和稳定性。提出的方法和算法被实现为特定领域的高性能软件和基准测试套件，以促进所开发的算法和代码的迭代改进。

Sparse numerical computations are at the heart of many science and engineering simulations. However, the complex irregularities in sparse methods limit the performance of many scientific software. This project integrates mathematical reformulation, algorithm redesign, and performance engineering to develop high-performance sparse solvers for heterogeneous parallel platforms. The outcomes of this research are innovative tools and methodologies that advance the field of large-scale scientific simulations. In addition, the project has a broader impact in training graduate students to perform interdisciplinary research. The project conducts an in-depth investigation of performance bottlenecks in sparse solvers and reformulates their standard variants to deliver end-to-end performance. Cross-layer solutions are developed to improve data locality, reduce communication, and increase inherent parallelism in sparse linear solvers. The solutions involve multi-level algorithm restructuring and performance tuning to significantly improve the scalability and performance of sparse computations while preserving their numerical accuracy, convergence, and stability. The proposed methods and algorithms are implemented as domain-specific high-performance software and a benchmark suite to promote iterative improvements of the developed algorithms and codes.