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.
