高阶稀疏矩阵向量乘的可扩展异构并行算法及其在电磁计算中的应用

Sparse matrix and vector multiplication(SpMV) is a fundamental problem in integral and differential methods of computational electromagnetics. Some tens of billions scale sparse matrices will be produced in large and complex electromagnetic scattering calculation process, and these sparse matrixes have irregularity which contains some isolated points, and the size has been reached billions result to new challenges of scalability for high performance computing. CPU/GPU-based parallel computing for normal SpMV is at a preliminary stage, while the research of unnnormal SpMV on the large scale heterogeneous parallel supercomputer is little and not enough. Nevertheless, the heterogenous parallel supercomputer is one of development trend for high performance computing area. To solve them in electromagnetic scattering calculation process, Some algorithmes for SpMV simply sacrifice certain accuracy in order to ensure the performance of the calculation.However, the results in such way are often not suit for the parctical inviroment. To take full advantage of the parallel computing power of thousands of heterogeneous compute nodes, it has great significance to research the efficient and scalable parallel algorithms and programs for more than billions scale SpMV in electromagnetic scattering computing based on the domestic large-scale heterogeneous Supercomputer platform. According to CPU/GPU/MIC heterogeneous computing features and available computing resources type, this project intends to carry out deep investigation work in blocked and compressed storage algorithm of sparse matrix, the computing tasks segmentation and the mapping strateges between the tasks and the computational resources, collaborative programming and compiling techniches, and the performance optimization methods for unnormal SpMV on heterogeneous Supercomputer platform, etc,. This study will explore large-scale heterogeneous parallel processing technology for SpMV which is a basic computational module in numerical computation, and thus it will has considerable significance to electromagnetism field and other engineering fields.

稀疏矩阵与向量的乘积（SpMV）是工程与科学计算的七个共性基础模块之一,也高性能计算重要应用领域电磁计算积分和微分法中的基础问题,复杂电磁场散射应用计算过程中产生的稀疏矩阵,不仅因不规则场导致矩阵中具有多孤立点不规则性,且规模已达数百亿量级,对高性能计算的可扩展性提出了新挑战。尽管规则SpMV基于CPU或GPU并行计算成果较丰，但少见对SpMV在近来不断涌现的P级异构超算上的协同并行研究.鉴此，本项目以电磁散射应用中百亿阶以上SpMV基于国产异构超算平台的可扩展并行算法为研究目标,拟研究不规则稀疏矩阵针对可用CPU/GPU/MIC异构结构的分块、压缩存储算法、计算任务的分割和映射，及其在异构超算平台的并行协同编程、编译以及算法性能优化技术,解决不规则SpMV并行负载不均衡、难协同计算等技术问题。本项目将不仅对SpMV的大规模异构并行处理技术展开研究，还将实践理论成果在电磁计算中的应用.

项目资助期间，立足于高性能异构并行计算的研究前沿，充分利用并行计算、并行调度、异构计算算等理论和技术成果，侧重于新理论、新技术和新方法的研究，采用理论和实验相结合的方式，针对来源于电磁计算应用的稀疏矩阵及稀疏矩阵向量乘算法在异构计算环境中的资源分配及数据存取过程，完成了稀疏矩阵稀疏模式及其压缩格式、异构环境中的 SpMV 协同编程技术、稀疏矩阵向量乘（SpMV）异构并行算法、面向CPU-GPU异构编程框架和任务调度及访问控制模型的建立等基础性研究工作；发表学术论文24篇，其中 IEEE/ACM Transactions 论文7篇，被 SCI 收录23篇，申请国家发明专利1项。