稀疏矩阵向量乘和稀疏矩阵-稀疏矩阵乘是稀疏线性方程组求解过程中频繁调用的计算内核，也是其主要的性能瓶颈。已有按行列分块的稀疏矩阵划分方式没有充分考虑稀疏矩阵中非零元素的数据分布特征，无法最大化利用异构计算平台的体系架构优势提升稀疏矩阵相关计算效率。本课题对大规模稀疏矩阵的划分及相关计算优化进行研究，拟提出一种基于形态学的稀疏矩阵划分方法，首先将稀疏矩阵转为二值图像，采用数学形态学方法将稀疏矩阵划分为非零元素分布形状明确、数据分布特征显著的多个子矩阵，并根据子矩阵数据分布和各计算设备体系架构特点，为稀疏子矩阵选择适合的稀疏编码格式和计算设备。针对SpMV和SpGEMM两种计算内核，设计面向异构计算平台的任务映射算法和负载均衡算法，最后使用典型算法应用对所提出方法进行验证。本课的研究成果能够显著提高稀疏线性方程组在异构计算平台上的求解效率，具有较高的理论价值和实际应用价值。

Sparse matrix vector multiplication and sparse matrix-sparse matrix multiplication are the common computational kernels for solving sparse linear equations, and also the main performance bottlenecks. The existing method of partitioning sparse matrices into rows and columns does not fully consider the data distribution characteristics of non-zero elements in sparse matrices, and can not make full use of the architecture advantages of heterogeneous computing platforms to improve the efficiency of sparse matrix-related computing. In this project, we study the partition of large-scale sparse matrices and the optimization of related computation. We propose a partition method of sparse matrices based on morphology. Firstly, we transform sparse matrices into binary images. By using mathematical morphology, we divide sparse matrices into several sub-matrices with clear shape of non-zero elements and prominent characteristics of data distribution, select suitable sparse encoding format and computing equipment for sparse sub-matrix. Aiming at the two computing kernels of SpMV and SpGEMM, task mapping algorithm and load balancing algorithm for heterogeneous computing platform are designed. Finally, typical algorithm and applications are used to verify the proposed algorithm. The research results of this project can significantly improve the efficiency of solving sparse linear equations on heterogeneous computing platforms. It has high theoretical value and practical application value.