天然地震走时反演矩阵顺序三角化算法的优化和并行化

The optimization and parallelization of sequential orthogonal triangularization algorithms used in seismic tomography

本文讨论了用于天然地震层析成像的矩阵顺序三角化算法,揭示了偏导数矩阵中非零元素的分布规律,在分析算法特点的基础上提出了对程序的几点优化措施,包括:采用合理的存储结构和计算次序以节省内存寻址时间;以一个一维数组存储上三角方阵以节省出一半的内存;对关键的Givens变换子程序进行优化和矢量化等,最终使程序的运行效率提高了数十倍.同时结合算法特点研究了矩阵顺序三角化的并行化方法,提出了两种并行化方案,在联想深腾6800超级计算机上实现了这两种并行算法;对计算量均衡等问题进行了讨论.

This paper addresses the sequential orthogonal triangularization （SOT） algorithms used in seismic tomography. We reveal the distribution feature of none-zero values in partial derivative matrix. Several measures about data structure, computational sequences and vectorization are presented, these measures make the speed increased by tens of times. Two set of parallelization designs for the SOT algorithms are also presented and tested.