基于压缩存储技术求解压力Poisson方程的BiCGSTAB算法

摘要

This paper presented a numerical analysis method for one-dimensional sparse storage structures to compress the large sparse matrix formed by the numerical discrete of the pressure Poisson equation with the numerical discrete projection algorithm,and only stored the non-zero elements.At the same time,it used the BiCGSTAB algorithm with optimized properties to solve the pressure Poisson equation to significantly improve the computational efficiency.Under the same initial conditions,it used the SOR(successive over relaxation) iteration method by Fortran90 to solve the linear equations obtained by numerical discretization of the pressure Poisson equation.The result shows that the BiCGSTAB algorithm based on compressed storage has obvious advantages in solving sparse linear equations.The algorithm is fast,efficient and reliable.%基于投影算法所得压力Poisson方程进行数值离散,对离散系统形成的稀疏线性方程组,由于线性方程组的系数矩阵存在大量的零元素,为降低内存存储,以一维稀疏存储结构对大规模的系数矩阵进行压缩处理,只存储非零元素;同时,以具有优化性质的BiCGSTAB算法求解压力Poisson方程,显著提高了计算效率.在相同初始条件下,利用Fortran90完成超松弛迭代法的程序求解压力Poisson方程数值离散所得到的线性方程组进行求解对比.结果表明基于压缩存储的BiCGSTAB算法在求解稀疏线性方程组具有明显的优势,该算法求解速度快、高效、可靠.