中文摘要：

为了提高数值求解大气方程的计算速度，我们研究了稀疏逼近逆预处理方法及其在数值求解浅水波方程中的应用，这是一种求解大型线性方程组的快速算法，该算法的核心内容是稀疏逼近逆非零元模式的选取。首先导出了一种稀疏逼近逆的非零元模式及其确定方法，然后以浅水方程的差分格式为例，借助于GMRES迭代算法，对这种预处理快速算法应用前后的计算速度进行了比较，发现该快速算法能大幅度提高运算速度。另外，该预处理快速算法简单、易于并行，是一种值得在大气方程中推广应用的方法。

英文摘要：

For improving the computation speed in numerically solving weather equations, we investigate the use of sparse approximate inverse preconditioners for numerically solving shallow water equations. This is a fast algorithm for solving large scale linear equations. Some strategies for determining the nonzero of an approximate inverse are described in this paper. As an example, we use the GMRES iterative algorithm to solve the finite difference equations of shallow equations and analyze the results that are obtained in preconditioned and un-preconditioned, respectively. It is shown that the computation speed is greatly improved after we use the preconditioning method. In addition, this preconditioning algorithm is simple and parallelizable. Therefore, the algorithm is potential in the applications of weather equations.