Abstract: The three-dimensional convection diffusion equation is discretized by the fourth order compact difference scheme, and the resulting linear algebraic system is given in the block triangular sparse matrix form. The linear algebraic system is solved by using three kinds of iterative accelerators, such as FGMRES, BICGSTAB and TFQMR, and combining with the preconditioners of incomplete factorization LU decomposition with dual threshold [(ILUT(τ,s))]. The accuracy, CPU time and iteration number under three different accelerators are compared. Moreover, the comparison of efficiency is also carried out between the traditional method with the preconditioned iterative method. Numerical results show that the preconditioned iterative method can not only ensure the accuracy of the fourth-order scheme, but also greatly improves the convergence efficiency.

Key words: three-dimensional convection-diffusion equation, sparse matrix storage, preconditioning technique, Krylov subspace methods

摘要： 基于四阶紧致格式对三维对流扩散方程进行离散，并给出所得到的离散线性方程组的块三角稀疏矩阵形式。以带双阈值的不完全因子化LU分解[(ILUT(τ,s))]作为预条件子，分别用FGMRES、BICGSTAB和TFQMR作为迭代加速器，对离散线性方程组进行求解验证了格式精度并比较了不同迭代法的CPU时间和迭代步。此外，通过比较传统迭代法和预条件迭代法的计算效率，表明预条件迭代法不仅能够保证格式的四阶精度，还能极大地提高收敛效率。

关键词: 三维对流扩散方程, 稀疏矩阵存储, 预条件技术, Krylov子空间方法