代数方程求解方法收敛速度比较及对算法健壮性的影响

将交替方向隐式（ADI）、强隐（SIP）及Krylov子空间法中的TFQMR、Bi-CGSTAB方法实施于SIMPLER算法，作为其内迭代求解方法，比较了不同代数方程求解方法的收敛速度，并首次分析了它们对算法健壮性的影响，结果发现：内迭代方法不同，SIMPLER算法所表现出的健壮性也会有较大差异，采用不同的求解方法以及调节求解方法中的参数可以有效调整SIMPLER算法的健壮性．通过对具体算例的研究表明：当SIP方法的抵消参数α取值较高时，能获得比ADI快30％～50％的平均收敛速度，但算法的健壮性减弱；减小α值，在获得与ADI方法相同的收敛速度下，算法的健壮性却能远好于ADI；ILU（0）预处理的Bi-CGSTAB方法收敛速度较ADI平均能快15％～40％；当SIP方法取某口值时也能获得此收敛速度，但算法所表现出的健壮性却差于Bi-CGSTAB方法；ILU（O）预处理的TFQMR方法收敛速度慢于以上各方法，但其健壮性最佳。

Comparison of Convergence Rate and Analysis of Robustness by Using Different Algebraic Equation Solution Methods

The alterative direct iterative (ADI), strong implicit procedure (SIP), preconditioning transpose-free variant of quasi-minimum residual method (TFQMR) and biconjugate gradient stabilized method (Bi-CGSTAB) of the Krylov subspace methods were implemented in SIMPLER algorithm to solve the algebraic equations. The convergence rate and the robustness comparisons were conducted for the solution procedure using the above-mentioned different iterative solution methods. It is found that the solution methods for the algebraic equations can affect the robustness of SIMPLER algorithm. By using different algebraic equation solution methods and the related parameters, the robustness of SIMPLER algorithm can be controlled to a certain degree. Through analysis of specific examples, it is found that the convergence rate of SIP method can be about 30% to 50% higher than that of ADI with high offset factor a, while the related robustness of SIMPLER is somewhat weakened. In contrast, decreasing a makes its convergence rate more or less the same as that of ADI, and the robustness is much better than that of ADI. The average convergence rate of ILU(0) preconditioning Bi-CGSTAB method is about 15% to 40% higher than that of ADI, which can be easily reached by SIP method with an appropriate value of offset factor a, but the robustness of SIP is worse than that of Bi-CGSTAB. The convergence rate of preconditioning TFQMR is the smallest, but the robustness is the best.