解非线性椭圆边值问题的逐层显式校正迭代法

An Explicit Corrective Iterative Method at Successive Levels for Solving Nonlinear Elliptic Partial Differential Equations

本文提出一种求解非线性离散椭圆边值问题的逐层显式校正迭代法.该方法有效地融合了多层网格方法和扰动迭代方法.有关数值分析表明,当网格分划较细且分划参数h较小时,在各网格层上仅需一次简单的迭代和显式校正步骤就可满足数值计算的要求.使用该方法的计算量是最佳阶的,它是最细网格层节点变量个数的同阶量.

Many numerical methods for solving nonlinear elliptic bounday value problems are available. Newton's method of iteration and the like are expensive as the amount of computing is very large. Besides, it is difficult to choose a good initial value. For the multilayer grid method, e.g., the full approximate algorithm, many MG cyclic steps are required at each layer. An explicit corrective iterative method at successive levels is proposed, in which the corrective method, disturbed iteration and multi grid method have been integrated. A numerical analysis shows that the initial value for iteration at finer levels is satisfied. Asymptotically only one simple iterative step and one corrective step per level are required. The global computing workload using the method proposed is found to be optimal