CAJ | 학술논문

将求解二维椭圆方程边值问题的拟多重网格预处理迭代法推广到二维抛物型方程中去，采用Crank-Nicolson格式来离散二维抛物型方程。由于网格节点顺序对迭代格式的构造至关重要，因此对每一时间层上的l层网格节点按照旋转红-黑序进行排序。数值试验表明，此方法迭代次数较SOR法有明显减少，迭代解与精确解的误差值相对较低，收敛速度较快。因此，在求解二维抛物型方程初边值问题中拟多重网格预处理迭代法是一种很有效的方法。
장구해이유타원방정변치문제적의다중망격예처리질대법추엄도이유포물형방정중거，채용Crank-Nicolson격식래리산이유포물형방정。유우망격절점순서대질대격식적구조지관중요，인차대매일시간층상적l층망격절점안조선전홍-흑서진행배서。수치시험표명，차방법질대차수교SOR법유명현감소，질대해여정학해적오차치상대교저，수렴속도교쾌。인차，재구해이유포물형방정초변치문제중의다중망격예처리질대법시일충흔유효적방법。
The solution of quasi multigrid preconditioned iteration method for boundary value problem of two-dimensional elliptic equation is generalized to two -dimensional parabolic equation and uses Crank -Nicolson format to discrete two -dimensional parabolic equation .Because it is essential for the network nodes order to form the structure of the iterative format , the grid nodes of L layer in each time are sorted in sequence according to the rotating red-black order .The numerical experiment shows that the number of this kind of iterations re-duces more obviously than SOR method and the iterative solution and the exact solution bear the features with a relatively low error and a faster rate of convergence .Therefore , the quasi multigrid preconditioned iteration meth-od for boundary value problem of two -dimensional parabolic equation is a very effective way to solve this prob-lem.