A new parallel alternating-direction algorithm for convection-dominated diffusion problems
首发时间:2017-11-29
Abstract:In this paper, a new parallel alternating-direction algorithm for convection-dominated diffusion problems is proposed. One direction calculation of the new algorithm includes two domain decomposition methods that are applied to compute the values at ($n+\frac{1}{2}$)st time level by use of known numerical solutions at $n$th time level, respectively, then the average of two above values is chosen to be the numerical solutions at ($n+\frac{1}{2}$)st time level. Next, the other direction calculation of the new algorithm will be used to solve the numerical solutions at ($n+1$)st time level by use of known values at ($n+\frac{1}{2}$)st time level above by the same technique. The new algorithm obtains high accuracy while maintaining parallelism and unconditional stability. Both error analysis and numerical examples show the accuracy and efficiency of the new algorithm.
keywords: convection-dominated diffusion problems alternating-direction finite difference unconditional stability parallelism
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对流占优扩散问题的一个新的并行交替方向算法
摘要:本文针对对流占优扩散问题提出了一个并行的交替方向算法,算法的第一个计算方向包括两个区域分解算法,当第$n$时间层的数值解已知时,分别利用两算法计算得到两个数值解,再取其平均值作为第($n+\frac{1}{2}$) 时间层的数值解;同理,算法的另一个计算方向根据所求得的第($n+\frac{1}{2}$) 时间层的数值解来计算得到第$(n+1)$时间层数值解.新算法在保持了并行性和无条件稳定性的同时,又得到了较高的计算精度.误差分析和数值算例揭示了新算法的精度和有效性.
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