In this paper, we propose a new domain decomposition method for the 2-D diffusion equation. The scheme is positivity-preserving with essential parallelism. First, we decompose the domain into many sub-domains, and then some new schemes are used on the sub-domains according to dimension. Moreover, only local communication is needed at each time level in the parallel programs. The method of discrete functional analysis is used to prove that the scheme is unconditionally stable with second-order accuracy. At last, some numerical tests are given to verify the theoretical results.

中文翻译：

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二维扩散方程的一种新的保正域分解方法

在本文中，我们为二维扩散方程提出了一种新的域分解方法。该方案是积极的，具有基本的并行性。首先，我们将域分解为许多子域，然后根据维度在子域上使用一些新方案。此外，并行程序中的每个时间级别只需要本地通信。用离散泛函分析的方法证明该方案在二阶精度下是无条件稳定的。最后通过数值试验对理论结果进行了验证。