A new positivity‐preserving domain decomposition method for the 2‐D diffusion equation

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. 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.