An alternating explicit–implicit domain decomposition method for the parallel solution of parabolic equations

Explicit–implicit domain decomposition (EIDD) is a class of globally non-iterative, non-overlapping domain decomposition methods for the numerical solution of parabolic problems on parallel computers, which are highly efficient both computationally and communicationally for each time step. In this paper an alternating EIDD method is proposed which is algorithmically simple, efficient for each time step, highly parallel, and satisfies a stability condition that imposes no additional restriction to the time step restriction imposed by the consistency condition, which guarantees a convergence of order O ( Δ th - 1 N B / N ) + O ( h 2 ) in an H 1 -type norm, where N B and N, respectively, denote the number of gridpoints on the interface boundaries B and the number of gridpoints on the entire discrete domain.