Domain decomposition method for parabolic problems with Neumann conditions

Many explicit/implicit and the modified implicit prediction (MIP) domain decomposition methods are used to solve parabolic partial differential equations with Dirichlet boundary conditions. The MIP algorithm is very effective on Dirichlet problems. In this paper we investigate the MIP algorithm on the parabolic equations with Neumann boundary conditions. The numerical experiments show that the MIP algorithm is unconditionally stable. Moreover it is proven that the speedup is linear when the MIP algorithm is applied to the Neumann boundary conditions.