Stable, Globally Non-Iterative, Non-Overlapping Domain Decomposition Parallel Solvers for Parabolic Problems

In this paper, we report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the parallel solution of parabolic problems, based on the explicit-implicit domain decomposition (EIDD) methods. EIDD methods are globally non-iterative, non-overlapping domain decomposition methods which, when compared with Schwarz alternating algorithm based parabolic solvers, are computationally and communicationally efficient for each simulation time step but suffer from time step size restrictions due to conditional stability or conditional consistency. By adding a stabilization step to the EIDD methods, the SEIDD methods are freed from time step size restrictions while retaining EIDD’s computational and communicational efficiency for each time step, rendering themselves excellent candidates for large-scale parallel simulations. Three algorithms of the SEIDD type are implemented, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.