Stabilized Explicit-Implicit Domain Decomposition Methods for the Numerical Solution of Parabolic Equations

We report a class of stabilized explicit-implicit domain decomposition (SEIDD) methods for the numerical solution of parabolic equations. Explicit-implicit domain decomposition (EIDD) methods are globally noniterative, nonoverlapping domain decomposition methods, which, when compared with Schwarz-algorithm-based parabolic solvers, are computationally and communicationally efficient for each simulation time step but suffer from small time step size restrictions. By adding a stabilization step to EIDD, the SEIDD methods retain the time-stepwise efficiency in computation and communication of the EIDD methods but exhibit much better numerical stability. Three SEIDD algorithms are presented in this paper, which are experimentally tested to show excellent stability, computation and communication efficiencies, and high parallel speedup and scalability.