Unconditional Stability of Corrected Explicit-Implicit Domain Decomposition Algorithms for Parallel Approximation of Heat Equations

A class of corrected explicit-implicit domain decomposition (CEIDD) methods is investigated for the parallel approximation of linear heat equations. Explicit-implicit domain decomposition (EIDD) methods are computationally and communicationally efficient for each time step but always suffer from small time step size restrictions. By adding an interface correction step to Kuznetsov's EIDD, the one-dimensional CEIDD procedure achieves unconditional stability without discarding the time-stepwise efficiency of the EIDD method. In order to maintain the virtues of the CEIDD method and improve the flexibility in domain partitioning, for solving multidimensional problems, special zigzag-shaped interfaces are suggested in the CEIDD method. Based on noncrossover and crossover types of zigzag interfaces, the resulting CEIDD-ZI algorithms are studied for two strategies of subdomain partition. By the energy method, it shows that the proposed algorithms, including their degenerate cases--the corrected explicit hopscotch schemes--are convergent in the discrete H¹ seminorm and L² norm. Numerical experiments confirm the results in our analysis.