Time lagging and explicit interface prediction for nonoverlapping domain decomposition with parallel additive splitting method for multi-dimensional parabolic problem

Two different interface predictions are considered, in this work, for the solution of multi-dimensional parabolic problem defined over nonoverlapping subdomains. These interface boundary conditions are predicted by the explicit prediction (EP) and the time lagging (TL) methods with δx and 2δx mesh spacings away from the interface lines. We considered the additive splitting up method with respect to the spatial variable to solve the multi-dimensional parabolic problem over each subdomains. For more accurate solution we present the correction for the explicit interface prediction and implement the proposed methods for the solution of two different model problems.