Timely Communicaton: An Analysis for a Nonoverlapping Domain Decomposition Iterative Procedure

An iterative procedure for nonoverlapping domain decomposition methods (DDM) is developed and analyzed, which can be parallelly implemented with local communications. It uses a Robin boundary condition as its transmission condition on the interfaces. The update of Robin data of its transmission condition is a very simple relaxation between the preceding Robin data and function value. It need not find any derivatives at each iterative step. This method can be easily applied to the discretization problems. Moreover, it is shown that it is indeed a variant of the Lions nonoverlapping DDM for the continuous problems. Also, it can be regarded as a generalization of Tang's generalized Schwarz alternating method (GSAM) in the nonoverlapping DDM.