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This paper deals with two domain decomposition methods for two dimensionallinear Schr{\"o}dinger equation, the Schwarz waveform relaxation method and thedomain decomposition in space method. After presenting the classicalalgorithms, we propose a new algorithm for the free Schr{\"o}dinger equationand a preconditioned algorithm for the general Schr{\"o}dinger equation. Thesealgorithms are studied numerically, which shows that the two new algorithmscould accelerate the convergence and reduce the computation time. Besides thetraditional Robin transmission condition, we also propose to use a newlyconstructed absorbing condition as the transmission condition.

Domain decomposition algorithms for two dimensional linear Schr\"odinger equation