New optimized Schwarz algorithms for one dimensional Schrödinger equation with general potential

The aim of this paper is to develop new optimized Schwarz algorithms for the one dimensional Schrödinger equation with linear and nonlinear potential. classical algorithm an iterative process. In case time-independent potential, we construct explicitly interface problem use direct LU method on problem. therefore turns be a Thus, independent transmission condition numerical computation smaller. To our knowledge, first time that constructed as Concerning time-dependent potential or propose pre-processed operator preconditioner which leads preconditioned algorithm. Numerically, convergence also condition. addition, both these implemented in parallel cluster are robust, scalable up 256 sub domains (MPI process) take much less than one, especially case.