Schwarz waveform relaxation method for one dimensional Schr{ö}dinger equation with general potential
This work addresses the need for efficient parallel solvers for the Schrödinger equation, which is important for quantum mechanics simulations, but the results are incremental as they extend existing domain decomposition methods to specific potential types.
The paper applies the Schwarz Waveform Relaxation method to the 1D Schrödinger equation with general potentials, proposing a new algorithm for time-independent linear potentials that is robust and scalable up to 500 subdomains, significantly reducing computation time. For time-dependent or nonlinear potentials, a preconditioned algorithm using the zero-potential linear operator ensures high scalability.
In this paper, we apply the Schwarz Waveform Relaxation (SWR) method to the one dimensional Schr{ö}dinger equation with a general linear or a nonlinear potential. We propose a new algorithm for the Schr{ö}dinger equation with time independent linear potential, which is robust and scalable up to 500 subdo-mains. It reduces significantly computation time compared with the classical algorithms. Concerning the case of time dependent linear potential or the non-linear potential, we use a preprocessed linear operator for the zero potential case as preconditioner which lead to a preconditioned algorithm. This ensures high scalability. Besides, some newly constructed absorbing boundary conditions are used as the transmission condition and compared numerically.