2015/06/18 by Christophe Besse, Feng Xing, Besse, Christophe +1
Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1506.05639
openalex publication_date 2015/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper deals with two domain decomposition methods for two dimensional linear Schrödinger equation, the Schwarz waveform relaxation method and the domain decomposition in space method. After presenting the classical algorithms, we propose a new algorithm for the free Schrödinger equation and a preconditioned algorithm for the general Schrödinger equation. These algorithms are studied numerically, which shows that the two new algorithms could accelerate the convergence and reduce the computation time. Besides the traditional Robin transmission condition, we also propose to use a newly constructed absorbing condition as the transmission condition.