On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation
Antoine, Xavier ; Emmanuel, Lorin
HAL, hal-01649736 / Harvested from HAL
Text on HAL
This paper is dedicated to the analysis of the rate of convergence of the classical and quasi-optimal Schwarz waveform relaxation (SWR) method for solving the linear Schrödinger equation with space-dependent potential. The strategy is based on i) the rewriting of the SWR algorithm as a fixed point algorithm in frequency space, and ii) the explicit construction of contraction factors thanks to pseudo-differential calculus. Some numerical experiments illustrating the analysis are also provided.
Publié le : 2018-07-04
Classification:  domain decomposition method,  Schrödinger equation,  pseudo-differential calculus,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA],  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 
@article{hal-01649736,
     author = {Antoine, Xavier and Emmanuel, Lorin},
     title = {On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schr\"odinger equation},
     journal = {HAL},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01649736}
}

Antoine, Xavier; Emmanuel, Lorin. On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01649736/