Lagrange-Schwarz Waveform Relaxation domain decomposition methods for linear and nonlinear quantum wave problems

A Schwarz Waveform Relaxation (SWR) algorithm is proposed to solve by Domain Decomposition Method (DDM) linear and nonlinear Schrödinger equations. The symbols of the transparent fractional transmission operators involved in Optimized Schwarz Waveform Relaxation (OSWR) algorithms are approximated by low order Lagrange polynomials to derive Lagrange-Schwarz Waveform Relaxation (LSWR) algorithms based on local transmission operators. The LSWR methods are numerically shown to be computationally efficient, leading to convergence rates almost similar to OSWR techniques.