Simulation of multiscale Schrödinger equation with extrapolated splitting approaches
Jürgen Geiser, Amirbahador Nasari · AIP conference proceedings · 2019
In this paper we present a novel splitting approach to solve scale-dependent Schrödinger equations, which are applied in quantum mechanical models. The energy potential is based on highly oscillating functions and we obtain a multiscale problem. We apply a multiscale solver, which is based on an operator splitting method and decouples the diffusion and reaction part of the Schödinger equation. We apply a large time step for the implicit time-discretization of the diffusion part and small time steps for the explicit time-discretization of the reaction part. With an extrapolation step, we can reduce the computational time in the highly-oscillating time-scale. We present the numerical analysis of the extrapolated operator splitting method. First numerical experiments indicate the benefit of the extrapolated splitting approaches.