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arXiv · 1805.11840

Simulations of Multiscale Schroedinger Equations with Multiscale Splitting Approaches: Theory and Application

Juergen Geiser·Amirbahador Nasari
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Abstract

In this paper we present a novel multiscale splitting approach to solve multiscale Schroedinger equation, which have large different time-scales. The energy potential is based on highly oscillating functions, which are magnitudes faster than the transport term. We obtain a multiscale problem and a highly stiff problem, while standard solvers need to small time-steps. We propose multiscale solvers, which are based on operator splitting methods and we decouple the diffusion and reaction part of the Schroedinger equation. Such a decomposition allows to apply a large time step for the implicit time-discretization of the diffusion part and small time steps for the explicit and highly oscillating reaction part. With extrapolation steps, we could reduce the computational time in the highly-oscillating time-scale, while we relax into the slow time-scale. We present the numerical analysis of the extrapolated operator splitting method. First numerical experiments verified the benefit of the extrapolated splitting approaches.

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Juergen Geiser, Amirbahador Nasari. 2018-05-30. Simulations of Multiscale Schroedinger Equations with Multiscale Splitting Approaches: Theory and Application. https://arxiv.org/abs/1805.11840

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