Berlin 2014 – wissenschaftliches Programm

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A: Fachverband Atomphysik

A 15: Poster: Interaction with strong or short laser pulses

A 15.9: Poster

Montag, 17. März 2014, 16:30–18:30, Spree-Palais

Comparison of split-operator methods for solving the three-dimensional time-dependent Schrödinger equation — •Paul Struszewski, Julius Rapp, and Dieter Bauer — Institut für Physik, Universität Rostock

We study numerical properties of different split-operator methods such as exponential operator splitting (EOS) and alternating direction implicit (ADI) for solving the three-dimensional time-dependent Schrödinger equation (TDSE) in Cartesian coordinates. The aim is to obtain accurate ab initio results for the interaction of a lithium model system with an intense laser field in order to benchmark methods such as time-dependent density functional theory (TDDFT) in several approximations. The operator splitting allows for a high-order time propagation via the solution of tridiagonal linear equations only, which performs very well and can be directly parallelized. In addition, a highly adjusted numerical grid is used to minimize storage space and computing time.

The results provide general indications which operator splitting method is most suitable for solving the TDSE in three dimensions. As expected, the unitary EOS is perfectly norm-conserving, whereas the ADI is not. However, for ADI the variation of norm over time is orders of magnitude smaller in comparison to an explicit scheme. For cases in which ADI is faster than EOS, ADI offers a good compromise between numerical effort and norm-conservation.