Parallel solver for the three-dimensional Cartesian-grid-based time-dependent Schrödinger equation and its applications in laser- H2+ interaction studies

Y. M. Lee, Jong-Shinn Wu*, Tsin-Fu Jiang, Y. S. Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A parallelized three-dimensional Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for molecules with a single electron, assuming the motion of the nucleus is frozen, is presented in this paper. An explicit stagger-time algorithm is employed for time integration of the TDSE, in which the real and imaginary parts of the wave function are defined at alternate times, while a cell-centered finite-volume method is utilized for spatial discretization of the TDSE on Cartesian grids. The TDSE solver is then parallelized using the domain decomposition method on distributed memory machines by applying a multilevel graph-partitioning technique. The solver is validated using a H2+ molecule system, both by observing the total electron probability and total energy conservation without laser interaction, and by comparing the ionization rates with previous two-dimensional axisymmetric simulation results with an aligned incident laser pulse. The parallel efficiency of this TDSE solver is presented and discussed; the parallel efficiency can be as high as 75% using 128 processors. Finally, examples of the temporal evolution of the probability distribution of laser incidence onto a H2+ molecule at inter-nuclear distance of 9 a.u. (χ=0° and 90°) and the spectral intensities of harmonic generation at internuclear distance of 2 a.u. (χ=0°, 30°, 60°, and 90°) are presented to demonstrate the powerful capability of the current TDSE solver. Future possible extensions of the present method are also outlined at the end of this paper.

Original languageEnglish
Article number013414
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume77
Issue number1
DOIs
StatePublished - 31 Jan 2008

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