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Chin. Phys. B, 2021, Vol. 30(7): 073201    DOI: 10.1088/1674-1056/abe1a4

HeTDSE: A GPU based program to solve the full-dimensional time-dependent Schrödinger equation for two-electron helium subjected to strong laser fields

Xi Zhao(赵曦)1,5,6, Gangtai Zhang(张刚台)2,†, Tingting Bai(白婷婷)3, Jun Wang(王俊)4,‡, and Wei-Wei Yu(于伟威)7,§
1 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China;
2 College of Physics and Optoelectronics Technology, Baoji University of Arts and Sciences, Baoji 721016, China;
3 College of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, China;
4 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China;
5 Department of Physics, Kansas State University, Manhattan, KS 66506, USA;
6 School of Physics and Electronics, Qiannan Normal College for Nationalities, Duyun 558000, China;
7 School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China
Abstract  Electron-electron correlation plays an important role in the underlying dynamics in physics and chemistry. Helium is the simplest and most fundamental two-electron system. The dynamic process of helium in a strong laser field is still a challenging issue because of the large calculation cost. In this study, a graphic processing unit (GPU) openACC based ab initio numerical simulations package HeTDSE is developed to solve the full-dimensional time-dependent Schrödinger equation of helium subjected to a strong laser pulse. HeTDSE uses B-spline basis sets expansion method to construct the radial part of the wavefunction, and the spherical harmonic functions is used to express for the angular part. Adams algorithm is employed for the time propagation. Our example shows that HeTDSE running on an NVIDIA Kepler K20 GPU can outperform the one on an Intel E5-2640 single CPU core by a factor of 147. HeTDSE code package can be obtained from the author or from the author's personal website (doi: 10.13140/RG.2.2.15334.45128) directly under the GPL license, so HeTDSE can be downloaded, used and modified freely.
Keywords:  strong field physics      TDSE      OPENACC      GPU      electron correlation      helium  
Received:  10 August 2020      Revised:  27 January 2021      Accepted manuscript online:  01 February 2021
PACS:  32.80.Rm (Multiphoton ionization and excitation to highly excited states)  
  42.50.Hz (Strong-field excitation of optical transitions in quantum systems; multiphoton processes; dynamic Stark shift)  
  42.65.Ky (Frequency conversion; harmonic generation, including higher-order harmonic generation)  
Fund: Project supported the National Natural Science Foundation of China (Grant Nos. 11904192, 11604119, 11627807, and 11604131), the Natural Science Basic Research Plan of Shaanxi Province of China (Grant No. 2016JM1012), the Natural Science Foundation of the Education Committee of Shaanxi Province of China (Grant No. 18JK0050), the Science Foundation of Baoji University of Arts and Sciences of China (Grant No. ZK16069), and the Natural Science Foundation of Liaoning Province of China (Grant No. LQ 2020022).
Corresponding Authors:  Gangtai Zhang, Jun Wang, Wei-Wei Yu     E-mail:;;

Cite this article: 

Xi Zhao(赵曦), Gangtai Zhang(张刚台), Tingting Bai(白婷婷), Jun Wang(王俊), and Wei-Wei Yu(于伟威) HeTDSE: A GPU based program to solve the full-dimensional time-dependent Schrödinger equation for two-electron helium subjected to strong laser fields 2021 Chin. Phys. B 30 073201

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