3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates

doi:10.1088/1674-1056/adee00

中国物理B ›› 2025, Vol. 34 ›› Issue (9): 94203-094203.doi: 10.1088/1674-1056/adee00

所属专题： Featured Column — COMPUTATIONAL PROGRAMS FOR PHYSICS

3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates

Ke Peng(彭科)¹, Aihua Liu(刘爱华)^2,†, Jun Wang(王俊)^2,‡, and Xi Zhao(赵曦)^1,§

1 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China;
2 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

收稿日期:2025-04-24 修回日期:2025-06-25 接受日期:2025-07-10 出版日期:2025-08-21 发布日期:2025-09-17
通讯作者: Aihua Liu, Jun Wang, Xi Zhao E-mail:aihualiu@jlu.edu.cn;wangjun86@jlu.edu.cn;zhaoxi719@snnu.edu.cn
基金资助:
This work was supported by the GHfund A (Grant No. ghfund202407013663), the Fundamental Research Funds for the Central Universities (Grant No. GK202207012), Shaanxi Province (Grant No. QCYRCXM-2022-241), the National Key Research and Development Program of China (Grant No. 2022YFE0134200), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011117), the Natural Science Foundation of Jilin Province (Grant No. 20220101016JC), and the National Natural Science Foundation of China (Grant Nos. 12374238, 11934004, and 11974230).

3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates

Ke Peng(彭科)¹, Aihua Liu(刘爱华)^2,†, Jun Wang(王俊)^2,‡, and Xi Zhao(赵曦)^1,§

1 School of Physics and Information Technology, Shaanxi Normal University, Xi'an 710062, China;
2 Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China

Received:2025-04-24 Revised:2025-06-25 Accepted:2025-07-10 Online:2025-08-21 Published:2025-09-17
Contact: Aihua Liu, Jun Wang, Xi Zhao E-mail:aihualiu@jlu.edu.cn;wangjun86@jlu.edu.cn;zhaoxi719@snnu.edu.cn
Supported by:
This work was supported by the GHfund A (Grant No. ghfund202407013663), the Fundamental Research Funds for the Central Universities (Grant No. GK202207012), Shaanxi Province (Grant No. QCYRCXM-2022-241), the National Key Research and Development Program of China (Grant No. 2022YFE0134200), Guangdong Basic and Applied Basic Research Foundation (Grant No. 2025A1515011117), the Natural Science Foundation of Jilin Province (Grant No. 20220101016JC), and the National Natural Science Foundation of China (Grant Nos. 12374238, 11934004, and 11974230).

摘要/Abstract

摘要： We present a graphics processing units (GPU) parallelization based three-dimensional time-dependent Schrödinger equation (3D-TDSE) code to simulate the interaction between single-active-electron atom/molecule and arbitrary types of laser pulses with either velocity gauge or length gauge in Cartesian coordinates. Split-operator method combined with fast Fourier transforms (FFT) is used to perform the time evolution. Sample applications in different scenarios, such as stationary state energies, photon ionization spectra, attosecond clocks, and high-order harmonic generation (HHG), are given for the hydrogen atom. Repeatable results can be obtained with the benchmark program PCTDSE, which is a 3D-TDSE Fortran solver parallelized using message passing interface (MPI) library. With the help of GPU acceleration and vectorization strategy, our code running on a single NVIDIA 3090 RTX GPU can achieve about 10 times faster computation speed than PCTDSE running on a 144 Intel Xeon CPU cores server with the same accuracy. In addition, 3D-GTDSE can also be modified slightly to simulate non-adiabatic dynamics involving the coupling of nuclear and electronic wave packets, as well as pure nuclear wave packet dynamics in the presence of strong laser fields within 3 dimensions. Additionally, we have also discussed the limitations and shortcomings of our code in utilizing GPU memory. The 3D-GTDSE code provides an alternative tool for studying the ultrafast nonlinear dynamics under strong laser fields.

关键词: GPU parallelization, high-order harmonic generation (HHG), time-dependent Schrödinger equation (TDSE), wave packet dynamics

Abstract: We present a graphics processing units (GPU) parallelization based three-dimensional time-dependent Schrödinger equation (3D-TDSE) code to simulate the interaction between single-active-electron atom/molecule and arbitrary types of laser pulses with either velocity gauge or length gauge in Cartesian coordinates. Split-operator method combined with fast Fourier transforms (FFT) is used to perform the time evolution. Sample applications in different scenarios, such as stationary state energies, photon ionization spectra, attosecond clocks, and high-order harmonic generation (HHG), are given for the hydrogen atom. Repeatable results can be obtained with the benchmark program PCTDSE, which is a 3D-TDSE Fortran solver parallelized using message passing interface (MPI) library. With the help of GPU acceleration and vectorization strategy, our code running on a single NVIDIA 3090 RTX GPU can achieve about 10 times faster computation speed than PCTDSE running on a 144 Intel Xeon CPU cores server with the same accuracy. In addition, 3D-GTDSE can also be modified slightly to simulate non-adiabatic dynamics involving the coupling of nuclear and electronic wave packets, as well as pure nuclear wave packet dynamics in the presence of strong laser fields within 3 dimensions. Additionally, we have also discussed the limitations and shortcomings of our code in utilizing GPU memory. The 3D-GTDSE code provides an alternative tool for studying the ultrafast nonlinear dynamics under strong laser fields.

Key words: GPU parallelization, high-order harmonic generation (HHG), time-dependent Schrödinger equation (TDSE), wave packet dynamics

中图分类号: (Frequency conversion; harmonic generation, including higher-order harmonic generation)

42.65.Ky

32.80.Rm (Multiphoton ionization and excitation to highly excited states) 31.15.xv (Molecular dynamics and other numerical methods)

Ke Peng(彭科), Aihua Liu(刘爱华), Jun Wang(王俊), and Xi Zhao(赵曦). 3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates[J]. 中国物理B, 2025, 34(9): 94203-094203.

Ke Peng(彭科), Aihua Liu(刘爱华), Jun Wang(王俊), and Xi Zhao(赵曦). 3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates[J]. Chin. Phys. B, 2025, 34(9): 94203-094203.

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3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates

3D-GTDSE: A GPU-based code for solving 3D-TDSE in Cartesian coordinates

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