摘要: 量子力学领域中对强激光场与原子分子相互作用的理论研究非常依赖于数值求解含时薛定谔方程.本文在强场电离的背景下并行求解氢原 子的三维含时薛定谔方程.基于球极坐标系，采用分裂算符-傅立叶变换 方法将含时薛定谔方程进行了离散化.由此可得到长度规范下的光电子 连续态波函数.图形处理器(GPU)可以依托多线程结构充分发挥细粒度 并行的优势，实现整体算法的并行加速.计算实验表明，相对于中央处 理器(CPU)，GPU 并行计算有着最高约 50 倍的加速比.由此可见，基于 GPU 加速数值求解三维含时薛定谔方程能够显著缩短计算耗费的时 间.这一工作对利用 GPU 快速求解三维含时薛定谔方程有着重要的指导意义.
Numerical solution of three-dimensional time-dependent Schrodinger equation based on graphic processing unit acceleration
- Received Date:
11 May 2020
Abstract: In the field of quantum mechanics, the theoretical study of the interaction between intense laser field and atoms and molecules depends very much on the numerical solution of the time-dependent Schrodinger equation. however, solving the three-dimensional time-dependent Schrodinger equation is not a simple task, and the analytical solution can not be obtained, so it can only be solved numerically with the help of computer. In order to shorten the computing time and get the results faster, it is necessary to use parallel methods to accelerate computing. In this paper, under the background of strong field ionization, the three-dimensional time-dependent Schrodinger equation of hydrogen atom is solved in parallel, and the suprathreshold ionization of hydrogen atom under the action of linearly polarized infrared laser electric field is taken as an example. Based on the spherical polar coordinate system, the time-dependent Schrodinger equation is discretized by the splitting operator-Fourier transform method, and the photoelectron continuous state wave function under the length gauge can be obtained. In Graphics processing unit (GPU) accelerated applications, the sequential portion of the workload runs on central processing unit (CPU) (which is optimized for single-threaded performance), while the compute-intensive part of the application runs in parallel on thousands of GPU cores. GPU can make full use of the advantage of fine-grained parallelism based on multi-thread structure to realize parallel acceleration of the whole algorithm. Two accelerated computing modes of CPU parallel and GPU parallel are adopted, and their parallel acceleration performance is discussed. compared with the existing physical laws, the calculation error is also within an acceptable range, and the result is also consistent with the existing physical laws of suprathreshold ionization, which also verifies the correctness of the program. In order to obtain a relatively accurate acceleration ratio, many different experiments have been carried out in order to find the optimal acceleration ratio. Computational experiments show that under the condition of ensuring accuracy, GPU parallel computing has a maximum speedup of about 60 times based on the computational performance of CPU. It can be seen that the accelerated numerical solution of three-dimensional time-dependent Schrodinger equation based on GPU can significantly shorten the computational time. This work has important guiding significance for the rapid solution of three-dimensional time-dependent Schrodinger equation by using GPU.