基于图形处理器加速数值求解三维含时薛定谔方程

Numerical solution of three-dimensional time-dependent Schrödinger equation based on graphic processing unit acceleration

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-傅里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.计算表明,相对于中央处理器(CPU),GPU并行计算有着最高约60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.

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 Schrödinger equation.However,solving the three-dimensional time-dependent Schrödinger equation is not a simple task,and the analytical solution cannot be obtained,so it can only be solved numerically with the help of computer.In order to shorten the computing time and obtain the results quickly,it is necessary to use parallel methods to speed up computing.In this paper,under the background of strong field ionization,the three-dimensional time-dependent Schrödinger 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 for example.Based on the spherical polar coordinate system,the time-dependent Schrödinger 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 computeintensive part of the application runs in parallel on thousands of GPU cores.The 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 results from the existing physical laws,the calculation error is also within an acceptable range,and the result is also consistent with the result from 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 are carried out.Computational experiments show that under the condition of ensuring accuracy,the GPU parallel computing speeds by up to about 60 times maximally based on the computational performance of CPU.It can be seen that the accelerated numerical solution of three-dimensional time-dependent Schrödinger equation based on GPU can significantly shorten the computational time.This work has important guiding significance for rapidly solving the threedimensional time-dependent Schrödinger equation by using GPU.