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

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 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 compute-intensive 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 three-dimensional time-dependent Schrödinger equation by using GPU.