Solving the 3D Schrödinger Equation on a GPU

Abstract

Abstract Solving the 3D Schrodinger equation is of great interests in many branches of physical sciences and is usually a computing intensive task. Modern graphics processing units (GPUs) are extensively employed in the general purpose computing domain due to their high performance parallel processing capability. In this paper, an algorithm for solving the time-independent 3D Schrodinger equation with a finite difference time domain (FDTD) method is presented, together with an implementation of the algorithm by using CUDA (Compute Unified Device architecture) C. The GPU-based solver is validated in four cases: 3D Coulomb potential, 3D harmonic oscillator, three coupled anharmonic oscillators, and H 2+. Additionally, a CPU-based solver that is a serial program is developed according to the same FDTD method for the purpose of testing the effectiveness of the GPU-based solver. Relative to the CPU-based solver that employs one core of a multi-core CPU, the GPU-based solver can achieve a speed-up of more than 90X, 60X, 40X, and 90X in the case of 3D Coulomb potential, 3D harmonic oscillator, three coupled anharmonic oscillators, and H 2+, respectively. The GPU-based solver can accelerate the solution of the 3D Schrodinger equation.