An object-oriented implementation of a solver of the time-dependent Schrödinger equation using the CUDA technology Original Research Article

We present a set of C++ classes which allow one to use the graphics card processorʼs cores for quantum ab initio simulations, i.e. a direct solving of the time-dependent Schrödinger equation, gaining the benefits from the parallel architecture of the graphical processor units. We use the Chebyshev polynomial and FFT algorithm. The solution is based on NVIDIA CUDA technology. The speed-up factor in the test runs of our classes performed using the graphics card processor can even be of order of 300 in comparison with the test runs using only the single core of CPU. Not only the Schrödinger equation can be integrated using the presented solver. With only small changes it can be used for solving the nonlinear Gross–Pitaevskii equation of BECʼs dynamics, the heat equation, the diffusion equation or other parabolic partial differential equations of second order.