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

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. 1Program summaryProgram title: QnDynCUDACatalogue identifier: AELE_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELE_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 101 359No. of bytes in distributed program, including test data, etc.: 3 165 228Distribution format: tar.gzProgramming language: C++, C for CUDAComputer: Graphics card with CUDA technology recommendedOperating system: No limits (tested on 32-bit and 64-bit Windows and 64-bit Linux)Has the code been vectorized or parallelized?: Yes, number of processors used – one CPU core and all CUDA cores of the selected processor of graphics cardRAM: Dependent on userʼs parameters, typically between several tens of megabytes and several gigabytes (this concerns also the graphics cardʼs memory)Supplementary material: Test input and output files (approx. 3.4 Gigabytes) are availableClassification: 2.7, 6.5Nature of problem: Solving the time-dependent Schrödinger equation.Solution method: FFT and Chebyshev polynomial algorithm, CUDA technology.Running time: Every test example included in the distribution package takes approximately an hour or so if the GPU is engaged and a day or so if only CPU is used.