An OpenCL implementation for the solution of TDSE on GPU and CPU architectures

Open Computing Language (OpenCL) is a parallel processing language that is ideally suited for running parallel algorithms on Graphical Processing Units (GPUs). In the present work we report on the development of a generic parallel single-GPU code for the numerical solution of a system of first-order ordinary differential equations (ODEs) based on the OpenCL model. We have applied the code in the case of the Time-Dependent Schr\"odinger Equation of atomic hydrogen in a strong laser field and studied its performance on NVIDIA and AMD GPUs against the serial performance on a CPU. We found excellent scalability and a significant speed-up of the GPU over the CPU device which tended towards a value of about 40 with significant speedups expected against multi-core CPUs.