An OpenCL implementation for the solution of the time-dependent Schrodinger equation on GPUs and CPUs

作者：Broin Cathal O^*; Nikolopoulos L A A

来源：Computer Physics Communications, 2012, 183(10): 2071-2080.

DOI：10.1016/j.cpc.2012.05.009

• General purpose graphical processing unit (GPGPU) programming
• Taylor series
• Runge-Kutta methods
• Time-dependent Schrodinger equation
• Quantum dynamics
• Ordinary differential equations

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 Schrodinger 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 speedup of the GPU over the CPU device. The speedup in the benchmark tended towards a value of about 40 with significant speedups expected against multi-core CPUs. Furthermore, though we do not present the detailed benchmarks here, we also have achieved speedup values of around 75 by performing a slight optimization of the described algorithm.