Accelerating the Fourier split operator method via graphics processing units
Abstract: Current generations of graphics processing units have turned into highly parallel devices with general computing capabilities. Thus, graphics processing units may be utilized, for example, to solve time dependent partial differential equations by the Fourier split operator method. In this contribution, we demonstrate that graphics processing units are capable to calculate fast Fourier transforms much more efficiently than traditional central processing units. Thus, graphics processing units render efficient implementations of the Fourier split operator method possible. Performance gains of more than an order of magnitude as compared to implementations for traditional central processing units are reached in the solution of the time dependent Schrodinger equation and the time dependent Dirac equation.
Conclusions and outlook
In this contribution we evaluated GPUs as a massively parallel computing architecture for the solution of time dependent partial differential equations by means of the Fourier split operator method. The computational complexity of the Fourier split operator method is dominated by the computational complexity of the fast Fourier transform. We demonstrated that GPUs reach much better performance in computing the fast Fourier transform than current CPUs. Depending on the problem size, the performance gain may exceed one order of magnitude as compared to sequential CPU implementations. Thus, the Fourier split operator method may be implemented very efficiently on GPU architectures as we demonstrated for the time dependent Schrödinger equation and the time dependent Dirac equation. The combination of a highly parallel architecture with a high-throughput memory makes graphics processing units a very attractive architecture for implementing the Fourier split operator method. Best performance is attained if all steps of the Fourier split operator method are carried out by the GPU avoiding data transfer between host memory and GPU memory.
The fast Fourier transform is a core building block for the solution of partial differential equations as well as of many other problems from computational physics, signal processing, tomography, computational finance and other fields. Thus, we expect that also these problems may be solved much more efficiently on GPU architectures than on conventional CPUs. Taking into account that GPU computing is a rather young field it is supposed that there is still plenty potential for GPU technology and codes to mature further and to find new applications.
| Subjects: | Computational Physics (physics.comp-ph); Quantum Physics (quant-ph) |
| Cite as: | arXiv:1012.3911v1 [physics.comp-ph] |
Category: Computer Science, Software
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