Abstract
This paper addresses the resolution of the transport (advection–diffusion) equation in 3D by the use of the finite difference method as a discretization technique. In particular, our focus is the comparison of different time schemes (implicit, explicit and predictor-corrector) from the viewpoint of the numerical accuracy and the performance scalability in the use of massively parallel platforms. More in detail, each scheme is implemented in two parallel codes (C+CUDA and C+OpenMP), and in a sequential one (in C). We evaluated the performance of each implementation using several sizes of grid, and also, we measured the precision of these schemes for different discretization levels. The obtained results show that the GPU-based implementations offer significant speed-ups as compared to the CPU counterpart. Moreover, the explicit methods offer a much better performance scalability on this kind of massively parallel devices. This situation reveals that explicit methods can outperform implicit ones even if the accuracy is considered at least in contexts of non stiff problems.
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Acknowledgments
The authors acknowledge support from Agencia Nacional de Investigación e Innovación (ANII), the Programa de Desarrollo de las Ciencias Básicas (PEDECIBA) and the Comisión Coordinadora del Interior (CCI) of the Universidad de la Repblica (UDELAR), Uruguay.
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Bondarenco, M., Gamazo, P. & Ezzatti, P. A comparison of various schemes for solving the transport equation in many-core platforms. J Supercomput 73, 469–481 (2017). https://doi.org/10.1007/s11227-016-1889-2
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DOI: https://doi.org/10.1007/s11227-016-1889-2