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Computation 2016, 4(3), 29;

DiamondTorre Algorithm for High-Performance Wave Modeling

Keldysh Institute of Applied Mathematics, Moscow 125047, Russia
Kintech Lab, Moscow 123298, Russia
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editor: Demos T. Tsahalis
Received: 12 May 2016 / Revised: 27 June 2016 / Accepted: 8 August 2016 / Published: 12 August 2016
(This article belongs to the Special Issue High Performance Computing (HPC) Software Design)
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Effective algorithms of physical media numerical modeling problems’ solution are discussed. The computation rate of such problems is limited by memory bandwidth if implemented with traditional algorithms. The numerical solution of the wave equation is considered. A finite difference scheme with a cross stencil and a high order of approximation is used. The DiamondTorre algorithm is constructed, with regard to the specifics of the GPGPU’s (general purpose graphical processing unit) memory hierarchy and parallelism. The advantages of these algorithms are a high level of data localization, as well as the property of asynchrony, which allows one to effectively utilize all levels of GPGPU parallelism. The computational intensity of the algorithm is greater than the one for the best traditional algorithms with stepwise synchronization. As a consequence, it becomes possible to overcome the above-mentioned limitation. The algorithm is implemented with CUDA. For the scheme with the second order of approximation, the calculation performance of 50 billion cells per second is achieved. This exceeds the result of the best traditional algorithm by a factor of five. View Full-Text
Keywords: LRnLA; wave equation; finite difference; stencil; GPGPU; CUDA LRnLA; wave equation; finite difference; stencil; GPGPU; CUDA

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Levchenko, V.; Perepelkina, A.; Zakirov, A. DiamondTorre Algorithm for High-Performance Wave Modeling. Computation 2016, 4, 29.

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