DiamondTorre Algorithm for High-Performance Wave Modeling
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 cr...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2016-08-01
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| Series: | Computation |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2079-3197/4/3/29 |
| _version_ | 1818683939142762496 |
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| author | Vadim Levchenko Anastasia Perepelkina Andrey Zakirov |
| author_facet | Vadim Levchenko Anastasia Perepelkina Andrey Zakirov |
| author_sort | Vadim Levchenko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-17T10:42:42Z |
| format | Article |
| id | doaj.art-018782ac37734543a3d5d4a86406c309 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-12-17T10:42:42Z |
| publishDate | 2016-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-018782ac37734543a3d5d4a86406c3092022-12-21T21:52:12ZengMDPI AGComputation2079-31972016-08-01432910.3390/computation4030029computation4030029DiamondTorre Algorithm for High-Performance Wave ModelingVadim Levchenko0Anastasia Perepelkina1Andrey Zakirov2Keldysh Institute of Applied Mathematics, Moscow 125047, RussiaKeldysh Institute of Applied Mathematics, Moscow 125047, RussiaKintech Lab, Moscow 123298, RussiaEffective 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.http://www.mdpi.com/2079-3197/4/3/29LRnLAwave equationfinite differencestencilGPGPUCUDA |
| spellingShingle | Vadim Levchenko Anastasia Perepelkina Andrey Zakirov DiamondTorre Algorithm for High-Performance Wave Modeling Computation LRnLA wave equation finite difference stencil GPGPU CUDA |
| title | DiamondTorre Algorithm for High-Performance Wave Modeling |
| title_full | DiamondTorre Algorithm for High-Performance Wave Modeling |
| title_fullStr | DiamondTorre Algorithm for High-Performance Wave Modeling |
| title_full_unstemmed | DiamondTorre Algorithm for High-Performance Wave Modeling |
| title_short | DiamondTorre Algorithm for High-Performance Wave Modeling |
| title_sort | diamondtorre algorithm for high performance wave modeling |
| topic | LRnLA wave equation finite difference stencil GPGPU CUDA |
| url | http://www.mdpi.com/2079-3197/4/3/29 |
| work_keys_str_mv | AT vadimlevchenko diamondtorrealgorithmforhighperformancewavemodeling AT anastasiaperepelkina diamondtorrealgorithmforhighperformancewavemodeling AT andreyzakirov diamondtorrealgorithmforhighperformancewavemodeling |