Detailed numerical simulation of shock-body interaction in 3D multicomponent flow using the RKDG numerical method and ”DiamondTorre” GPU algorithm of implementation

Korneev, Boris; Levchenko, V. D.

doi:10.1088/1742-6596/681/1/012046

Cited by 7 publications

(4 citation statements)

References 5 publications

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“…Such codes are relevant, for example, in electromagnetic wave simulation with the FDTD method, elastic wave simulation with the Levander scheme. More complex multi-level numerical schemes often use the cross stencil as one of the computation stages as well [17]. As is, the wave equation simulation is used both in optics and in seismic codes.…”

Section: Resultsmentioning

confidence: 99%

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Performance Limits Study of Stencil Codes on Modern GPGPUs

Pershin

Levchenko

Perepelkina

2019

JSFI

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We study the performance limits of different algorithmic approaches to the implementation of a sample problem of wave equation solution with a cross stencil scheme. With this, we aim to find the highest limit of the achievable performance efficiency for stencil computing. To estimate the limits, we use a quantitative Roofline model to make a thorough analysis of the performance bottlenecks and develop the model further to account for the latency of different levels of GPU memory. These estimates provide an incentive to use spatial and temporal blocking algorithms. Thus, we study stepwise, domain decomposition, and domain decomposition with halo algorithms in that order. The knowledge of the limit incites the motivation to optimize the implementation. This led to the analysis of the block synchronization methods in CUDA, which is also provided in the text. After all optimizations, we have achieved 90% of the peak performance, which amounts to more than 1 trillion cell updates per second on one consumer level GPU device.

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Section: Resultsmentioning

confidence: 99%

“…This foreshadowed the trend for 2.5D blocking 1D streaming algorithm [13,24,31], which may be used in conjunction with temporal blocking [20]. The best performance of the applied stencil codes reaches about 30% of the peak theoretical performance [17,18,29].…”

Section: Introductionmentioning

confidence: 98%

Performance Limits Study of Stencil Codes on Modern GPGPUs

Pershin

Levchenko

Perepelkina

2019

JSFI

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“…The algorithm was implemented with the use of GPU. It was used in optics [16], seismic wave propagation [17], plasma physics [18], gas dynamics [19].…”

Section: Time-space Decompositionmentioning

confidence: 99%

The DiamondCandy Algorithm for Maximum Performance Vectorized Cross-Stencil Computation

Perepelkina

Levchenko

2018

KIAM Prepr.

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Алгоритм DiamondCandyV для повышения производительности конечноразностных вычислений c применением векторизации На основе поиска оптимальной пространственно-временной декомпозиции 3D1T пространства операций построен новый алгоритм DiamondCandyV для эффективной реализации конечно-разностных вычислений с использованием аппаратной векторизации. Базовый элемент разбиения пространства операций DiamondCandy получен пересечением областей зависимостей и влияния (конусоидов) для схем с шаблоном типа крест. Благодаря этому алгоритм характеризуется высокой вычислительной интенсивностью и локализует обрабатываемые данные на верхних уровнях иерархии памяти современных компьютеров. Ключевой особенностью алгоритма является легко реализуемая в программном коде поддержка двух основных средств повышения производительности современных процессоров, а именно аппаратной векторизации (с использованием SIMD расширения AVX) и вычислительных потоков с общей памятью (many-core CPU). Обсуждаются детали программной реализации поддержки параллельности различных уровней на примере численного решения волнового уравнения. Результаты тестирования реализации алгоритма показывают повышение производительности на порядок по сравнению с традиционными алгоритмами с пошаговой синхронизацией. Также, в отличие от традиционного подхода, с увеличением размера обрабатываемых данных производительность не деградирует.

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“…It has also been successfully implemented for finite difference time domain methods (FDTD) [26], the Runge-Kutta discrete Galerkin method [22,27] and particle-in-cell plasma simulation [23]. The LRnLA method of algorithm construction may also be applied for any other numerical methods with local dependencies and other computer systems and methods of parallelism.…”

Section: Generalizationmentioning

confidence: 99%

DiamondTorre Algorithm for High-Performance Wave Modeling

2016

Self Cite

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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.

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Detailed numerical simulation of shock-body interaction in 3D multicomponent flow using the RKDG numerical method and ”DiamondTorre” GPU algorithm of implementation

Cited by 7 publications

References 5 publications

Performance Limits Study of Stencil Codes on Modern GPGPUs

Performance Limits Study of Stencil Codes on Modern GPGPUs

The DiamondCandy Algorithm for Maximum Performance Vectorized Cross-Stencil Computation

DiamondTorre Algorithm for High-Performance Wave Modeling

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