DiamondTorre Algorithm for High-Performance Wave Modeling

Abstract

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.

The DiamondCandy Algorithm for Maximum Performance Vectorized Cross-Stencil Computation

“…• DiamondTorre algorithm [4] implemented for CPU with the use of SIMD (instead of CUDA threads) and OpenMP (instead of CUDA blocks).…”

“…The shape in the time-space can be thought of as a code block for computation of the points inside it. Then an LRnLA algorithm is defined as a shape with its subdivision rule [4].…”

“…The need for more asynchrony which arose with the introduction of GPU to scientific computing led to the construction of the DiamondTorre LRnLA algorithm [4].…”

“…The construction is essentially a generalization of the DiamondTorre algorithm to the 3D1T decomposition. Thus, the reader may refer to [4] for a better understanding of the illustrations.…”

Aiwlib library as the instrument for creating numerical modeling applications

“…On the contrary, quite a few tools, provided to the developer in modern C++ language, significantly speed up effective implementation of complex computational algorithms. In particular, LRnLA (locally recursive non-local-asynchronous) algorithms, which provide extremely high performance in problems of numerical simulation [6,7,8,9], were implemented on combination of C++ and Python languages with heavy use of the C++ templates mechanisms.…”