Parallelizing a High-Order CFD Software for 3D, Multi-block, Structural Grids on the TianHe-1A Supercomputer

Xu, Chuanfu; Deng, Xiaogang; Zhang, Lilun; Jiang, Yi; Cao, Wei; Fang, Jianbin; Che, Yue; Wang, Yongxian; Liu, Wei

doi:10.1007/978-3-642-38750-0_3

Cited by 6 publications

(2 citation statements)

References 24 publications

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“…Large scale applications and algorithms in science and engineering such as neutron transport [90][91][92], light transport [93], computational fluid dynamics [94,95], molecular dynamics [96], and computational finance and different numerical methods [97] rely on parallel computing [98,99].…”

Section: Parallel Computingmentioning

confidence: 99%

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

Gong

Bao

Tang

et al. 2015

Mathematical Problems in Engineering

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We present a survey of fractional differential equations and in particular of the computational cost for their numerical solutions from the view of computer science. The computational complexities of time fractional, space fractional, and space-time fractional equations areO(N2M),O(NM2), andO(NM(M+N)) compared withO(MN) for the classical partial differential equations with finite difference methods, whereM,Nare the number of space grid points and time steps. The potential solutions for this challenge include, but are not limited to, parallel computing, memory access optimization (fractional precomputing operator), short memory principle, fast Fourier transform (FFT) based solutions, alternating direction implicit method, multigrid method, and preconditioner technology. The relationships of these solutions for both space fractional derivative and time fractional derivative are discussed. The authors pointed out that the technologies of parallel computing should be regarded as a basic method to overcome this challenge, and some attention should be paid to the fractional killer applications, high performance iteration methods, high order schemes, and Monte Carlo methods. Since the computation of fractional equations with high dimension and variable order is even heavier, the researchers from the area of mathematics and computer science have opportunity to invent cornerstones in the area of fractional calculus.

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Section: Parallel Computingmentioning

confidence: 99%

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

Gong

Bao

Tang

et al. 2015

Mathematical Problems in Engineering

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“…Parallel computing is used to solve computation intensive applications simultaneously [17][18][19]. In recent years, the computing accelerators such as graphics processing unit (GPU) provided a new parallel method of accelerating computation intensive simulations [20][21][22]. The use of general purpose GPU is possible by the advance of programming models and hardware resources.…”

Section: Introductionmentioning

confidence: 99%

Solving the Caputo Fractional Reaction-Diffusion Equation on GPU

Liu

Gong

Bao

et al. 2014

Discrete Dynamics in Nature and Society

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We present a parallel GPU solution of the Caputo fractional reaction-diffusion equation in one spatial dimension with explicit finite difference approximation. The parallel solution, which is implemented with CUDA programming model, consists of three procedures: preprocessing, parallel solver, and postprocessing. The parallel solver involves the parallel tridiagonal matrix vector multiplication, vector-vector addition, and constant vector multiplication. The most time consuming loop of vector-vector addition and constant vector multiplication is optimized and impressive performance improvement is got. The experimental results show that the GPU solution compares well with the exact solution. The optimized GPU solution on NVIDIA Quadro FX 5800 is 2.26 times faster than the optimized parallel CPU solution on multicore Intel Xeon E5540 CPU.

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GPU parallelization of multigrid RANS solver for three-dimensional aerodynamic simulations on multiblock grids

2018

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Parallelizing a High-Order CFD Software for 3D, Multi-block, Structural Grids on the TianHe-1A Supercomputer

Cited by 6 publications

References 24 publications

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

Computational Challenge of Fractional Differential Equations and the Potential Solutions: A Survey

Solving the Caputo Fractional Reaction-Diffusion Equation on GPU

GPU parallelization of multigrid RANS solver for three-dimensional aerodynamic simulations on multiblock grids

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