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Volume 6, Issue 1
Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogeneous Computers

Chunsheng Feng, Shi Shu, Jinchao Xu & Chen-Song Zhang

Adv. Appl. Math. Mech., 6 (2014), pp. 1-23.

Published online: 2014-06

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  • Abstract

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements. A central challenge in implementing GMG on GPUs, though, is that computational work on coarse levels cannot fully utilize the capacity of a GPU. In this work, we perform numerical studies of GMG on CPU-GPU heterogeneous computers. Furthermore, we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver, Fast Fourier Transform, in the cuFFT library developed by NVIDIA.

  • AMS Subject Headings

65M10, 78A48

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COPYRIGHT: © Global Science Press

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@Article{AAMM-6-1, author = {Feng , ChunshengShu , ShiXu , Jinchao and Zhang , Chen-Song}, title = {Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogeneous Computers}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {1}, pages = {1--23}, abstract = {

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements. A central challenge in implementing GMG on GPUs, though, is that computational work on coarse levels cannot fully utilize the capacity of a GPU. In this work, we perform numerical studies of GMG on CPU-GPU heterogeneous computers. Furthermore, we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver, Fast Fourier Transform, in the cuFFT library developed by NVIDIA.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m87}, url = {http://global-sci.org/intro/article_detail/aamm/2.html} }
TY - JOUR T1 - Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogeneous Computers AU - Feng , Chunsheng AU - Shu , Shi AU - Xu , Jinchao AU - Zhang , Chen-Song JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 1 EP - 23 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m87 UR - https://global-sci.org/intro/article_detail/aamm/2.html KW - High-performance computing, CPU–GPU heterogeneous computers, multigrid method, fast Fourier transform, partial differential equations. AB -

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the error at a number of frequencies simultaneously. Graphics processing units (GPUs) have recently burst onto the scientific computing scene as a technology that has yielded substantial performance and energy-efficiency improvements. A central challenge in implementing GMG on GPUs, though, is that computational work on coarse levels cannot fully utilize the capacity of a GPU. In this work, we perform numerical studies of GMG on CPU-GPU heterogeneous computers. Furthermore, we compare our implementation with an efficient CPU implementation of GMG and with the most popular fast Poisson solver, Fast Fourier Transform, in the cuFFT library developed by NVIDIA.

Chunsheng Feng, Shi Shu, Jinchao Xu & Chen-Song Zhang. (2020). Numerical Study of Geometric Multigrid Methods on CPU-GPU Heterogeneous Computers. Advances in Applied Mathematics and Mechanics. 6 (1). 1-23. doi:10.4208/aamm.2013.m87
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