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

[An open-access article; the PDF is free to any online user.]

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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.

  • Keywords

High-performance computing CPU-GPU heterogeneous computers multigrid method fast Fourier transform partial differential equations

  • AMS Subject Headings

65M10 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-1, author = {}, 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 JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 1 EP - 23 PY - 2014 DA - 2014/06 SN - 6 DO - http://dor.org/10.4208/aamm.2013.m87 UR - https://global-sci.org/intro/aamm/2.html KW - High-performance computing KW - CPU-GPU heterogeneous computers KW - multigrid method KW - fast Fourier transform KW - 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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