Volume 27, Issue 2
A GPU-Accelerated Hybridizable Discontinuous Galerkin Method for Linear Elasticity

Maurice S. Fabien

Commun. Comput. Phys., 27 (2020), pp. 513-545.

Published online: 2019-12

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

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  • Abstract

We design and analyze an efficient GPU-accelerated hybridizable discontinuous Galerkin method for linear elasticity. Performance analysis of the method is done using the state-of-the-art Time-Accuracy-Size (TAS) spectrum. TAS is a new performance measure which takes into account the accuracy of the solution. Standard performance measures, like floating point operations or run-time, are not completely appropriate for gauging the performance of approximations of continuum mechanics problems, as they neglect the solutions accuracy. A standard roofline model demonstrates that our method is utilizing computational resources efficiently, and as such, significant speed ups over a serial implementation are obtained. By combining traditional performance measures and the novel time-accuracy measures [7] into our performance model, we are able to draw more complete conclusions about which discretizations are best suited for an application. Several numerical experiments validate and verify our numerical scheme.

  • Keywords

GPU-acceleration, discontinuous Galerkin, hybridization, multigrid, performance analysis.

  • AMS Subject Headings

65Y05, 74S05, 65N30, 65N55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

fabien@rice.edu (Maurice S. Fabien)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-27-513, author = {Fabien , Maurice S. }, title = {A GPU-Accelerated Hybridizable Discontinuous Galerkin Method for Linear Elasticity}, journal = {Communications in Computational Physics}, year = {2019}, volume = {27}, number = {2}, pages = {513--545}, abstract = {

We design and analyze an efficient GPU-accelerated hybridizable discontinuous Galerkin method for linear elasticity. Performance analysis of the method is done using the state-of-the-art Time-Accuracy-Size (TAS) spectrum. TAS is a new performance measure which takes into account the accuracy of the solution. Standard performance measures, like floating point operations or run-time, are not completely appropriate for gauging the performance of approximations of continuum mechanics problems, as they neglect the solutions accuracy. A standard roofline model demonstrates that our method is utilizing computational resources efficiently, and as such, significant speed ups over a serial implementation are obtained. By combining traditional performance measures and the novel time-accuracy measures [7] into our performance model, we are able to draw more complete conclusions about which discretizations are best suited for an application. Several numerical experiments validate and verify our numerical scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0235}, url = {http://global-sci.org/intro/article_detail/cicp/13457.html} }
TY - JOUR T1 - A GPU-Accelerated Hybridizable Discontinuous Galerkin Method for Linear Elasticity AU - Fabien , Maurice S. JO - Communications in Computational Physics VL - 2 SP - 513 EP - 545 PY - 2019 DA - 2019/12 SN - 27 DO - http://dor.org/10.4208/cicp.OA-2018-0235 UR - https://global-sci.org/intro/article_detail/cicp/13457.html KW - GPU-acceleration, discontinuous Galerkin, hybridization, multigrid, performance analysis. AB -

We design and analyze an efficient GPU-accelerated hybridizable discontinuous Galerkin method for linear elasticity. Performance analysis of the method is done using the state-of-the-art Time-Accuracy-Size (TAS) spectrum. TAS is a new performance measure which takes into account the accuracy of the solution. Standard performance measures, like floating point operations or run-time, are not completely appropriate for gauging the performance of approximations of continuum mechanics problems, as they neglect the solutions accuracy. A standard roofline model demonstrates that our method is utilizing computational resources efficiently, and as such, significant speed ups over a serial implementation are obtained. By combining traditional performance measures and the novel time-accuracy measures [7] into our performance model, we are able to draw more complete conclusions about which discretizations are best suited for an application. Several numerical experiments validate and verify our numerical scheme.

Maurice S. Fabien. (2019). A GPU-Accelerated Hybridizable Discontinuous Galerkin Method for Linear Elasticity. Communications in Computational Physics. 27 (2). 513-545. doi:10.4208/cicp.OA-2018-0235
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