Exploiting batch processing on streaming architectures to solve 2D elliptic finite element problems: a hybridized discontinuous Galerkin (HDG) case study. Numerical methods for elliptic partial differential equations (PDEs) within both continuous and hybridized discontinuous Galerkin (HDG) frameworks share the same general structure: local (elemental) matrix generation followed by a global linear system assembly and solve. The lack of inter-element communication and easily parallelizable nature of the local matrix generation stage coupled with the parallelization techniques developed for the linear system solvers make a numerical scheme for elliptic PDEs a good candidate for implementation on streaming architectures such as modern graphical processing units (GPUs). We propose an algorithmic pipeline for mapping an elliptic finite element method to the GPU and perform a case study for a particular method within the HDG framework. This study provides comparison between CPU and GPU implementations of the method as well as highlights certain performance-crucial implementation details. The choice of the HDG method for the case study was dictated by the computationally-heavy local matrix generation stage as well as the reduced trace-based communication pattern, which together make the method amenable to the fine-grained parallelism of GPUs. We demonstrate that the HDG method is well-suited for GPU implementation, obtaining total speedups on the order of 30-35 times over a serial CPU implementation for moderately sized problems.

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  1. Gong, Minjiang; Xiong, Chengwang; Mao, Xuerui; Cheng, Liang; Wang, Shi-Ping; Zhang, A-Man: Non-modal growth of finite-amplitude disturbances in oscillatory boundary layer (2022)
  2. Jaiswal, Shashank: Non-linear Boltzmann equation on hybrid-unstructured non-conforming multi-domains (2022)
  3. Laughton, Edward; Zala, Vidhi; Narayan, Akil; Kirby, Robert M.; Moxey, David: Fast barycentric-based evaluation over spectral/\textithpelements (2022)
  4. Pan, Yu; Yan, Zhen-Guo; Peiró, Joaquim; Sherwin, Spencer J.: Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver (2022)
  5. Ye, Ximeng; Qin, Guoliang; Zhuo, Ya; Li, Miaomiao: Analysis/application of stabilization by the over-integration technique in CBS-SEM for incompressible flow (2022)
  6. Zeifang, Jonas; Schütz, Jochen: Implicit two-derivative deferred correction time discretization for the discontinuous Galerkin method (2022)
  7. Arthurs, Christopher J.; King, Andrew P.: Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations (2021)
  8. Basso, R. L. G.; Hwang, Y.; Assi, G. R. S.; Sherwin, S. J.: Instabilities and sensitivities in a flow over a rotationally flexible cylinder with a rigid splitter plate (2021)
  9. Dürrwächter, Jakob; Kurz, Marius; Kopper, Patrick; Kempf, Daniel; Munz, Claus-Dieter; Beck, Andrea: An efficient sliding mesh interface method for high-order discontinuous Galerkin schemes (2021)
  10. Fehn, Niklas; Heinz, Johannes; Wall, Wolfgang A.; Kronbichler, Martin: High-order arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the incompressible Navier-Stokes equations (2021)
  11. Fortunato, Daniel; Hale, Nicholas; Townsend, Alex: The ultraspherical spectral element method (2021)
  12. Frontin, Cory V.; Walters, Gage S.; Witherden, Freddie D.; Lee, Carl W.; Williams, David M.; Darmofal, David L.: Foundations of space-time finite element methods: polytopes, interpolation, and integration (2021)
  13. Hester, Eric W.; Vasil, Geoffrey M.; Burns, Keaton J.: Improving accuracy of volume penalised fluid-solid interactions (2021)
  14. He, Wei; Timme, Sebastian: Triglobal infinite-wing shock-buffet study (2021)
  15. Jiang, Hongyi: Formation mechanism of a secondary vortex street in a cylinder wake (2021)
  16. Jiang, Hongyi: Three-dimensional wake transition of a diamond-shaped cylinder (2021)
  17. Kopriva, David A.; Gassner, Gregor J.: A split-form, stable CG/DG-SEM for wave propagation modeled by linear hyperbolic systems (2021)
  18. Krais, Nico; Beck, Andrea; Bolemann, Thomas; Frank, Hannes; Flad, David; Gassner, Gregor; Hindenlang, Florian; Hoffmann, Malte; Kuhn, Thomas; Sonntag, Matthias; Munz, Claus-Dieter: FLEXI: a high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws (2021)
  19. Laughton, Edward; Tabor, Gavin; Moxey, David: A comparison of interpolation techniques for non-conformal high-order discontinuous Galerkin methods (2021)
  20. Mengaldo, Gianmarco; Moxey, David; Turner, Michael; Moura, Rodrigo Costa; Jassim, Ayad; Taylor, Mark; Peiró, Joaquim; Sherwin, Spencer: Industry-relevant implicit large-eddy simulation of a high-performance road car via spectral/(hp) element methods (2021)

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