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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.


References in zbMATH (referenced in 43 articles , 1 standard article )

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  1. Cantwell, Chris D.; Nielsen, Allan S.: A minimally intrusive low-memory approach to resilience for existing transient solvers (2019)
  2. Abide, Stéphane; Viazzo, Stéphane; Raspo, Isabelle; Randriamampianina, Anthony: Higher-order compact scheme for high-performance computing of stratified rotating flows (2018)
  3. Badia, Santiago; Martín, Alberto F.; Principe, Javier: \textttFEMPAR: an object-oriented parallel finite element framework (2018)
  4. Kopriva, David A.: Stability of overintegration methods for nodal discontinuous Galerkin spectral element methods (2018)
  5. Mengaldo, Gianmarco; De Grazia, Daniele; Moura, Rodrigo C.; Sherwin, Spencer J.: Spatial eigensolution analysis of energy-stable flux reconstruction schemes and influence of the numerical flux on accuracy and robustness (2018)
  6. Mengaldo, G.; Moura, R. C.; Giralda, B.; Peiró, J.; Sherwin, S. J.: Spatial eigensolution analysis of discontinuous Galerkin schemes with practical insights for under-resolved computations and implicit LES (2018)
  7. Minjeaud, Sebastian; Pasquetti, Richard: High order (C^0)-continuous Galerkin schemes for high order PDEs, conservation of quadratic invariants and application to the Korteweg-de Vries model (2018)
  8. Xin, Dabo; Zhang, Hongfu; Ou, Jinping: Secondary wake instability of a bridge model and its application in wake control (2018)
  9. Xiong, Chengwang; Cheng, Liang; Tong, Feifei; An, Hongwei: Oscillatory flow regimes for a circular cylinder near a plane boundary (2018)
  10. Xiong, Chengwang; Cheng, Liang; Tong, Feifei; An, Hongwei: Influence of plane boundary proximity on the Honji instability (2018)
  11. Xiong, Chengwang; Cheng, Liang; Tong, Feifei; An, Hongwei: On regime C flow around an oscillating circular cylinder (2018)
  12. Yu, Jian; Yan, Chao; Jiang, Zhenhua: Revisit of dilation-based shock capturing for discontinuous Galerkin methods (2018)
  13. Chun, Sehun: Method of moving frames to solve time-dependent Maxwell’s equations on anisotropic curved surfaces: applications to invisible cloak and ELF propagation (2017)
  14. Chun, S.; Eskilsson, C.: Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces (2017)
  15. Docampo-Sánchez, Julia; Ryan, Jennifer K.; Mirzargar, Mahsa; Kirby, Robert M.: Multi-dimensional filtering: reducing the dimension through rotation (2017)
  16. He, W.; Gioria, R. S.; Pérez, J. M.; Theofilis, V.: Linear instability of low Reynolds number massively separated flow around three NACA airfoils (2017)
  17. Jomo, John N.; Zander, Nils; Elhaddad, Mohamed; Özcan, Ali; Kollmannsberger, Stefan; Mundani, Ralf-Peter; Rank, Ernst: Parallelization of the multi-level (hp)-adaptive finite cell method (2017)
  18. Moura, R. C.; Mengaldo, G.; Peiró, J.; Sherwin, S. J.: On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence (2017)
  19. Santiago Badia, Alberto F. Martin, Javier Principe: FEMPAR: An object-oriented parallel finite element framework (2017) arXiv
  20. Serson, D.; Meneghini, J. R.; Sherwin, S. J.: Direct numerical simulations of the flow around wings with spanwise waviness at a very low Reynolds number (2017)

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