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Exploiting Batch Processing on Streaming Architectures to Solve 2D Elliptic Finite Element Problems: A Hybridized Discontinuous Galerkin (HDG) Case Study

James King, Sergey Yakovlev, Zhisong Fu, Robert M. Kirby, Spencer J. Sherwin
2013 Journal of Scientific Computing  
elliptic problems as well as per-stage benefits and the runtime trends for different stages; (b) to propose a pipeline for solving 2D elliptic finite element problems on GPUs and provide a case study  ...  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.  ...  Acknowledgments We would like to thank Professor B. Cockburn (U. Minnesota) for the helpful discussions on this topic.  ... 
doi:10.1007/s10915-013-9805-x fatcat:ravje3gtsjbcvhfzpb42xt4mxy

Hybrid multigrid methods for high-order discontinuous Galerkin discretizations [article]

Niklas Fehn, Peter Munch, Wolfgang A. Wall, Martin Kronbichler
2019 arXiv   pre-print
The present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems.  ...  Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE solver.  ...  Acknowledgments The research presented in this paper was partly funded by the German Research Foundation (DFG) under the project "High-order discontinuous Galerkin for the EXA-scale" (ExaDG) within the  ... 
arXiv:1910.01900v1 fatcat:7dfh25442ngezart4vkhhesaqa

A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers

Martin Kronbichler, Wolfgang A. Wall
2018 SIAM Journal on Scientific Computing  
This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin method  ...  For the hybridized discontinuous Galerkin method, a multigrid approach that combines a grid transfer from the trace space to the space of linear finite elements with algebraic multigrid on further levels  ...  Acknowledgments The authors would like to thank Katharina Kormann and Niklas Fehn for discussions about the manuscript.  ... 
doi:10.1137/16m110455x fatcat:o7o7ddc7fnhstnzcgrwld7mpoy

A GPU-Accelerated Hybridizable Discontinuous Galerkin Method for Linear Elasticity

Maurice S. Fabien
2020 Communications in Computational Physics  
We design and analyze an efficient GPU-accelerated hybridizable discontinuous Galerkin method for linear elasticity.  ...  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.  ...  Acknowledgments The author would like to thank Professor R. A. Tapia for directing the XSEDE Scholars Program (2011-2017), as well as A. Weeden and Dr. R.  ... 
doi:10.4208/cicp.oa-2018-0235 fatcat:3tovcggsxvbp5dy5qfmvjtz5fi

Proceedings of the FEniCS Conference 2017

Jack S. Hale
2017 Figshare  
Proceedings of the FEniCS Conference 2017 that took place 12-14 June 2017 at the University of Luxembourg, Luxembourg.You can cite individual articles in the proceedings using the following bibtex as a  ...  Additionally, there is a useful project called Batch Shipyard [2] which simplifies the deployment of Docker on Azure. The performance is very good for medium sized problems.  ...  Because of privilege restrictions on HPC, it is necessary to use a different runtime, such as Shifter or Singularity, rather than Docker.  ... 
doi:10.6084/m9.figshare.5086369.v1 fatcat:siyz4enqijbp5byzmdrvi75owm