Fast Matrix-Free Evaluation of Hybridizable Discontinuous Galerkin Operators
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This paper proposes a new algorithm for fast matrix-free evaluation of linear operators based on hybridizable discontinuous Galerkin discretizations with sum factorization, exemplified for the convection-diffusion equation on quadrilateral and hexahedral elements. The matrix-free scheme is based on a formulation of the method in terms of the primal variable and the trace. The proposed method is shown to be up to an order of magnitude faster than the traditionally considered matrix-based formulation in terms of the trace only, despite using more degrees of freedom. The impact of the choice of basis on the evaluation cost is discussed, showing that Lagrange polynomials with nodes co-located with the quadrature points are particularly efficient.
This work was supported by the German Research Foundation (DFG) under the project “High-order discontinuous Galerkin for the exa-scale” (ExaDG) within the priority program “Software for Exascale Computing” (SPPEXA), grant agreement no. KO5206/1-1, KR4661/2-1 and WA1521/18-1.
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