Linearizing the hybridizable discontinuous Galerkin method: A linearly scaling operator

07/23/2020

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by   Immo Huismann, et al.

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This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from application of tensor-product bases on cuboidal Cartesian elements, a specific choice for the penalty parameter, and the fast diagonalization technique. In combination with a linearly scaling, face-wise preconditioner, a linearly scaling iteration time for a conjugate gradient method is attained. This allows for solutions in 1 μ s per unknown on one CPU core - a number typically associated with low-order methods.