Linearizing the hybridizable discontinuous Galerkin method: A linearly scaling operator

Abstract

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 $\mu s$ per unknown on one CPU core - a number typically associated with low-order methods.

References in corpus (4)

• Fast matrix-free evaluation of discontinuous Galerkin finite element operators
• Robust multigrid for high-order discontinuous Galerkin methods: A fast Poisson solver suitable for high-aspect ratio Cartesian grids
• Scaling to the stars -- a linearly scaling elliptic solver for $p$-multigrid
• Factorizing the factorization - a spectral-element solver for elliptic equations with linear operation count