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This work proposes a basis for improved throughput of matrix-free evaluationof discontinuous Galerkin symmetric interior penalty discretizations onhexahedral elements. The basis relies on ideas of Hermite polynomials. It isused in a fully discontinuous setting not for higher order continuity but tominimize the effective stencil width, namely to limit the neighbor access of anelement to one data point for the function value and one for the derivative.The basis is extended to higher orders with nodal contributions derived fromroots of Jacobi polynomials and extended to multiple dimensions with tensorproducts, which enable the use of sum factorization. The beneficial effect ofthe reduced data access on modern processors is shown. Furthermore, theviability of the basis in the context of multigrid solvers is analyzed. While aplain point-Jacobi approach is less efficient than with the best nodalpolynomials, a basis change via sum-factorization techniques enables thecombination of the fast matrix-vector products with effective multigridconstituents. The basis change is essentially for free on modern hardwarebecause these computations can be hidden behind the cost of the data access.

A Hermite-like basis for faster matrix-free evaluation of interior penalty discontinuous Galerkin operators