From h to p Efficiently: Selecting the Optimal Spectral/hp Discretisation in Three Dimensions

There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations for evaluating operators over the space of discretisations with a desired solution tolerance, we demonstrate how the optimal discretisation and operator implementation may be selected for a specified problem. Furthermore, this demonstrates the need for codes to support both low- and high-order discretisations.