From h to p efficiently: Implementing finite and spectral/ hp element methods to achieve optimal performance for low- and high-order discretisations
Abstract
The spectral/ hp element method can be considered as bridging the gap between the - traditionally low-order - finite element method on one side and spectral methods on the other side. Consequently, a major challenge which arises in implementing the spectral/ hp element methods is to design algorithms that perform efficiently for both low- and high-order spectral/ hp discretisations, as well as discretisations in the intermediate regime. In this paper, we explain how the judicious use of different implementation strategies can be employed to achieve high efficiency across a wide range of polynomial orders. Furthermore, based upon this efficient implementation, we analyse which spectral/ hp discretisation (which specific combination of mesh-size h and polynomial order P) minimises the computational cost to solve an elliptic problem up to a predefined level of accuracy. We investigate this question for a set of both smooth and non-smooth problems.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- July 2010
- DOI:
- 10.1016/j.jcp.2010.03.031
- Bibcode:
- 2010JCoPh.229.5161V