Improved Performance for Nodal Spectral Element Operators

Abstract

The computational performance of the nodal spectral element method (SEM) for tetrahedral grids is evaluated in the context of a high-performance computing platform. The elemental SEM operator is accelerated by the symmetry-based factorization technique of Hesthaven and Teng (SIAM J. Sci. Comp. 21, p. 2352, 2000), which results in a reduced number of floating point operations and memory accesses. However, performance evaluation reveals that a naive implementation of the algorithm causes a severe degradation of computational efficiency. Two algorithmic modifications are proposed which regain (and partly exceed) the efficiency of the original, non-factorized operator and thus recover the asymptotic 9/5 speedup due to factorization.