Computational performance of a parallelized three-dimensional high-order spectral element toolbox

In this paper, a comprehensive performance review of an MPI-based high-order three-dimensional spectral element method C++ toolbox is presented. The focus is put on the performance evaluation of several aspects with a particular emphasis on the parallel efficiency. The performance evaluation is analyzed with the help of a time prediction model based on a parameterization of the application and the hardware resources. Two tailor-made benchmark cases in computational fluid dynamics (CFD) are introduced and used to carry out this review, stressing the particular interest for clusters with up to thousands of cores. Some problems in the parallel implementation have been detected and corrected. The theoretical complexities with respect to the number of elements, to the polynomial degree, and to communication needs are correctly reproduced. It is concluded that this type of code has a nearly perfect speedup on machines with thousands of cores, and is ready to make the step to next-generation petaFLOP machines.