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.

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  1. Latt, Jonas; Malaspinas, Orestis; Kontaxakis, Dimitrios; Parmigiani, Andrea; Lagrava, Daniel; Brogi, Federico; Belgacem, Mohamed Ben; Thorimbert, Yann; Leclaire, Sébastien; Li, Sha; Marson, Francesco; Lemus, Jonathan; Kotsalos, Christos; Conradin, Raphaël; Coreixas, Christophe; Petkantchin, Rémy; Raynaud, Franck; Beny, Joël; Chopard, Bastien: Palabos: parallel lattice Boltzmann solver (2021)
  2. Afzal, Asif; Ansari, Zahid; Rimaz Faizabadi, Ahmed; Ramis, M. K.: Parallelization strategies for computational fluid dynamics software: state of the art review (2017)
  3. Sengupta, Tapan K.; Sengupta, Aditi; Saurabh, Kumar: Global spectral analysis of multi-level time integration schemes: numerical properties for error analysis (2017)
  4. Schillinger, Dominik; Evans, John A.; Frischmann, Felix; Hiemstra, René R.; Hsu, Ming-Chen; Hughes, Thomas J. R.: A collocated (C^0) finite element method: reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics (2015)
  5. Obrecht, Christian; Asinari, Pietro; Kuznik, Frédéric; Roux, Jean-Jacques: High-performance implementations and large-scale validation of the link-wise artificial compressibility method (2014)
  6. Bosshard, Christoph; Dehbi, Abdelouahab; Deville, Michel; Leriche, Emmanuel; Puragliesi, Riccardo; Soldati, Alfredo: Large eddy simulation of the differentially heated cubic cavity flow by the spectral element method (2013)
  7. Wang, Shizhao; He, Guowei; Zhang, Xing: Parallel computing strategy for a flow solver based on immersed boundary method and discrete stream-function formulation (2013)
  8. Bosshard, Christoph; Bouffanais, Roland; Deville, Michel; Gruber, Ralf; Latt, Jonas: Computational performance of a parallelized three-dimensional high-order spectral element toolbox (2011)
  9. Gruber, R.; Ahusborde, E.; Azaïez, M.; Keller, V.; Latt, J.: High performance computing for partial differential equations (2011)
  10. Bosshard, Christoph; Bouffanais, Roland; Clémençon, Christian; Deville, Michel O.; Fiétier, Nicolas; Gruber, Ralf; Kehtari, Sohrab; Keller, Vincent; Latt, Jonas: Computational performance of a parallelized three-dimensional high-order spectral element toolbox (2009) ioport