Abstract
This paper concentrates on an OpenMP implementation of the TVD–Hopmoc method with executions performed on Intel® Many Integrated Core and Xeon® Scalable Processor architectures. Specifically, this paper evaluates an improved OpenMP implementation of the TVD–Hopmoc method based on a cluster of points when applied to the convection–diffusion equation in 1–D. Aiming at avoiding fine-grained parallelism employed in a basic OpenMP implementation of the TVD–Hopmoc method, this approach groups variables (located at stencil points) to be calculated simultaneously in parallel instead of calculating them individually. Numerical experiments performed on Intel® Many Integrated Core and Scalable Processor architectures show that the improved OpenMP implementation of the TVD–Hopmoc method based on a cluster of points provides further worthwhile gains when compared both with our previous implementation based only on parallel chunk loops and a basic OpenMP implementation of this method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Holstad, A.: The Koren upwind scheme for variable gridsize. Appl. Num. Math. 37, 459–487 (2001)
Oliveira, S.R.F., de Oliveira, S.L.G., Kischinhevsky, M.: Convergence analysis of the Hopmoc method. Int. J. Comput. Math. 86, 1375–1393 (2009)
Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49, 357–393 (1983)
Brandão, D.N., Gonzaga de Oliveira, S.L., Kischinhevsky, M., Osthoff, C., Cabral, F.: A total variation diminishing hopmoc scheme for numerical time integration of evolutionary differential equations. In: Gervasi, O., et al. (eds.) ICCSA 2018. LNCS, vol. 10960, pp. 53–66. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-95162-1_4
Ma, H., Zhao, R., Gao, X., Zhang, Y.: Barrier optimization for OpenMP program. In: Proceedings of 10th ACIS International Conference on Software Engineering, Artificial Intelligences, Networking, Parallel and Distributed Computing, pp. 495–500 (2009)
Caballero, D., Duran, A., Martorell, X.: An OpenMP* barrier using SIMD Instructions for Intel® Xeon PhiTM coprocessor. In: Rendell, A.P., Chapman, B.M., Müller, M.S. (eds.) IWOMP 2013. LNCS, vol. 8122, pp. 99–113. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40698-0_8
Cabral, F.L., Osthoff, C., Kischinhevsky, M., Brandão, D.: Hybrid MPI/OpenMP/OpenACC implementations for the solution of convection diffusion equations with HOPMOC Method. In: Proceedings of 14th International Conference on Computational Science and Its Applications (ICCSA), pp. 196–199 (2014)
Cabral, F.L., Osthoff, C., Costa, G.P., Brandão, D., de Oliveira, S.L.G.: Tuning up TVD HOPMOC method on Intel MIC Xeon Phi architectures with Intel Parallel Studio Tools. In: Proceedings of the International Symposium on Computer Architecture and High Performance Computing Workshops (SBAC-PADW), pp. 19–23 (2017)
Gourlay, A.R., McKee, S.: The construction of Hopscotch methods for parabolic and elliptic equations in two space dimensions with mixed derivative. J. Comput. Appl. Math. 3, 201–206 (1977)
van Leer, B.: Towards the ultimate conservative difference schemes. J. Comput. Phys. 361–370 (1974)
Douglas Jr., J., Russel, T.F.: Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures. SIAM J. Num. Anal. 19, 871–885 (1982)
Acknowledgement
The Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), and Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) supported this work. We would like to thank the Núcleo de Computação Científica at Universidade Estadual Paulista (NCC/UNESP) for letting us execute our simulations on its heterogeneous multi-core cluster. These resources were partially funded by Intel® through the projects entitled Intel Parallel Computing Center, Modern Code Partner, and Intel/Unesp Center of Excellence in Machine Learning.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Cabral, F. et al. (2019). An Improved OpenMP Implementation of the TVD–Hopmoc Method Based on a Cluster of Points. In: Senger, H., et al. High Performance Computing for Computational Science – VECPAR 2018. VECPAR 2018. Lecture Notes in Computer Science(), vol 11333. Springer, Cham. https://doi.org/10.1007/978-3-030-15996-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-15996-2_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-15995-5
Online ISBN: 978-3-030-15996-2
eBook Packages: Computer ScienceComputer Science (R0)