Abstract
We are interested in the resolution of the 3D Helmholtz equation for real applications. Solving this problem numerically is a computational challenge due to the large memory requirements of the matrices and vectors involved.For these cases, the massive parallelism of GPU architectures and the high performance at lower energy of the multicores can be exploited. To do a fair comparison between the benefit of accelerating the three-dimensional Helmholtz equation using GPU architectures and multicore platforms, this paper describes three different parallelization schemes on a multi-GPU cluster and also includes an evaluation of their performance. The three parallel schemes consist of:(1) using the multicore processors (CPU version), (2) using the GPU devices (GPU version); and (3) using a hybrid implementation which combines CPU cores and GPU devices simultaneously (hybrid version).Experimental results show that our hybrid implementation outperforms the other approaches in terms of performance.
Chapter PDF
Similar content being viewed by others
References
Top 500 List (June 2013), http://www.top500.org/lists/2013/06/
Babuska, I.M., Sauter, S.A.: Is the pollution effect of the FEM Avoidable for the Helmholtz Equation considering high wave numbers? SIAM Rev. 42(3), 451–484 (2000)
Balay, S., et al.: PETSc Users Manual. Revision 3.3
Bao, G., Wei, G.W., Zhao, S.: Numerical solution of the Helmholtz equation with high wave numbers. Int. J. Numer. Meth. Eng. 59, 389–408 (2004)
Dautray, R., Lions, J.L.: Mathematical analysis and numerical methods for science and technology. Springer, Berlin (1990)
Ihlenburg, F., Babuska, I.: Solution of Helmholtz problems by knowledge-based FEM. CAMES 4, 397–415 (1997)
Jacobsen, D.A., Thibault, J.C., Senocak, I.: An MPI-CUDA Implementation for Massively Parallel Incompressible Flow Computations on Multi-GPU Clusters. In: Proc. of the 48th American Institute of Aeronautics and Astronautics (AIAA) Aerospace Science Meeting, Floria, USA (2010)
Junger, M.C., Feit, D.: Sound, Structures, and Their Interaction, 2nd edn. The MIT Press (1986)
Knibbe, H., Oosterlee, C.W., Vuik, C.: GPU implementation of a Helmholtz Krylov solver preconditioned by a shifted Laplace multigrid method. J. Comput. Appl. Math. 236(3), 281–293 (2011)
Lanczos, C.: An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Nat. Bur. Stand. 45, 255–282 (1950)
Lastovetsky, A.L.: Special issue of journal of parallel and distributed computing: Heterogeneity in parallel and distributed computing. J. Parallel Distrib. Comput. 72(10), 1397 (2012)
Duraiswami, R., Gumerov, N.A.: Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. Elsevier Science (2004)
NVIDIA. CUDA Programming guide. Version 4 (2011)
NVIDIA. Du-06702-001_v5.5 CUBLAS user guide. Technical report (July 2013)
Ortega, G., Garzón, E.M., Vázquez, F., García, I.: Exploiting the regularity of differential operators to accelerate solutions of PDEs on GPUs. In: Proc. of CMMSE, Benidorm, Spain, June 26-30, pp. 908–917 (2011)
Ortega, G., Garzón, E.M., Vázquez, F., García, I.: The BiConjugate gradient method on GPUs. J. Supercomput. 64, 49–58 (2013)
Ortega, G., Lobera, J., Arroyo, M.P., García, I., Garzón, E.M.: High Performance Computing for Optical Diffraction Tomography. In: Proc. of HPCS, Madrid, Spain, July 2-6, pp. 195–201 (2012)
Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM (April 2003)
Sadiku, M.N.O.: Numerical Techniques in Electromagnetics, 2nd edn. CRC Press (July 2000)
Snir, M., Otto, S., Huss-Lederman, S., Walker, D., Dongarra, J.: MPI-The Complete Reference, 2nd revised edn. The MPI Core, vol.1. MIT Press, Cambridge (1998)
Van der Vorst, H.A., Ciarlet, P.G., Iserles, A., Kohn, R.V., Wright, M.H.: Iterative Krylov Methods for Large Linear Systems. Cambridge Univ. Press (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ortega, G., García, I., Martín Garzón, G.E. (2014). A Hybrid Approach for Solving the 3D Helmholtz Equation on Heterogeneous Platforms. In: an Mey, D., et al. Euro-Par 2013: Parallel Processing Workshops. Euro-Par 2013. Lecture Notes in Computer Science, vol 8374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54420-0_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-54420-0_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54419-4
Online ISBN: 978-3-642-54420-0
eBook Packages: Computer ScienceComputer Science (R0)