Finite element assembly strategies on multi-core and many-core architectures

International Journal for Numerical Methods in Fluids

Volumn 71, Issue 1, 2013, Pages 80-97

  Markall, G R ^a   Slemmer, A ^a   Ham, D A ^a   Kelly, P H J ^a   Cantwell, C D ^a   Sherwin, S J ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

FEM; GPU; Many core; Multi core

Indexed keywords

ADVECTION-DIFFUSION; DISCONTINUOUS GALERKIN METHODS; FINITE ELEMENT; GPU; HIGH-LEVEL STRUCTURE; HIGH-PERFORMANCE ARCHITECTURE; LOSS OF PERFORMANCE; MANY-CORE; MANY-CORE ARCHITECTURE; MATRIX APPROACH; MEMORY ACCESS; MULTI CORE; MULTICORE ARCHITECTURES; NUMERICAL INVESTIGATIONS; PERFORMANCE POTENTIALS; REDUNDANT DATA; SPECTRAL ELEMENT METHOD;

ALGORITHMS; DATA STRUCTURES; FINITE ELEMENT METHOD; OPTIMIZATION;

MEMORY ARCHITECTURE;

EID: 84871030508     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.3648     Document Type: Article

References (37)

1. Filipovic J, Peterlik I, Fousek J. GPU Acceleration of equations assembly in finite elements method - preliminary results. SAAHPC : Symposium on Application Accelerators in HPC, 2009.
2. Komatitsch D, Michéa D, Erlebacher G. Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA. Journal of Parallel and Distributed Computing 2009; 69(5):451-460.
3. Komatitsch D, Göddeke D, Erlebacher G, Michéa D. Modeling the propagation of elastic waves using spectral elements on a cluster of 192 GPUs. Computer Science Research and Development 2010; 25(1-2):75-82. DOI: 10.1007/s00450-010-0109-1.
4. Maciol P, Plaszewski P, Banas K. 3D finite element numerical integration on GPUs. Procedia Computer Science 2010; 1(1):1087-1094, DOI: 10.1016/j.procs.2010.04.121. ICCS 2010.
5. Cecka C, Lew A, Darve E. Assembly of finite element methods on graphics processors. International Journal for Numerical Methods in Engineering 2011; 85(5):640-669.
6. Aho AV, Lam MS, Sethi R, Ullman JD. Compilers: Principles, Techniques, and Tools, (2nd edn), Addison Wesley: Hardcover, 2006.
7. Cantwell C, Sherwin S, Kirby R, Kelly P. From h to p efficiently: Strategy selection for operator evaluation on hexahedral and tetrahedral elements. Computers & Fluids 2011; 43:23-28. DOI: 10.1016/j.compfluid.2010.08.012. URL http://www.sciencedirect.com/science/article/B6V26-50V208D-1/2/5aa26c0ff5f8a0791ccdeb0651c17f61.
8. Cantwell CD, Sherwin SJ, Kirby RM, Kelly PHJ. From h to p efficiently: selecting the optimal spectral/hp discretisation in three dimensions. Mathematical Modelling of Natural Phenomena 2011; 6:84-96. DOI: 10.1051/mmnp/20116304.
9. Vos PEJ, Sherwin SJ, Kirby RM. From h to p efficiently: implementing finite and spectral/hp element methods to achieve optimal performance for low- and high-order discretisations. Journal of Computational Physics 2010; 229(13):5161-5181. DOI: http://dx.doi.org/10.1016/j.jcp.2010.03.031.
10. Logg A. Automating the finite element method. Archives of Computational Methods in Engineering 2007; 14(2):93-138.
11. NVidia. NVidia CUDA programming guide version 2.3.1, August 2009. URL: http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/NVIDIA_CUDA_Programming_Guide_2.3.pdf.
12. KhronosGroup T. OpenCL 1.0 working specification. 2008. URL http://www.khronos.org/registry/cl/specs/opencl-1.0.29.pdf.
13. NVidia. Fermi white paper, 2010. http://www.nvidia.com/content/PDF/fermi/_white/_papers/NVIDIAFermiComputeArchitectureWhitepaper.pdf, Retrieved 19 May 2011.
14. Devices AM. AMD: Unleashing the Power of Parallel Compute. SIGGRAPH Asia presentation, 2009. http://sa09.idav.ucdavis.edu/docs/SA09_AMD_IHV.pdf.
15. Filipovic J, Fousek J, Matyska L, Peterlik I. Decomposition-fusion scheme for medium-grained problems on GPU, 2010. Unpublished manuscript.
16. Asouti VG, Trompoukis XS, Kampolis IC, Giannakoglou KC. Unsteady CFD computations using vertex-centered finite volumes for unstructured grids on graphics processing units. International Journal for Numerical Methods in Fluids 2011; 67(2):232-246. DOI: 10.1002/fld.23.52.
17. Georgescu S, Okuda H. Conjugate gradients on multiple GPUs. International Journal for Numerical Methods in Fluids 2010; 64(10-12):1254-1273. DOI: 10.1002/fld.2462.
18. Engsig-Karup AP, Madsen MG, Glimberg SL. A massively parallel GPU-accelerated model for analysis of fully nonlinear free surface waves. International Journal for Numerical Methods in Fluids 2011. DOI: 10.1002/fld.2675.
19. Corrigan A, Camelli FF, Lhner R, Wallin J. Running unstructured grid-based CFD solvers on modern graphics hardware. International Journal for Numerical Methods in Fluids 2011; 66(2):221-229. DOI: 10.1002/fld.2254. URL http://dx.doi.org/10.1002/fld.2254.
20. Kirby RC, Logg A. A compiler for variational forms. ACM Transactions on Mathematical Software 2006; 32(3):417-444. URL http://home.simula.no/~logg/pub/papers/KirbyLogg2006a.pdf.
21. Sharif Z. An AEcute framework for accelerating unstructured mesh based computation using the CUDA programming model. Master's Thesis, Imperial College London, 2010.
22. Giles M. A framework for parallel unstructured grid applications on GPUs. Plenary talk at the SIAM conference on parallel processing for scientific computing (PP10), Seattle, February 2010.
23. Corrigan A, Camelli F, Lhner R, Mut F. Semi-automatic porting of a large-scale Fortran CFD code to GPUs. International Journal for Numerical Methods in Fluids 2011. DOI: 10.1002/fld.2560.
24. Corrigan A, Lhner R. Semi-automatic porting of a large-scale CFD code to multi-graphics processing unit clusters. International Journal for Numerical Methods in Fluids 2011. DOI: 10.1002/fld.2664.
25. Karniadakis GEM, Sherwin SJ. Spectral/hp Element Methods for CFD. Oxford University Press: Oxford, UK, 1999.
26. Barrett R, Berry M, Chan TF, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C, der Vorst HV. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd edition. SIAM: Philadelphia, PA, 1994.
27. Applied modelling and computation group, Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, London, SW7 2AZ, UK. Fluidity manual. Version 4.0-release edn. November 2010. Available at http://hdl.handle.net/10044/1/7086.
28. Piggott MD. About ICOM, 2010. http://amcg.ese.ic.ac.uk/index.php?title=ICOM, Retrieved 30 Sep.
29. Markall G, Kelly PHJ. Accelerating unstructured mesh computational fluid dynamics using the NVidia Tesla GPU Architecture. ISO Report, Imperial College London, 2009.
30. Balay S, Buschelman K, Gropp WD, Kaushik D, Knepley MG, McInnes LC, Smith BF, Zhang H. PETSc Web page, 2009. http://www.mcs.anl.gov/petsc.
31. Geuzaine C, Remacle JF. GMSH: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering 2009; 79(11):1309-1331.
32. Markall GR, Ham DA, Kelly PHJ. Towards generating optimised finite element solvers for GPUs from high-level specifications. Procedia Computer Science 2010; 1(1):1809-1817. DOI: 10.1016/j.procs.2010.04.203. ICCS 2010.
33. NVidia. Visual profiler user guide.
34. AMD. AMD Radeon 5870 Specifications. http://www.amd.com/us/products/desktop/graphics/ati-radeon-hd-5000/hd-5870/Pages/ati-radeon-hd-5870-overview.aspx/#2, Retrieved 30 Sep 2010.
35. NVidia. NVidia Geforce GTX480 specifications. http://www.nvidia.com/object/product_geforce_gtx_480_us.html, Retrieved 30 Sep 2010.
36. Solin P, Segeth K, Dolezel I. Higher-Order Finite Element Methods. Chapman and Hall/CRC: Boca Raton, Florida, 2003.
37. Hesthaven JS, Warburton T. Nodal Discontinuous Galerkin Methods. Springer: New York, 2007.