Generation of large finite-element matrices on multiple graphics processors

International Journal for Numerical Methods in Engineering

Volumn 94, Issue 2, 2013, Pages 204-220

  Dziekonski, A ^a   Sypek, P ^a   Lamecki, A ^a   Mrozowski, M ^a  

^a GDANSK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Fermi; Finite element method; Matrix generation; Multicore CPUs; Multiple GPUs; Parallel computing

Indexed keywords

FERMI; GENERATION PROCESS; GRAPHICS ACCELERATORS; GRAPHICS PROCESSING UNITS; GRAPHICS PROCESSOR; LARGE SPARSE LINEAR SYSTEMS; MULTI-CORE CPUS; MULTIPLE GPUS;

COMPUTER GRAPHICS; COMPUTER GRAPHICS EQUIPMENT; FINITE ELEMENT METHOD; ITERATIVE METHODS; LINEAR SYSTEMS; PARALLEL ARCHITECTURES; PARALLEL PROCESSING SYSTEMS; RANDOM ACCESS STORAGE;

PROGRAM PROCESSORS;

EID: 84875625015     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.4452     Document Type: Article

References (39)

1. Corrigan A, Camelli FF, Löhner 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.
2. Elsen E, LeGresley P, Darve E.Large calculation of the flow over a hypersonic vehicle using a GPU. Journal of Computational Physics 2008; 227(24):10148-10161. DOI: 10.1016/j.jcp.2008.08.023.
3. Mossaiby F, Rossi R, Dadvand P, Idelsohn S.OpenCL-based implementation of an unstructured edge-based finite element convection-diffusion solver on graphics hardware. International Journal for Numerical Methods in Engineering 2011; 89:1635-1651. DOI: 10.1002/nme.3302.
4. Göddeke D, Wobker H, Strzodka R, Mohd-Yusof J, McCormick P, Turek S.Co-processor acceleration of an unmodified parallel solid mechanics code with FEASTGPU. International Journal of Computational Science and Engineering 2009; 4(4):254-269. DOI: 10.1504/IJCSE.2009.029162.
5. Brad A, Bauer BA, Davis JE, Taufer M, Patel S.Molecular dynamics simulations of aqueous ions at the liquid-vapor interface accelerated using graphics processors. Journal of Computational Chemistry 2011; 32(3):375-385. DOI: 10.1002/jcc.21578.
6. Ganesan N, Bauer BA, Lucas TR, Patel S, Taufer M.Structural, dynamic, and electrostatic properties of fully hydrated DMPC bilayers from molecular dynamics simulations accelerated with graphical processing units (GPUs). Journal of Computational Chemistry 2011; 32(14):2958-2973. DOI: 10.1002/jcc.21871.
7. Inman MJ, Elsherbeni AZ.GPU acceleration of linear systems for computational electromagnetic simulations, Antennas and Propagation Society International Symposium, 1-5 June 2009. APSURSI '09. IEEE, Charleston SC, USA;1-4.
8. Tao YB, Lin H, Bao HJ.From CPU to GPU: GPU-based electromagnetic computing (GPUECO). Progress In Electromagnetics Research 2008; 81:1-19.
9. Tubbs KR, Tsai FT-C.GPU accelerated lattice Boltzmann model for shallow water flow and mass transport. International Journal for Numerical Methods in Engineering 2011; 86(3):316-334. DOI: 10.1002/nme.3066.
10. Takahashi T, Hamada T.GPU-accelerated boundary element method for Helmholtz' equation in three dimensions. International Journal for Numerical Methods in Engineering 2009; 80(10):1295-1321. DOI: 10.1002/nme.2661.
11. Takahashi T, Cecka C, Fong W, Darve E.Optimizing the multipole-to-local operator in the fast multipole method for graphical processing units. International Journal for Numerical Methods in Engineering 2012; 89(1):105-133. DOI: 10.1002/nme.3240.
12. Sypek P, Dziekonski A, Mrozowski M.How to render FDTD computations more effective using a graphics accelerator. IEEE Transactions on Magnetics 2009; 45(3):1324-1327. DOI: 10.1109/TMAG.2009.2012614.
13. Weldon M, Maxwell L, Cyca D, Hughes M, Whelan C, Okoniewski M.A Practical Look at GPU-Accelerated FDTD Performance. Journal of Applied Computational Electromagnetics Society 2010; 25(4):315-322.
14. Markall G, Slemmer A, Ham D, Kelly P, Cantwell C, Sherwin S.Finite element assembly strategies on multi-core and many-core architectures. International Journal for Numerical Methods in Fluids January 2013; 71(1):80-97.
15. Dziekonski A, Lamecki A, Mrozowski M.Tuning a Hybrid GPU-CPU V-Cycle multilevel preconditioner for solving large real and complex systems of FEM equations. IEEE Antennas and Wireless Propagation Letters 2011; 10:619-622. DOI: 10.1109/LAWP.2011.2159769.
16. Dziekonski A, Lamecki A, Mrozowski M.GPU Acceleration of multilevel solvers for analysis of microwave components with finite element method. IEEE Microwave and Wireless Components Letters 2011; 21(1):1-3. DOI: 10.1109/LMWC.2010.2089974.
17. Klockner A, Warburton T, Bridge J, Hesthaven JS.Nodal discontinuous Galerkin methods on graphics processors. Journal of Computational Physics 2009; 228(21):7863-7882. DOI: 10.1016/j.jcp.2009.06.041.
18. Zienkiewicz OC, Taylor RL.Finite Element Method Volume 1 - The Basis, 5th edn. Butterworth-Heinemann: Oxford, 2000.
19. Jin J.The Finite Element Method in Electromagnetics, 2nded. John Wiley and Sons Inc: New Jersey, 2002.
20. Asghar Bhatti M.Fundamental Finite Element Analysis and Applications: with Mathematica and Matlab Computations. John Wiley and Sons Inc: New Jersey, 2005.
21. Antoine X, Bendali A, Darbas M.Analytic preconditioners for the electric field integral equation. International Journal for Numerical Methods in Engineering 2004; 61(8):1310-1331. DOI: 10.1002/nme.1106.
22. Liu J, Jin J-M.A highly effective preconditioner for solving the finite element-boundary integral matrix equation of 3-D scattering. IEEE Transactions on Antennas and Propagation 2002; 50(9):1212-1221. DOI: 10.1109/TAP.2002.801377.
23. Dziekonski A, Lamecki A, Mrozowski M.A memory efficient and fast sparse matrix vector product on a GPU. Progress In Electromagnetics Research 2011; 116:49-63. DOI: 10.2528/PIER11031607.
24. Dehnavi MM, Fernandez DM, Giannacopoulos D.Finite-element sparse matrix vector multiplication on graphic processing units. IEEE Transactions on Magnetics 2010; 46(8):2982-2985. DOI: 10.1109/TMAG.2010.2043511.
25. Maciol P, Plaszewski P, Banas K.3D finite element numerical integration on GPUs. Procedia Computer Science 2010; 1(1):1093-1100.
26. Plaszewski P, Banas K, Maciol P.Higher order FEM numerical integration on GPUs with OpenCL. Proceedings of the 2010 International Multiconference on Computer Science and Information Technology (IMCSIT), Wisla, Poland, 18-20 October 2010; 337-342.
27. Cecka C, Lew AJ, Darve E.Assembly of finite element methods on graphics processors. International Journal for Numerical Methods in Engineering 2011; 85(5):640-669. DOI: 10.1002/nme.2989.
28. Cecka C, Lew AJ, Darve E.Application of assembly of finite element methods on graphics processors for real-time elastodynamics. GPU Computing Gems Emerald Edition, chapter 16. Elsevier Inc.: Burlington, July 2011; 187-205.
29. Dziekonski A, Sypek P, Lamecki A, Mrozowski M.Finite element matrix generation on a GPU. Progress In Electromagnetics Research 2012; 128:249-265. DOI: 10.2528/PIER12040301.
30. Whitepaper-NVIDIA's next generation CUDA compute architecture Fermi. Available from: http://www.nvidia.com/content/PDF/fermi_white_papers/NVIDIA_Fermi_Compute_Architecture_Whitepaper.pdf. [Accessed date: 2012].
31. Saad Y.Iterative Methods for Sparse Linear Systems. SIAM: Philadelphia, 2004.
32. Website of the Intel Math Kernel Library (Intel MKL). Available from: http://software.intel.com/en-us/intel-mkl. [Accessed date: 2012].
33. Sanders J, Kandrot E.CUDA by Example: An Introduction to General-purpose GPU Programming. NVIDIA Corporation: Santa Clara, 2011.
34. NVIDIA Corporation, CUDA API Reference Manual, 2011. [Accessed date: 2011].
35. Website of the UMFPACK (unsymmetric multifrontal sparse LU factorization package). Available from: http://www.cise.ufl.edu/research/sparse/umfpack. [Accessed date: 2012].
36. Whitepaper-NVIDIA's next generation CUDA compute architecture Kepler GK110. Available from: http://www.nvidia.com/content/PDF/kepler/NVIDIA-Kepler-GK110-Architecture-Whitepaper.pdf. [Accessed date: 2012].
37. Zhang L, Cui T, Liu H.A set of symmetric quadrature rules on triangles and tetrahedra. Journal of Computational Mathematics 2009; 27(1):89-96.
38. Ingelstrom P.A new set of H(curl)-conforming hierarchical basis functions for tetrahedral meshes. IEEE Transactions on Microwave Theory and Techniques 2006; 54(1):106-114. DOI: 10.1109/TMTT.2005.860295.
39. Website of the Thrust library. Available from: http://code.google.com/p/thrust/. [Accessed date: 2012].