Architecting the finite element method pipeline for the GPU

Journal of Computational and Applied Mathematics

Volumn 257, Issue , 2014, Pages 195-211

  Fu, Zhisong ^b   James Lewis, T ^b   Kirby, Robert M ^b   Whitaker, Ross T ^a  

^a University of Utah   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

Algebraic multigrid (AMG); Finite element method (FEM); Graphical processing units (GPUs)

Indexed keywords

ALGEBRAIC MULTIGRID METHODS; ALGEBRAIC MULTIGRIDS; FINE-GRAINED PARALLELISM; GRAPHICAL PROCESSING UNIT (GPUS); GRAPHICAL PROCESSING UNITS; MANY-CORE ARCHITECTURE; PARTIAL DIFFERENTIAL EQUATIONS (PDES); SCIENCE AND ENGINEERING;

ALGEBRA; ALGORITHMS; COMPUTER ARCHITECTURE; CONJUGATE GRADIENT METHOD; DISTRIBUTED COMPUTER SYSTEMS; FINITE ELEMENT METHOD; LINEAR SYSTEMS; PARALLEL ARCHITECTURES; PARTIAL DIFFERENTIAL EQUATIONS; PIPELINES; PROGRAM PROCESSORS;

COMPUTER GRAPHICS EQUIPMENT;

EID: 84884657209     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2013.09.001     Document Type: Article

References (40)

1. T.J.R. Hughes The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 1987 Prentice-Hall
2. G. Karniadakis, and S.J. Sherwin Spectral/hp element methods for CFD Numerical Mathematics and Scientific Computation 1999 Oxford University Press
3. NVIDIA, Nvidia cuda programming guide. URL: http://developer.nvidia.com/ nvidia-gpu-computing-documentation.
4. G. Markall, A. Slemmer, D. Ham, P. Kelly, C. Cantwell, and S. Sherwin Finite element assembly strategies on multi-core and many-core architectures International Journal for Numerical Methods in Fluids 71 2013 80 97
5. A. Dziekonski, P. Sypek, A. Lamecki, and M. Mrozowski Accuracy, memory, and speed strategies in GPU-based finite-element matrix-generation Antennas and Wireless Propagation Letters, IEEE 11 2012 1346 1349
6. A. Dziekonski, P. Sypek, A. Lamecki, and M. Mrozowski Finite element matrix generation on a GPU Progress in Electromagnetics Research 128 2012 249 265
7. A. Dziekonski, P. Sypek, A. Lamecki, and M. Mrozowski Generation of large finite-element matrices on multiple graphics processors International Journal for Numerical Methods in Engineering 94 2 2013 204 220
8. C. Cecka, A.J. Lew, and E. Darve Assembly of finite element methods on graphics processors International Journal for Numerical Methods in Engineering 85 2011 640 669
9. L.N. Trefethen, and D.B. III Numerical Linear Algebra 1997 SIAM: Society for Industrial and Applied Mathematics
10. J.W. Demmel Applied Numerical Linear Algebra 1997 SIAM: Society for Industrial and Applied Mathematics
11. N. Bell, S. Dalton, and L. Olson Exposing fine-grained parallelism in algebraic multigrid methods SIAM Journal on Scientific Computing 34 4 2012 C123 C152
12. G. Haase, M. Liebmann, C.C. Douglas, and G. Plank A parallel algebraic multigrid solver on graphics processing units W. Zhang, Z. Chen, C.C. Douglas, W. Tong, HPCA (China) Lecture Notes in Computer Science vol. 5938 2009 Springer 38 47
13. M. Potse, B. Dube, J. Richer, A. Vinet, and R. Gulrajani A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart IEEE Transactions on Biomedical Engineering 53 12 2006 2425 2435 (Pubitemid 46019529)
14. J. Bolz, I. Farmer, E. Grinspun, and P. Schröder Sparse matrix solvers on the GPU: conjugate gradients and multigrid ACM Transactions on Graphics 22 3 2003 917 924
15. J. Rodríguez-Navarro, A.S. Sánchez, Non structured meshes for cloth GPU simulation using FEM, 2006.
16. A. Klöckner, T. Warburton, J. Bridge, and J.S. Hesthaven Nodal discontinuous Galerkin methods on graphics processors Journal of Computational Physics 228 21 2009 7863 7882
17. D. Komatitsch, D. Michéa, and G. Erlebacher Porting a high-order finite-element earthquake modeling application to NVIDIA graphics cards using CUDA Journal of Parallel and Distributed Computing 69 5 2009 451 460
18. P.E.J. Vos, S.J. Sherwin, and R.M. Kirby 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 229 2010 5161 5181
19. I. Kiss, S. Gyimothy, Z. Badics, and J. Pavo Parallel realization of the element-by-element fem technique by cuda IEEE Transactions on Magnetics 48 2 2012 507 510
20. C. Cantwell, S. Sherwin, R. Kirby, and P. Kelly From h to p efficiently: strategy selection for operator evaluation on hexahedral and tetrahedral elements Computers & Fluids 43 2011 23 28
21. Y. Saad Iterative Methods for Sparse Linear Systems second ed. 2003 SIAM
22. R. Li, and Y. Saad GPU-accelerated Preconditioned Iterative Linear Solvers, Tech. Rep., Technical Report, University of Minnesota 2010
23. S.F. McCormick Multigrid Methods 1987 SIAM Publications
24. A. Brandt, and O. Livne Multigrid Techniques: 1984 Guide With Applications to Fluid Dynamics Revised ed., Classics in Applied Mathematics 2011 Society for Industrial and Applied Mathematics
25. V.E. Henson, and U.M. Yang BoomerAMG: a parallel algebraic multigrid solver and preconditioner Applied Numerical Mathematics: Transactions of IMACS 41 1 2002 155 177 (Pubitemid 34154710)
26. P. Vanek, J. Mandel, and M. Brezina Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems Computing 56 3 1996 179 196 (Pubitemid 126633416)
27. M. Adams, and J. Demmel Parallel multigrid solver for 3D unstructured finite element problems Proceedings of Supercomputing'99 (CD-ROM) 1999 ACM SIGARCH and IEEE Portland, OR
28. A.H. Baker, R.D. Falgout, T.V. Kolev, and U.M. Yang Multigrid smoothers for ultraparallel computing SIAM Journal on Scientific Computing 33 5 2011 2864 2887
29. R.S. Tuminaro, C. Tong, Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines, in: SuperComputing 2000 Proceedings, 2000.
30. N. Bell, and M. Garland Efficient Sparse Matrix-Vector Multiplication on CUDA, NVIDIA Technical Report NVR-2008-004 2008 NVIDIA Corporation
31. M. Geveler, D. Ribbrock, D. Goddeke, P. Zajac, and S. Turek Towards a complete fem-based simulation toolkit on GPUs: unstructured grid finite element geometric multigrid solvers with strong smoothers based on sparse approximate inverses Computers & Fluids 80 0 2013 327 332
32. A. Dziekonski, A. Lamecki, and M. Mrozowski GPU acceleration of multilevel solvers for analysis of microwave components with finite element method Microwave and Wireless Components Letters, IEEE 21 1 2011 1 3
33. A. Dziekonski, A. Lamecki, and M. Mrozowski Tuning a hybrid GPU-CPU v-cycle multilevel preconditioner for solving large real and complex systems of fem equations Antennas and Wireless Propagation Letters, IEEE 10 2011 619 622
34. N. Alon, L. Babai, and A. Itai A fast and simple randomized parallel algorithm for the maximal independent set problem Journal of Algorithms 7 1986 567 583
35. NVIDIA, Nvidias next generation cuda compute architecture: Fermi. URL: http://www.nvidia.com/content/PDF/fermi-white-papers/NVIDIA-Fermi-Compute- Architecture-Whitepaper.pdf.
36. A. Buttari, J. Dongarra, J. Kurzak, J. Langou, J. Langou, P. Luszczek, and S. Tomov Exploiting mixed precision floating point hardware in scientific computations L. Grandinetti, High Performance Computing (HPC) and Grids in Action Advances in Parallel Computing vol. 16 2008 IOS Press Amsterdam 19 36
37. M. Emans, and A. van der Meer Mixed-precision AMG as linear equation solver for definite systems Procedia CS 1 1 2010 175 183
38. NVIDIA, Cusp library. URL: http://developer.nvidia.com/cusp.
39. LLNL, Hypre library. URL: https://computation.llnl.gov/casc/hypre/ software.html.
40. L. Buatois, G. Caumon, and B. Levy Concurrent number cruncher - a GPU implementation of a general sparse linear solver International Journal of Parallel, Emergent and Distributed Systems 24 3 2009 205 223