Conjugate gradients on multiple GPUs

International Journal for Numerical Methods in Fluids

Volumn 64, Issue 10-12, 2010, Pages 1254-1273

  Georgescu, Serban ^a   Okuda, Hiroshi ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Communication computation overlapping; Conjugate Gradients; GPGPU; Mixed precision; Poisson's equation

Indexed keywords

COMPUTATIONAL ASPECTS; CONDITION NUMBERS; CONJUGATE GRADIENT; CONJUGATE-GRADIENT SOLVERS; DATA FORMAT; DOUBLE PRECISION; GPGPU; ILL-CONDITIONED; ITERATIVE REFINEMENT; LOW-BANDWIDTH; MATRIX VECTOR MULTIPLICATION; MIXED PRECISION; NUMERICAL CHARACTERISTICS; ORDER OF MAGNITUDE; POISSON'S EQUATION; POWER EFFICIENCY; SINGLE PRECISION; TIME SPENT;

COMMUNICATION; COMPUTATIONAL FLUID DYNAMICS; CONJUGATE GRADIENT METHOD; NUMBER THEORY; POISSON EQUATION; PROGRAM PROCESSORS;

MATRIX ALGEBRA;

EID: 78649682552     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2462     Document Type: Article

References (16)

1. Hestenes Magnus R, Stiefel E. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards 1952; 49:409-436.
2. Vuduc R. Automatic performance tuning of sparse matrix kernels. Ph.D. Thesis, University of California at Berkeley, 2003.
3. NVIDIA Corporation. CUDA Programming Guide, version 2.0, NVIDIA Corporation, 2008.
4. Strzodka R, Doggett M, Kolb A. Scientific computation for simulations on programmable graphics hardware. Simulation Modeling Practice and Theory 2005; 13:667-680.
5. Owens D et al. A survey of general-purpose computation on graphics hardware. Computer Graphics Forum 2007; 26:80-113.
6. Bolz J et al. Sparse matrix solvers on the GPU: conjugate gradients and multigrid. ACM Transactions on Graphics 2003; 22:917-924.
7. Buatois L et al. Concurrent Number Cruncher: An Efficient Sparse Linear Solver on the GPU. Lecture Notes in Computer Science, vol. 4782. Springer: Berlin, 2007; 358-371.
8. Göddeke D, Strzodka R, Turek S. Performance and accuracy of hardware-oriented native-, emulated- and mixed-precision solvers in FEM simulations. International Journal of Parallel, Emergent and Distributed Systems 2007; 22:221-256.
9. Menon S, Perot JB. Implementation of an efficient Conjugate Gradients algorithm for Poisson Solutions on Graphic Processors. Proceedings of CFD2007, 2007.
10. Davis T. University of Florida Sparse Matrix Collection. Available from.
11. Göddeke D et al. GPU acceleration of an unmodified parallel finite element Navier-Stokes solver. High Performance Computing and Simulation 2009, Logos Verlag, Berlin, 2009; 12-21.
12. Aubry R et al. Deflated preconditioned conjugate gradient solvers for the Pressure-Poisson equation. Journal of Computational Physics 2008; 227:10196-10208.
13. Saad Y. Iterative Methods for Sparse Linear Systems (2nd edn). SIAM: Philadelphia, PA, 2003.
14. Langou J et al. Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy. Proceedings of the 2006 ACM/IEEE Conference on Supercomputing, Tampa, FL, 2006.
15. Bell N, Garland M. Efficient sparse matrix-vector multiplication on CUDA. Techreport, NVIDIA Corporation, 2008.
16. Dongarra J et al. Numerical Linear Algebra for High Performance Computers. SIAM: Philadelphia, PA, 1998; 166-168.