Sparse matrix solvers on the GPU: Conjugate gradients and multigrid

ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

Volumn , Issue , 2003, Pages 917-924

  Bolz, Jeff ^a   Farmer, Ian ^a   Grinspun, Eitan ^a   Schröoder, Peter ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

conjugate gradient; fluid simulation; GPU computing; mesh smoothing; multigrid; Navier Stokes; numerical simulation

Indexed keywords

CONJUGATE GRADIENT; FLUID SIMULATIONS; GPU COMPUTING; MULTI-GRID; NAVIER STOKES; NUMERICAL SIMULATION;

CONJUGATE GRADIENT METHOD; FLUIDS; INTERACTIVE COMPUTER GRAPHICS; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS;

COMPUTER SIMULATION;

EID: 77953998137     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1201775.882364     Document Type: Conference Paper

References (40)

1. ARVIND, AND IANNUCCI, R. A. 1987. Two Fundamental Issues in Multiprocessing. In Proceedings of DFVLR - Conference 1987, Parallel Processing in Science and Engineering.
2. nd ed. SIAM.
3. BLELLOCH, G. E. 1990. Vector Models for Data-Parallel Computing. MIT Press.
4. nd ed. SIAM.
5. CARR, N. A., HALL, J. D., AND HART, J. C. 2002. The Ray Engine. In SIGGRAPH/Eurographics Workshop on Graphics Hardware.
6. COHEN, M. F., CHEN, S. E., WALLACE, J. R., AND GREENBERG, D. P. 1988. A Progressive Refinement Approach to Fast Radiosity Image Generation. Computer Graphics (Proceedings of SIGGRAPH) 22, 75-84.
7. DEMMEL, J. W. 1997. Applied Numerical Linear Algebra. SIAM, Philadelphia, PA.
8. DESBRUN, M., MEYER, M., SCHRÖDER, P., AND BARR, A. H. 1999. Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow. In Proceedings of SIGGRAPH, 317-324.
9. DESBRUN, M., MEYER, M., AND ALLIEZ, P. 2002. Intrinsic Parameterizations of Surface Meshes. Computer Graphics Forum (Proceedings of Eurographics) 21, 3, 209-218.
10. DIEWALD, U., MORIGI, S., AND RUMPF, M. 2002. A Cascadic Geometric Filtering Approach to Subdivision. Comput. Aided Geom. Des. 19, 9, 675-694.
11. FEDKIW, R., STAM, J., AND JENSEN, H. W. 2001. Visual Simulation of Smoke. In Proceedings of SIGGRAPH, 15-22.
12. GOODNIGHT, N., LEWIN, G., LUEBKE, D., AND SKADRON, K. 2003. A Multigrid Solver for Boundary Value Problems Using Programmable Graphics Hardware. Tech. Rep. CS-2003-03, University of Virginia.
13. HACKBUSCH, W. 1985. Multi-Grid Methods and Applications. Springer Verlag, Berlin.
14. HALL, J. D., CARR, N. A., AND HART, J. C. 2003. Cache and Bandwidth Aware Matrix Multiplication on the GPU. Tech. rep., University of Illinois.
15. HARRIS, M. J., COOMBE, G., SCHEUERMANN, T., AND LASTRA, A. 2002. Physically-Based Visual Simulation on Graphics Hardware. In SIGGRAPH/ Eurographics Workshop on Graphics Hardware.
16. HARRIS, M. J. 2002. Analysis of Error in a CML Diffusion Operation. Tech. Rep. TR02-015, UNC Chapel Hill.
17. HILLESLAND, K. E., MOLINOV, S., AND GRZESZCZUK, R. 2003. Nonlinear Optimization Framework for Image-Based Modeling on Programmable Graphics Hardware. ACM Transactions on Graphics.
18. HOFF, K. E., KEYSER, J., LIN, M., MANOCHA, D., AND CULVER, T. 1999. Fast Computation of Generalized Voronoi Diagrams Using Graphics Hardware. In Proceedings of SIGGRAPH, 277-286.
19. KASS, M., AND MILLER, G. 1990. Rapid, Stable Fluid Dynamics for Computer Graphics. Computer Graphics (Proceedings of SIGGRAPH) 24, 4, 49-57.
20. KELLER, A. 1997. Instant Radiosity. In Proceedings of SIGGRAPH, 49-56.
21. KHAILANY, B., DALLY, W. J., RIXNER, S., KAPASI, U. J., MATTSON, P., NAMKOONG, J., OWENS, J. D., TOWLES, B., AND CHANG, A. 2001. Imagine: Media Processing with Streams. IEEE Micro 21, 2, 35-46.
22. KHAILANY, B., DALLY, W. J., RIXNER, S., KAPASI, U. J., OWENS, J. D., AND TOWLES, B. 2003. Exploring the VLSI Scalability of Stream Processors. In Proceedings of the Ninth Symposium on High Performance Computer Architecture.
23. KOBBELT, L., CAMPAGNA, S., VORSATZ, J., AND SEIDEL, H.-P. 1998. Interactive Multi-Resolution Modeling on Arbitrary Meshes. In Proceedings of SIGGRAPH, 105-114.
24. KRÜGER, J., AND WESTERMANN, R. 2003. Linear algebra operators for gpu implementation of numerical algorithms. ACM Transactions on Graphics.
25. LARSEN, E. S., AND MCALLISTER, D. K. 2001. Fast Matrix Multiplies using Graphics Hardware. In Supercomputing.
26. LEISERSON, C., ROSE, F., AND SAXE, J. 1993. Optimizing synchronous circuitry by retiming. In Third Caltech Conference On VLSI.
27. LENGYEL, J., REICHERT, M., DONALD, B. R., AND GREENBERG, D. P. 1990. Real-Time Robot Motion Planning Using Rasterizing Computer Graphics Hardware. Computer Graphics (Proceedings of SIGGRAPH) 24, 327-335.
28. LI, W., WEI, X., AND KAUFMAN, A. 2003. Implementing Lattice Boltzmann Comptuation on Graphics Hardware. The Visual Computer. To appear.
29. LINDHOLM, E., KILGARD, M. J., AND MORETON, H. 2001. A User-Programmable Vertex Engine. In Proceedings of SIGGRAPH, 149-158.
30. MÜLLER, M., DORSEY, J., MCMILLAN, L., JAGNOW, R., AND CUTLER, B. 2002. Stable Real-Time Deformations. In ACM SIGGRAPH Symposium on Computer Animation, 49-54.
31. OLANO, M., Ed. 2002. Real-Time Shading Languages. Course Notes. ACM SIGGRAPH.
32. OWENS, J. D., KHAILANY, B., TOWLES, B., AND DALLY, W. J. 2002. Comparing Reyes and OpenGL on a Stream Architecture. In SIGGRAPH/Eurographics Workshop on Graphics Hardware, 47-56.
33. PURCELL, T. J., BUCK, I., MARK, W. R., AND HANRAHAN, P. 2002. Ray Tracing on Programmable Graphics Hardware. ACM Transactions on Graphics 21, 3, 703-712.
34. SEMICONDUCTOR INDUSTRY ASSOCIATION, 2002. International Technology Roadmap for Semiconductors. http://public.itrs.net/, December.
35. SHEWCHUCK, J. R. 1994. An Introduction to the Conjugate Gradient Method without the Agonizing Pain. http://www.cs.cmu.edu/~quake-papers/painless- conjugate-gradient.ps., August.
36. STAM, J. 1999. Stable Fluids. In Proceedings of SIGGRAPH, 121-128.
37. STRZODKA, R., AND RUMPF, M. 2001. Nonlinear Diffusion in Graphics Hardware. In Visualization, 75-84.
38. STRZODKA, R. 2002. Virtual 16 Bit Precise Operations on RGBA8 Textures. In Vision, Modeling and Visualization.
39. nd ed. Thinking Machines Corporation.
40. THOMPSON, C. J., HAHN, S., AND OSKIN, M. 2002. Using Modern Graphics Architectures for General-Purpose Computing: A Framework and Analysis. In International Symposium on Microarchitecture.