An efficient multigrid method for the simulation of high-resolution elastic solids

ACM Transactions on Graphics

Volumn 29, Issue 2, 2010, Pages

  Zhu, Yongning ^a   Sifakis, Eftychios ^a   Teran, Joseph ^b   Brandt, Achi ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b DISNEY RESEARCH   (United States)

^c WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Corotational linear elasticity; Deformable models; Near incompressible solids; Parallel simulation

Indexed keywords

DEFORMABLE MODELS; ELASTIC SOLIDS; FRAMES PER SECONDS; HIGH RESOLUTION; INCOMPRESSIBLE MATERIAL; INCOMPRESSIBLE SOLIDS; LINEAR ELASTICITY; MATERIAL PARAMETER; MULTI-GRID; MULTIGRID METHODS; PARALLEL SIMULATIONS; SHARED MEMORY MULTIPROCESSOR; TEST MODELS;

ANIMATION; DEFORMATION; ELASTICITY; SECURITY OF DATA;

SHAPE MEMORY EFFECT;

EID: 77951276013     PISSN: 07300301     EISSN: 15577368     Source Type: Journal    
DOI: 10.1145/1731047.1731054     Document Type: Article

References (47)

1. BARBIC, J. AND JAMES, D. 2005. Real-Time subspace integration of St. Venant-Kirchoff deformable models. ACM Trans. Graph. 24, 3, 982-990.
2. BOLZ, J., FARMER, I., GRINSPUN, E., AND SCHRODER, P. 2003. Sparse matrix solvers on the GPU: Conjugate gradients and multigrid. ACM Trans. Graph. 22, 3, 917-924.
3. BONET, J. AND WOOD, R. 1997. Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press.
4. BRANDT, A. 1977. Multi-Level adaptive solutions to boundary-value problems. Math. Comput. 31, 138, 333-390.
5. BRANDT, A. 1986. Algebraic multigrid theory: The symmetric case. Appl. Math. Comput. 19, 1-4, 23-56.
6. 2-norm. SIAM J. Numer. Anal. 31, 1695-1695
7. BRANDT, A. AND DINAR, N. 1978. Multigrid solutions to elliptic flow problems. In Numerical Methods for Partial Differential Equations, 53-147.
8. BREZZI, F. AND FORTIN, M. 1991. Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York.
9. CAPELL, S., GREEN, S., CURLESS, B., DUCHAMP, T., AND POPOVIĆ, Z. 2002. A multiresolution framework for dynamic deformations. In Proceedings of the ACM SIGGRAPH Symposium on Computer Animation. ACM Press, 41-48.
10. DEBUNNE, G., DESBRUN, M., CANI, M., AND BARR, A. 2001. Dynamic real-time deformations using space and time adaptive sampling. In Proceedings of the SIGGRAPH. Vol.20. 31-36. (Pubitemid 33047287)
11. DICK, C., GEORGII, J., BURGKART, R., AND WESTERMANN, R. 2008. Computational steering for patient-specific implant planning in orthopedics. In Proceedings of Visual Computing for Biomedicine Conference. 83-92.
12. GASPAR, F., GRACIA, J., LISBONA, F., AND OOSTERLEE, C. 2008. Distributive smoothers in multigrid for problems with dominating grad-div operators. Numer. Linear Algeb. Appl. 15, 8, 661-683.
13. GEORGII, J. AND WESTERMANN, R. 2006. A multigrid framework for real-time simulation of deformable bodies. Comput. Graph. 30, 3, 408-415. (Pubitemid 44226309)
14. GEORGII, J. AND WESTERMANN, R. 2008. Corotated finite elements made fast and stable. In Proceedings of the 5th Workshop On Virtual Reality Interaction and Physical Simulation.
15. GOODNIGHT, N., WOOLLEY, C., LEWIN, G., LUEBKE, D., AND HUMPHREYS, G. 2003. A multigrid solver for boundary value problems using programmable graphics hardware. In Proceedings of the ACM SIGGRAPH/Eurographics Conference on Graphics Hardware. 102-111.
16. GREEN, S., TURKIYYAH, G., AND STORTI, D. 2002. Subdivision-based multilevel methods for large scale engineering simulation of thin shells. In Proceedings of the 7th ACM Symposium on Solid Modeling and Applications. ACM, New York, 265-272. (Pubitemid 34991560)
17. GRIEBEL, M., OELTZ, D., AND SCHWEITZER, M. A. 2003. An algebraic multigrid method for linear elasticity. SIAM J. Sci. Comput. 25, 407.
18. GRINSPUN, E., KRYSL, P., AND SCHRÖDER, P. 2002. CHARMS: A simple framework for adaptive simulation. ACM Trans. Graph. 21, 281-290.
19. HARLOW, F. AND WELCH, J. 1965. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182-2189.
20. HAUTH, M. AND STRASSER, W. 2004. Corotational Simulation of De-formable Solids. In Proceedings of the International Conferences in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG). 137-145.
21. HUGHES, C., GRZESZCZUK, R., SIFAKIS, E., KIM, D., KUMAR, S., SELLE, A., CHHUGANI, J., HOLLIMAN, M., AND CHEN, Y.-K. 2007. Physical simulation for animation and visual effects: Parallelization and characterization for chip multiprocessors. In Proceedings of the International Symposium on Computer Architecture. (Pubitemid 47582105)
22. HUGHES, T. 1987. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice Hall.
23. IRVING, G., SCHROEDER, C., AND FEDKIW, R. 2007. Volume conserving finite element simulations of deformable models. ACM Trans. Graph. 26, 3. (Pubitemid 47219847)
24. JAMES, D. AND FATAHALIAN, K. 2003. Precomputing interactive dynamic deformable scenes. ACM Trans. Graph. 22, 879-887.
25. KAUFMANN, P., MARTIN, S., BOTSCH, M., AND GROSS, M. 2008. Flexible Simulation of Deformable Models Using Discontinuous Galerkin FEM. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation.
26. KAUFMANN, P., MARTIN, S., BOTSCH, M., AND GROSS, M. 2009. Flexible simulation of deformable models using discontinuous Galerkin FEM. Graph. Models 71, 4, 153-167.
27. KAZHDAN, M. AND HOPPE, H. 2008. Streaming multigrid for gradient-domain operations on large images. ACM Trans. Graph. 27, 3.
28. LEE, S.-H., SIFAKIS, E., AND TERZOPOULOS, D. 2009. Comprehensive biomechanical modeling and simulation of the upper body. ACM Trans. Graph. 28, 4, 1-17.
29. LEKIEN, F. AND MARSDEN, J. 2005. Tricubic interpolation in three dimensions. Int. J. Numer. Methods Engin. 63, 3, 455-471. (Pubitemid 40714163)
30. LOSASSO, F., GIBOU, F., AND FEDKIW, R. 2004. Simulating water and smoke with an octree data structure. ACM Trans. Graph. 23, 457-462. (Pubitemid 40163740)
31. MOLINO, N., BAO, Z., AND FEDKIW, R. 2004. A virtual node algorithm for changing mesh topology during simulation. ACM Trans. Graph. 23, 385-392. (Pubitemid 40163731)
32. MÜ LLER, M., DORSEY, J., MCMILLAN, L., JAGNOW, R., AND CUTLER, B. 2002. Stable real-time deformations. In Proceedings of the ACM SIGGRAPH Symposium on Computer Animation. 49-54.
33. MÜ LLER, M. AND GROSS, M. 2004. Interactive virtual materials. In Proceedings of the Conference on Graphics Interface. 239-246.
34. MÜLLER, M., HEIDELBERGER, B., TESCHNER, M., AND GROSS, M. 2005. Meshless deformations based on shape matching. ACM Trans. Graph. 24, 3, 471-478.
35. MÜLLER, M., TESCHNER, M., AND GROSS, M. 2004. Physically-based simulation of objects represented by surface meshes. In Proceedings of the Computer Graphics International Conference. 156-165.
36. NI, X., GARLAND, M., AND HART, J. 2004. Fair Morse functions for extracting the topological structure of a surface mesh. ACM Trans. Graph. 23, 3, 613-622. (Pubitemid 40163758)
37. O'BRIEN, J. AND HODGINS, J. 1999. Graphical modeling and animation of brittle fracture. In Proceedings of the SIGGRAPH. 137-146.
38. OTADUY, M. A., GERMANN, D., REDON, S., AND GROSS, M. 2007. Adaptive deformations with fast tight bounds. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA'07). 181-190.
39. RIVERS, A. AND JAMES, D. 2007. FastLSM: Fast lattice shape matching for robust real-time deformation. ACM Trans. Graph. 26, 3. (Pubitemid 47219915)
40. SHI, L., YU, Y., BELL, N., AND FENG, W. 2006. A Fast multigrid algorithm for mesh deformation. ACM Trans. Graph., 1108-1117. (Pubitemid 44481074)
41. SIFAKIS, E., SHINAR, T., IRVING, G., AND FEDKIW, R. 2007. Hybrid simulation of deformable solids. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 81-90.
42. TERAN, J., SIFAKIS, E., IRVING, G., AND FEDKIW, R. 2005. Robust quasistatic finite elements and flesh simulation. In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation. 181-190.
43. TERZOPOULOS, D. AND FLEISCHER, K. 1988. Deformable models. Visual Comput. 4, 6, 306-331.
44. TERZOPOULOS, D., PLATT, J., BARR, A., AND FLEISCHER, K. 1987. Elastically deformable models. ACM Comput. Graph. 21, 4, 205-214.
45. THOMASZEWSKI, B., PABST, S., AND BLOCHINGER, W. 2007. Exploiting parallelism in physically-based simulations on multi-core processor architectures. In Proceedings of the EG Symposium on Parallel Graphics and Visualization.
46. TROTTENBERG, U., OOSTERLEE, C., AND SCHULLER, A. 2001. Multigrid. Academic Press, San Diego, CA.
47. WU, X. AND TENDICK, F. 2004. Multigrid integration for interactive deformable body simulation. In Proceedings of the International Symposium on Medical Simulation. ACM, New York, 92-104 (Pubitemid 38851641)