AN APPROACH TO EFFICIENT FEM SIMULATIONS ON GRAPHICS PROCESSING UNITS USING CUDA

Abstract The paper presents a highly efficient way of simulating the dynamic behavior of deformable objects by means of the finite element method (FEM) with computations performed on Graphics Processing Units (GPU). The presented implementation reduces bottlenecks related to memory accesses by grouping the necessary data per node pairs, in contrast to the classical way done per element. This strategy reduces the memory access patterns that are not suitable for the GPU memory architecture. Furthermore, the presented implementation takes advantage of the underlying sparse-block-matrix structure, and it has been demonstrated how to avoid potential bottlenecks in the algorithm. To achieve plausible deformational behavior for large local rotations, the objects are modeled by means of a simplified co-rotational FEM formulation. References Yang, Y., Xiao, R., He Z., 2011, Real-time deformations simulation of soft tissue by combining mass-spring model with pressure based method, Proceedings of the 3rd IEEE International Conference on Advanced Computer Control (ICACC '11), Harbin, China, pp. 506?510. Erleben, K., Sporring, J., Henrikssen K., Dohlman, H., 2005, Physics-Based animation, Charles river media, USA. Zehn, M., 2005, MBS and FEM: A Marriage-of-Convenience or a Love Story?, BENCHmark Int. Magazine for Eng. Design&Analysis, pp. 12-15. Mueller M., Dorsey J., McMillan L., Jagnow R., Cutler B., 2002, Stable Real-Time Deformations, Proceedings of 2002 ACM SIGGRAPH/Eurographic symposium on Computer animation, San Antonio, USA, pp. 49-54. Hauth, M., Strasser W., 2004, Corotational simulation of deformable solids, Journal of WSCG, 12(1), pp. 137-144. Mueller, M., Gross, M., 2004, Interactive Virtual Materials, Proceedings of Graphics Interface 2004, Waterloo, Canada, pp 239-246. Marinković, D., Zehn, M., Marinković Z., 2012, Finite element formulations for effective computations of geometrically nonlinear deformations, Advances in Engineering Software, 50, pp. 3-11. Hestenes, M. R., Stiefel, E., 1952, Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, 49(6), pp. 409-436. Benzi, M. 2002, Preconditioning Techniques for Large Linear Systems: A Survey, Journal of Computational Physics, 182(2), pp. 418-477. Cecka C., Lew A. J., Darve, E., 2011, Assembly of Finite Element Methods on Graphics Processors, International Journal for Numerical Methods in Engineering, 85(5), pp. 640-669. Mafi, R., Sirouspour, S., 2013, GPU-based acceleration of computations in nonlinear finite element deformation analysis, International Journal for Numerical Methods in Biomedical Engineering, doi: 10.1002/cnm.2607 Georgescu S., Chow, P., Okuda, H., 2013, GPU Acceleration for FEM-Based Structural Analysis, Archives of Computational Methods in Engineering 20(2), pp. 111-121 Bathe, K. J., 1982, Finite element procedures in engineering analysis, Prentice-Hall, Inc., Englewood Cliffs, New Jersey. Harris, M., Optimizing parallel reduction in CUDA, available at: http://developer.download.nvidia.com/compute/cuda/1.1-Beta/x86_website/projects/reduction/doc/reduction.pdf (access date: 14.02.2014.)