
M.A. Krivov, A.I. Novikov, A.A. Yudanov Performance Comparison of Hypre and NVIDIA AmgX Libraries on Fume Modeling Problem 

Abstract.This paper considers the task of interaction of incompressible fluid with multiple objects that was introduced in computer graphics and can be reduced to three dimensional Euler equations. We proposed an approach to estimating an acceptable error under projection stage that is equal to solving of Poisson equation with mixed type boundaries on structured grid. For this stage, we used third party libraries Hypre (CPU) and NVIDIA AmgX (GPU) as an implementation of methods for SLAE solving with sparse matrices. The testing of the proposed solver was performed on system with CPU Xeon E52697v3 (14 cores) and GPU Tesla K40 with different numerical methods, scene types and grid sizes. It was demonstrated that the effective performance highly depends on scene specifics, therefore the questions of library, hardware and algorithm choosing are quite ambiguous. In particular, the speedup of GPU library over its CPUbased analogue was ranged from 20% to 273 folds. Keywords: mathematical modeling, visualization, fume, multigrid method, biconjugate gradient stabilized method, CPU, GPU, Hypre, NVIDIA AmgX PP. 1428. References 1. G.Y. Gardner. Visual Simulation of Clouds // Computer Graphics (SIGGRAPH 85 Conference Proceedings). 1985. pp. 297–384. 2. W. Reeves. Particle Systems  A Technique for Modeling a Class of Fuzzy Objects // ACM Transactions on Graphics 2(2). April 1983. pp. 91108. 3. W. Dong, X. Zhang, C. Zhang. Smoke Simulation Based on Particle System in Virtual Environments // 2010 International Conference on Multimedia Communications. 2010. 4. N. Foster, D. Metaxas. Realistic Animation of Liquids // Graphical Models and Image Processing 58(5). 1996. pp. 471–483. 5. J. Stam. Stable Fluids // SIGGRAPH 99 Conference Proceedings, Annual Conference Series. 1999. pp. 121–128. 6. R. Fedkiw, J. Stam, H. Jensen. Visual Simulation of Smoke // Proceedings of SIGGRAPH 2001. 2001. pp. 15–22. 7. M. Harris. Fast Fluid Dynamics Simulation on the GPU // GPU Gems: Programming Techniques, Tips and Tricks for RealTime Graphics. AddisonWesley. 2004. pp. 637–665. 8. K. Crane, I. Llamas, S. Tariq. RealTime Simulation and Rendering of 3D Fluids // GPU Gems 3. AddisonWesley. 2007. pp. 633–675. 9. S. He, H. Wong, W. Pang, U. Wong. Realtime smoke simulation with improved turbulence by spatial adaptive vorticity confinement // Computer Animation & Virtual Worlds 22(23). 2011. pp. 107–114. 10. T. Pfaff, N. Thuerey, J. Cohen, S. Tariq, M. Gross. Scalable Fluid Simulation using Anisotropic Turbulence Particles // Proceedings of ACM SIGGRAPH Asia (Seoul, Korea, December 1518, 2010), ACM Transactions on Graphics 29(5). pp. 174:1174:8. 11. R.D. Falgout, J.E. Jones, U.M. Yang. The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners // Numerical Solution of Partial Differential Equations on Parallel Computers 51(2006). pp. 267294. 12. S. Posey, S. See, M. Wang. GPU Progress and Directions in Applied CFD // Proceedings of Eleventh International Conference on CFD in the Minerals and Process Industries. 2015 13. M. Naumov et al.. AMGX: a Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods // SIAM Journal on Scientific Computing 37(5). October 2015. pp. 602626. 14. Q. Dai, X. Yang. Interactive smoke simulation and rendering on the GPU // Proceedings of the 12th ACM SIGGRAPH International Conference on VirtualReality Continuum and Its Applications in Industry. Hong Kong. November 2013. pp. 177182. 15. Accelerating ANSYS Fluent 15.0 Using NVIDIA GPUs (NVIDIA, 2014). Available at: https://www.nvidia.com/content/tesla/pdf/ansysfluentnvidiagpuuserguide.pdf (accessed May 4, 2017). 16. Krivov, M.A, Grizan, S.A. Opyt razrabotki gibridnyh versij reshatelej razrezhennyh SLAU [On Development of Hybrid Versions of Sparse SLAE Solvers]. Parallel'nye vychislitel'nye tehnologii (PaVT’2012): trudy mezhdunarodnoj nauchnoj konferencii [In Proceedings of Parallel Computing Technologies (PaCT’2012)]. Chelyabinsk. 2012. pp. 553–558.
