N-Body Simulation. Uwe Ehmann, Hanna Ketterle

Transcription

1 N-Body Simulation Uwe Ehmann, Hanna Kettele

2 Agenda 1. Backgound 2. CUDA Implementation 3. CUDA/OpenGL Inteopeability 4. OpenGL 5. Gavity vs. MD simulation 6. Test Scenaios

3 Backgound What is an N-Body system? System of N paticles Paticles inteact with each othe Example: sola system Tasks: Definition: paticle popeties Calculation: inteaction foces Integation: time evolving behavio Visualization: Paticle positions Input-File CUDA OpenGL

4 Backgound Foce Calculation: Dependent on distance between paticles Total foce = sum of all inteaction foces F tot = n i=1 F i fo each paticle F 1 Motion: Newton fomula: F = m a(t) = m x(t) F 2 Integation: Eule Integation: x n+1 = x n + v n t + O( t 2 ) v n+1 = v n + a n t + O( t 2 ) Velocity-Velet Integation: x n+1 = x n + v n t a n t 2 + O( t 4 ) v n+1 = v n + (a n+a n+1 ) 2 t + O( t 2 ) positions at t n positions at t n+1

5 CUDA Implementation Main Calculations with CUDA: Foce calculation Integation Evey thead calculates foce on one paticle Special featues of implementation: Usage of shaed memoy Selection between diffeent foce-models possible Selection between diffeent integatos possible Used algoithm: fast N-Body simulation (Nyland et. Al)

6 CUDA Implementation Used algoithm: fast N-Body simulation (Nyland et. Al) N paticles One cell: Inteaction between two paticles N paticles

7 CUDA Implementation Used algoithm: fast N-Body simulation (Nyland et. Al) N paticles Whole line: Total foce on one paticle N paticles Executed by one thead

8 CUDA Implementation Used algoithm: fast N-Body simulation (Nyland et. Al) N paticles One block, blocksize: p theads N paticles, N/p blocks

9 CUDA/OpenGL Inteopeability What is OpenGL? API to ende 2D and 3D gaphics scenes. Povides inteface fo dawing basic gaphics pimitves (e.g. vetex, line, tiangle) Visualization of paticles: Position of paticles in 3D Time evolving system Why do we need inteopeability of OpenGL and CUDA? Update positions smoothly CUDA buffes not visible to OpenGL Avoid copying data to CPU

10 CUDA/OpenGL Inteopeability OpenGL (Gaphics) glbuffedata( ) Shade (GLSL) Memoy Managment Computations CUDA (Simulation) cudamalloc( ) CUDA Kenel (C/C++) OpenGL Memoy Space Inteopeabilty Buffe Mapping CUDA Memoy Space

11 CUDA/OpenGL Inteopeability OpenGL (Gaphics) glgenbuffe ( ) glbuffedata ( ) gldawaays( ) Memoy Managment Inteopeabilty Buffe Mapping Computations Rendeing CUDA (Simulation) cudagaphicsglregistebuffe( ) cudagaphicsmapresouces( ) cudagaphicsresoucegetmappedpo inte(&pt, ) kenel<<< >>>(pt, ) cudagaphicsunmapresouces( )

12 OpenGL Paticle Visualization in OpenGL: No default geometic shapes usable with OpenGL inteopeability Define vetex meshes: calculate vetices, nomals, faces, scale, move, Define shade: Pogam to update each pixel of sceen (lighting, colo, ) Implement extended visibility: enable zooming and otating of scene, enable window esizing

13 Gavity vs. MD simulation Similaities: N-Body systems Diffeences: Inteaction Potential: Algoithm (fast N-Body simulation) V Dynamics accoding to Newtons law V Long Range V = 4ε σ 12 σ 6 Shot Range V = GM F = V

14 Gavity vs. MD simulation Similaities: N-Body systems Diffeences: Inteaction Potential: Algoithm (fast N-Body simulation) V Dynamics accoding to Newtons law V Long Range V = 4ε σ 12 σ 6 Shot Range V = GM F = V

15 Test Scenaios Enjoy!