PARTICLE SIMULATIONS ON THE GPU

Transcription

1 PARTICLE SIMULATIONS ON THE GPU Summary by Øystein Krg based n presented articles fr TDT 24 Fall 2009 Instructr: Anne C. Elster "Particle-Based Fluid Simulatin fr Interactive Applicatins", Matthias Muller, David Charypar and Markus Grss, Eurgrpahics/Siggraph 2003, D. Breeen, M. Lin Editrs "Smthed Particle Hydrdynamics n GPU", Takahir Harada et. al,

2 PARTICLE SIMULATIONS ON THE GPU Why are particle simulatins s interesting fr the GPU? Relatively easy t parallelize BUT, nt trivial because (fr ur needs) we need t handle particle interactins Sme interesting implementatins that use particle simulatins: HOOMD Highly Optimized Object-riented Mlecular Dynamics Uses CUDA Open Surce Fast, ne GPU can cmpete with small clusters (~36 cres) PhysX NVidia Real-time physics engine Particles used in particular in the fluid simulatin Uses SPH Smthed Particle Hydrdynamics Why SPH? Need t handle cllisins/interactin with rigid bjects Cnserves vlume Supprt fr large vlumes (i.e. sparse fluid in large envirnment) Supprt multiple independent fluids per scene Fast and efficient

3 SMOOTHED PARTICLE HYDRODYNAMICS SOURCES: Particle-based fluid simulatin fr interactive applicatins - Matthias Müller Smthed Particle Hydrdynamics n GPUs - Takahir Harada WHAT IS SPH? Particle based Fluid Simulatin - Simn Green/NVidia (slides frm NVidia presentatin at GDC08) Particle system with inter-particle frces/interactins Interactins gives O(n^2) cmputatinal cmplexity Define interactin cutff distance Less cmplexity Easier t parallelize First develped fr use in astrphysics Simulatin f stars / galaxies Different frm a lt f ther fluid simulatin methds (CFD methds) Mesh-free (des nt cnsider any "surfaces") Interplatin methd fr particle systems Each particle is affected nly by the particles in a specific radius arund it (cutff distance) Uses a "radial symmetrical smthing kernel" t define the cutff WHY USE SPH? Advantages: Very fast/efficient cmpared t ther fluid simulatin methds. Guarantees cnservatin f mass (particles themselves are the mass) (if weighted functins are nrmalized) Cmputes pressure frm weighted cntributins f neighbring particles (instead f slving linear systems f equatins) Disadvantages Still have t recnstruct a surface t render (marching cubes, splatting etc) Need a lt f particles fr realistic simulatin HOW DO WE EFFICIENTLY PARALLELIZE THIS? Use a spatial subdivisin data structure A unifrm grid Fill particles int grid with spacing h Only search ptential neighbrs in adjacent cells. Mre n this later

4 HOW DO THE PARTICLES INTERACT? We have lcal smthing fields that sum tgether int a glbal field Kernel functin Specifies hw we smth between particles Very imprtant fr behavir and stability THE EQUATIONS OF SPH Equatins frm Mueller unless therwise nted. The particle at lcatin r is calculated as a weighted sum f neighbring particles (, are mass, psitin, density and field quantity f particle j) In the discretized functins, W(r, h) is the smthing kernel. If the kernel is Even W(r, h) = W(-r,h) ) and Nrmalized the kernel is f secnd rder accuracy The gverning equatins (mass and mmentum cnservatin) are simplified Navier-Stkes (cnservatin f mass) - density v - velcity P - pressure - dynamic viscsity cefficient (cnservatin f mmentum) g - external frce density field / gravitatinal acceleratin

5 Can simplify even mre Cnstant number f particles w/cnstant mass per particle mass cnservatin s can mit (6) cmpletely Can simplify (7) because "since the particles mve with the fluid the substantial derivative f the velcity field is simply the time derivate f the velcity f the particles meaning that the cnvective term is nt needed fr particle systems We have three frce density fields n the right hand side f (7) Pressure, density, viscsity f is the "change f mmentum n the left hand side" End up with an expressin fr the acceleratin f particle i: are velcity, frce density field and the density field at the lcatin f particle i DISCRETIZATION The density f fluid The pressure f fluid (mdified versin fr symmetry) The viscsity f fluid (mdified versin fr symmetry) (pssible interpretatin; "lk at the neighbrs f particle i frm i s wn mving frame f reference. Then particle i is accelerated in the directin f the relative speed f its envirnment.") Als applies tech. fr surface tensin External frces are simply applied directly t the particles withut any use f SPH SMOOTHING KERNELS Stability, accuracy and speed is highly dependent n the chice f smthing kernels Several cnsideratins, specific smthing kernels fr difference frce fields etc. Example kernel frm Mueller:

6 BOUNDARY CONDITIONS (COLLISIONS, E.G. WALLS) Mueller d nt use specific bundary cnditins, Simply affects the velcity/psitin f the particles directly. Particle abut t tuch wall ==> deflect velcity Harada use mre advanced techniques: Pressure - Apply "pressure frce" frm the bundary: We have cnstant pressure d is the distance between particles If we cllide it will be with a distance less than d, "Push" the particle back t the distance d in the nrmal directin f the "wall" Density If particles are within a given range f a bundary, the bundary affects density INTEGRATION Harada "simple Euler Saw n instability..

7 Mueller "Leap-Frg", a secnd rder scheme. SPH ON THE GPU GPU CONSIDERATIONS Each particle can be given its wn thread N need fr synchrnizatin r cmmunicatin between threads A particle has many neighbrs high arithmetic intensity Particles have variable number f neighbrs hwever verall there is a cherence in the wrklad PARALLELIZATION / THE NEIGHBORING PARTICLE PROBLEM We need t knw hw t efficiently and quickly find the neighbring particles in a given radius. A naïve exhaustive search requires n^2 cmparisns. Slutin: Use a spatial subdivisin (data) structure Cnsideratins: The data structure shuld enable sparse fluids in large envirnments Can t simply d a 64x64x64 vlume because that s t small Can t just use a huge vlume because that requires t much memry Optins KD-tree / Octree NOT gd because requires recursin (bad fr GPU) Unifrm grid (used by Mueller) Simplest pssible subdivisin Since the SPH smthing kernels have finite supprt h (cutff "range") a cmmn way t reduce cmputatinal cmplexity is t use grid cells f size h. Reduces frm O(n^2) t O(nm), where n is cells and m is average number f particles per grid cell. A particle is nly cmpared against particles in neighbring cells Large vlumes require a lt f memry Hashed unifrm grid (used by PhysX SPH) Cncrete grid (64x64x64) Abstract grid maps t the cncrete grid (x,y,z) (x%64,y%64,z%64) Fast neighbr finding (if we assume n cllisins..) Prblem; false neighbrs (a neighbr will actually be far away) Fr SPH we ignre this because the SPH smthing functin means that far away particles will be ignred Buckets (used by Harada) Cnceptually the same as a unifrm grid Implemented as a 3D texture where each vxel can have 4 particles (RGBA) If mre than 4 particles in a vxel ==> ignre... (unlikely t happen thugh) Neighbring particles are fund by lking at adjacent vxels Sliced grid (used by Harada in later paper) Mdificatin that enables even mre sparse fluids Dynamically build a grid that nly cvers where the fluid exists

8 Ignre all the empty space in the vlume THE ALGORITHM Build spatial data structure n particles Fr each particle 1. Find neighbrs 2. Cmpute density 3. Cmpute frce and update velcity 4. (Fr cllisins with slids) Find neighbring triangles, check cllisin and update psitin On GPU d everything in parallel VISUALIZATION SPH gives us a particle field, but n surfaces Hw d we visualize this? Pssiblities: Extract a surface frm the particle set 3D issurface extractin ( marching cubes etc ) Ray-Marching "Ray tracing" f the particle set Pint splatting Image-space tricks ( billbarding, blur etc) Can use infrmatin we have in the particles t get a better effect Example; use density in particles, can apply blur etc PERFORMANCE/ RESULTS Müeller - Particle-Based Fluid Simulatin fr Interactive Applicatins (2003): On the CPU 1.8 GHz P4 w/ Gefrce particles

9 20 fps fr a and b, 5 fps fr c (marching cubes) Harada: On the GPU, but nt CUDA, uses textures and shaders. Cre2 2.93GHz 2GB RAM 8800GTX C++ / pengl with Cg fr shaders fps 28x times faster n GPU

10