Direct N-Body Simulation with Graphic Processing Units: dynamical evolution of galactic collisions

重力多體問題的模擬，在天文研究中向來扮演重要角色，尤其是利用直接積分法，更可以達到高解析度的結果。但受限於電腦運算效能低落，人們被迫採取近似法以減少運算時間。於顯示卡具有多處理器、平行運算的特性，我們利用它取代中央處理器，來計算重力直接積分問題。本實驗室首先建構了顯示卡電腦群，由16台個人電腦與32張顯示卡組成，經實測證明，由顯示卡處理直接多體問題的效能，比起中央處理器的效能快了300多倍。操作顯示卡的方法，以及我們數值模擬的程式碼將被詳細討論。們用電腦群模擬星系碰撞的問題，本篇論文主要探討兩個星系碰撞並融合的演化過程，並且討論星系中心二維與三維質量密度的變化。經模擬發現，具有 Sersic model 分布的星系，經碰撞融合後，其 Sersic index 會由小變大，且其變化與初始條件的動能有關係；此外，我們亦發現，不論碰撞前與碰撞後，星系三維密度都遵守 NFW model 的分布。口試委員會審定書................................................................................i言.......................................................................................................ii要......................................................................................................iiiontents ..............................................................................................ivhapter 1 Introduction .......................................................................1hapter 2 Direct N-Body Simulation ................................................3.1 Numerical simulation ......................................................................3.2 The Hermite scheme ........................................................................4.3 The Ring algorithm .........................................................................7.4 Time-step treatments .......................................................................9hapter 3 The GPU cluster .............................................................10.1 Something about GPU ...................................................................10.2 Structure and efficiency of GPU clusters .....................................11.3 From Cg and OpenGL to N-body code ........................................13.4 Details of our force calculation code .............................................19hapter 4 Initial Conditions ............................................................22.1 Galaxy cluster halos .......................................................................22.2 Density profiles of initial galaxies .................................................23.3 Several situations of galactic collisions .........................................24hapter 5 Outcome of simulation ...................................................27.1 Energy analysis ..............................................................................27.2 2D density profile ...........................................................................31.3 3D density profile ...........................................................................33hapter 6 Conclusions .....................................................................35.1 High performance, high accuracy, low cost .................................35.2 Future work.....................................................................................35eference ...........................................................................................37ppendix 1. .......................................................................................38ppendix 2. .......................................................................................40ppendix 3. .......................................................................................6