臺灣博碩士論文加值系統

目前在旋轉機械與工具機中，流體薄膜潤滑軸承是當中非常重要的關鍵元素，而一個軸承表現通常可以藉由求解一個設定與該軸承有著一致狀態的雷諾方程式來預測其表現。而多核心中央處理器(Multicore CPU)和圖形顯示卡(GPU)的計算能力在這幾年間以指數般的速度飛快的成長，而採用平行計算的重點便是如何有效率的使用這些快速的計算能力。
在本篇論文中，藉由研究不同連續過鬆弛法與嘗試運用多核心CPU與GPU進行加速，進而求解不可壓縮流體雷諾方程式與可壓縮流體雷諾方程式。本硏究使用之平行語言指令為OpenMP與OpenACC，該兩個指令分別為多核心CPU與GPU的標準，進行串行及平行計算之各種SOR結果比較。而在判定如何使得SOR方法停止時仍保有準確性與效率時，本次藉由一個基於截斷誤差分析而得到之停止條件進行計算。為了加速計算效率，本篇研究中也測試了一個使用兩張顯示卡作計算基礎的CPU-GPU混合架構，而該結果與之前之結果亦進行分析與討論。
模擬結果顯示，使用OpenMP與OpenACC能讓兩張顯示卡可同時進行平行計算，使得同時運用多核心處理器及多張顯示卡進行平行計算的技術成為可能，可以進一歩提昇高性能計算在潤滑分析時的效能。

Fluid-film lubricated bearings are the key elements in many rotating machinery and machine tools. The performance of a bearing can usually be predicted by solving a proper Reynolds equation which is consistent with the operation conditions of that bearing. The computational capability of multicore CPUs and GPUs (graphics processing units) are improved exponentially in recent years and parallel computing is the only means to effectively use the advanced computing power. In this study, the SOR (successive-over-relaxation) type methods are applied to solve the incompressible- and compressible-fluid Reynolds equations by either the multicore CPU or GPUs. The computing paradigms used are OpenACC and OpenMP, which are the standards for multithreaded and GPU computing. The results of serial and parallel versions of the SOR type methods are presented and compared. A stopping criterion based on the truncation error analysis is used to terminate the SOR iterations with sufficient accuracy and efficiency. To speed up the computation a CPU-GPU hybrid setup with simultaneously 2 GPUs computing is tested and the simulation results are also presented and discussed.
The simulation results show that this study can successfully apply the multicore processor and two GPUs to perform the parallel computing for solving the Reynolds equations. A similar setup and coding can be used in the future to increase the computing capability for fluid-film lubrication analysis.

指導教授推薦書
口試委員會審定書
致謝 iii
摘要 iv
英文摘要(abstract) v
目錄 vi
圖目錄 ix
表目錄 xi
第一章 前言 1
1-1研究背景 1
1-2研究目的與規劃 1
1-3系統 2
1-4文獻回顧 3
1-4-1使用OpenMP對流體與流體-顆粒系統的平行計算[1] 3
1-4-2使用粒子群最佳化法進行空氣箔片軸承分析[2] 3
1-4-3使用OpenACC加速PIC碼的可攜平台與其應用[4] 4
1-4-4利用硬體異質性之兩階段平行流體力學演算法[5] 5
1-4-5負載平衡與OpenMP之巢狀平行的實施[6] 6
1-4-6用於混合CPU-GPU系統之平行可變鄰域搜索法[7] 6
1-4-7雷諾方程式之迭代方法的收斂條件[14] 7
第二章 雷諾方程式 9
2-1不可壓縮流體雷諾方程式 9
2-2可壓縮流體雷諾方程式模型 11
第三章 平行計算 13
3-1串行計算與平行計算 13
3-2 OpenMP 14
3-3 OpenACC 15
第四章 迭代方法 17
4-1高斯迭代法與連續過鬆弛法 17
4-2帶狀連續過鬆弛法 (SPSOR) 18
4-3紅黑連續過鬆弛法 (RBSOR) 19
第五章 數據結果 20
5-1鬆弛係數 20
5-2收斂條件 21
5-3 MS-Windows作業系統與Linux作業系統之比較 24
5-4 Fortran程式語言與MATLAB程式語言之比較 26
5-5 SOR法與RBSOR法之比較 28
5-6不同加速方法之比較 32
5-7收斂條件之比較 34
5-8計算可壓縮流體雷諾方程式之結果 36
5-9 混合運用OpenMP與OpenACC 38
5-10顯卡與兩張顯卡之比較 39
5-11其他平行加速方法比較 42
第六章 結論 44
參考文獻 46
附錄 49
 
圖目錄
圖 1、MPI, OpenMP, OpenACC的運算時間比較 5
圖 2、平行操作兩張顯示卡示意圖 7
圖 3、串行與平行 13
圖 4、SPSOR邊界問題[13] 18
圖 5、標準RBSOR點分佈圖[13] 19
圖 6、程式流程圖 22
圖 7、可壓縮流體雷諾方程式流程圖 24
圖 8、MS-Windows與CentOS 7的計算時間 26
圖 9、Fortran與MATLAB的比較 27
圖 10、SOR與RBSOR的計算時間 29
圖 11、SOR與RBSOR的壓力值 29
圖 12、收斂條件下SOR與RBSOR之計算時間 31
圖 13、收斂條件下SOR與RBSOR之迭代次數 31
圖 14、不同過鬆弛法與不同加速方式的比較 33
圖 15、各格點的收斂條件與數值 35
圖 16、不同收斂條件的比較 36
圖 17、每一次壓力的變化量 37
圖 18、壓力變化量 37
圖 19、混合OpenMP與OpenACC之方法 38
圖 20、以不同執行緒數控制顯卡之計算速度的比較 41
圖 21、一張顯卡與兩張顯卡進行加速的時間 41
圖 22、以section指令混合兩個平行語法 43

 
表目錄
表 1、平行最佳化效率比較 4
表 2、MS-Windows與CentOS 7的計算時間 25
表 3、MATLAB與Fortran的運算速度之比較 27
表 4、固定迭代次數下的SOR法與RBSOR法 28
表 5、收斂條件下的SOR法與RBSOR法 30
表 6、各個加速比之比較 34
表 7、不同加速方法之結果 42

1. A. Amritkar, D. Tafti, R. Liu, R. Kufrin, and B. Chapman, “OpenMP parallelism for fluid and fluid-particulate systems,” Parallel Computing, Volume 38, Issue 9, September 2012, Pages 501-517.
2. N. Wang, H.-C. Huang, and C.-R. Hsu, “Parallel optimum design of foil bearing using particle swarm optimization method,” Tribology Transactions, Volume 56, 2013, Pages 453-460.
3. X. Tian, J. P. Hoeflinger, G. Haab, Y.-K. Chen, M. Girkar, and S. Shah, “A compiler for exploiting nested parallelism in OpenMP programs,” Parallel Computing, Volume 31, Issues 10–12, October–December 2005, Pages 960-983.
4. F. Hariri, T.M. Tran, A. Jocksch, E. Lanti, J. Progsch, P. Messmer, S. Brunner, C. Gheller, and L. Villard, “A portable platform for accelerated PIC codes and its application to GPUs using OpenACC,” Computer Physics Communications, Volume 207, October 2016, Pages 69-82.
5. I. Huismann, J. Stiller, and J. Fröhlich, “Two-level parallelization of a fluid mechanics algorithm exploiting hardware heterogeneity,” Computers & Fluids, Volume 117, August 2015, Pages 114-124.
6. R. Blikberg and T. Sørevik, “Load balancing and OpenMP implementation of nested parallelism,” Parallel Computing, Volume 31, Issues 10–12, October–December 2005, Pages 984-998.
7. Nikolaos Antoniadis, Angelo Sifaleras, “A hybrid CPU-GPU parallelization scheme of variable neighborhood search for inventory optimization problems,” Electronic Notes in Discrete Mathematics, Volume 58, April 2017, Pages 47-54
8. Y.-C. Lin, “Parallel MATLAB computing of multi-objective optimization of air bearing,” Master Thesis, Department of Mechanical Engineering, Chang Gung University, June 2016.
9. W.-C. Jeun, Y.-S. Kee, S. Ha, and C. Kee, “Overcoming performance bottlenecks in using OpenMP on SMP clusters,” Parallel Computing, Volume 34, Issue 10, October 2008, Pages 570-592.
10. K. Fürlinger, “OpenMP application profiling — state of the art and directions for the future,” Procedia Computer Science, Volume 1, Issue 1, 2010, Pages 2107-2114.
11. OpenMP FAQ, “http://openmp.org/openmp-faq.html”
12. C.-Y. Wang, “Application of particle swarm optimization method for the Multi-Objective optimum design of hydrostatic bearings,” Master Thesis, Department of Mechanical Engineering, Chang Gung University, July 2012.
13. N. Wang, K.-C. Cha, H.-C. Huang, and C.-R. Hsu, “Effect of CPU cache size on OpenMP computing performance in fluid-film lubrication analysis,” Journal of Mechanics, Volume 31, Issue 2, April 2015, Pages 123-129.
14. N. Wang, S.-H. Chang, and H.-C. Huang, “Stopping Criterion in Iterative Solution Methods for Reynolds Equations,” Tribology Transactions, Volume 53, Pages 739-747,2010.
15. A. Z. Szeri, “Fluid Film Lubrication Theory & Design,” Cambridge, Pages 394-396,1998.
16. S.-H. Chang, “Parallel Iterative Methods for Modeling Foil Air Bearings,” Master Thesis, Department of Mechanical Engineering, Chang Gung University, June 2012.
17. NVIDIA Tesla C2075,https://www.techpowerup.com/gpudb/563/tesla-c2075.
18. NVIDIA Quadro k620,https://www.techpowerup.com/gpudb/2600/ quadro-k620
19. PGI Compilers for Heterogeneous Supercomputing, “OpenACC for Fortran”.