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研究生： 陳勁銘
Jing-Ming Chen
論文名稱： 以分散式及共享式記憶體架構下執行高速平行計算求解納維爾－斯托克斯方程式研究
Study of High-Performance Computing for Solving Navier-Stokes Equation in Architectures of Distributed and Shared Memory.
指導教授： 陳明志
Ming-Jyh Chern
口試委員: 謝佑明
Yo-Ming Hsieh
王謹誠
Chin-Cheng Wang
學位類別： 碩士
Master
系所名稱： 工程學院 - 機械工程系
Department of Mechanical Engineering
論文出版年： 2023
畢業學年度： 111
語文別： 英文
論文頁數： 72
中文關鍵詞： 直接施力邊界沈浸法 、高效能運算 、計算流體力學 、普松方程式 、物件導向程式設計
外文關鍵詞： Direct-forcing Immersed Boundart (DFIB), High-Performance Computing (HPC), Computational Fluid Dynamics (CFD), Poisson's Equation, Objective-oriented Programming Design
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    • Chinese Abstract................................... i Abstract........................................... ii Acknowledgements .................................. iv Contents ........................................... v Nomenclatures ....................................viii ListofTables....................................... x ListofFigures .................................... xi 1 INTRODUCTION 1 1.1 Motivation.................................... 1 1.2 LiteratureReview................................ 2 1.2.1 Computational Fluid Dynamics and Direct-Forcing ImmersedBoundaryMethod ..................... 2 1.2.2 Prediction-correction Process on DFIB method . . . . . . . . . . . 4 1.2.3 N-SSolverwithParallelComputing ................. 4 1.2.4 Iterative Methods for the Solution of Large Linear System . . . . . 6 1.2.5 SIMD .................................. 6 1.2.6 ArithmeticIntensity .......................... 7 1.3 Synopsis..................................... 7 2 METHODOLOGY 9 2.1 LESGoverningEquationandModels..................... 9 2.1.1 LESGoverningEquation ....................... 9 2.1.2 Prediction-correction Model for FSI Problem . . . . . . . . . . . . 11 2.2 CompilerOptimization............................. 13 2.3 ParallelComputing............................... 14 2.4 ComputationalEnvironment,Taiwania3................... 15 2.4.1 DataLocalityinCC-NUMA...................... 16 2.5 PerformanceTool................................ 17 2.6 VisualizationandPLOT3DFileFormat ................... 18 2.7 ProgramArchitecture ............................. 18 3 PARALLEL COMPUTATIONAL STRATEGIES FOR SOLVING POISSON’S EQUATION 21 3.1 DiscretizationofPoisson’sEquation...................... 21 3.2 ConvergenceConditionfortheIterativeMethod . . . . . . . . . . . . . . . 23 3.3 BiCGSTAB................................... 23 3.4 BiCGSTABwithMPI ............................. 25 3.5 Performance Evaluation for Inner Product Computation . . . . . . . . . . 26 3.6 SparseMatrixFormat ............................. 27 3.7 ELLSparseMatrixformat........................... 28 3.7.1 Insert Method and he Method for Extraction CSR Format . . . . 28 3.7.2 ELL SpMV Computational Optimization and Analysis Method . . 32 3.8 SPESparseMatrixformat........................... 33 3.9 SPE-2SparseMatrixformat.......................... 34 3.10 TheDataStructuresinCSR,ELL,andSPEformat. . . . . . . . . . . . . 35 3.11 PerformanceEvaluationsforSpMVComputations. . . . . . . . . . . . . . 37 4 RESULTS AND DISCUSSION 39 4.1 ComparisonwithinELLandCSRformat .................. 39 4.1.1 Introductiontothe2DConductionProblem . . . . . . . . . . . . . 39 4.1.2 Introduction to the System Matrix Provided COMSOL FEM Solver 40 4.1.3 PerformanceEvaluationsandDiscussion . . . . . . . . . . . . . . . 42 4.2 FlowPastCylinderatRe=40 ........................ 43 4.2.1 The Relationship Between the ?∗ and Parallel Performance . . . . . 46 4.2.2 A Comparison Based Algorithms for Solving Poisson’s Equation . . 48 5 CONCLUSIONS AND FUTURE WORKS 50 5.1 Conclusions................................... 50 5.2 FutureWorks.................................. 51 BIBLIOGRAPHY.................................51

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