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研究生: 賴俊彰
Lai, Chun-Chang
論文名稱: 薄板中的暫態彈性波計算與平行化
Computation of 2D Transient Elastic Waves in Thin Plate with Free Surface by BEM and OpenMP
指導教授: 沈士育
Shen, Shih-Yu
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2014
畢業學年度: 102
語文別: 英文
論文頁數: 54
中文關鍵詞: 彈性波邊界元素法平行計算
外文關鍵詞: elastic waves, BEM, OpenMP
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  • 本研究探討彈性波在薄板內的計算。主要工具為邊界元素法並以其相關數值方法作為計算的基礎。
    考慮的問題為透過計算描述具自由表面彈性薄板於一點受對稱表面應力時.其餘點從暫態到震盪的位移變化。主要目的為:
    1.計算薄板內各點的位移作為進一步研究的工具
    2. 提升運算效率以處理更複雜的情況
    本研究引入OpenMP 的平行計算並達成顯著的效率提升.使原本用於短時間暫態的計算方法可以涵蓋更複雜的問題或更長的時間。

    This paper considers an elastic thin plate with free surface subject to a symmetric sinusoidal loading. Boundary element method (BEM) and numerical methods developed in is used to compute transient waves
    The main purposes are to:
    1.Compute the displacement of elastic waves in a thin plate which can be used for further study
    2.Improve computation efficiency to cover a wider range of problems
    This paper incorporates OpenMP, an industrial application interface for parallel computing, to the programming. The work done here then extends existing codebase to handle computation-heavier problems.

    摘要 I ABSTRACT II ACKOWLEDGEMENT III CONTENTS IV LIST OF FIGURES VI CHAPTER I INTRODUCTION - 1 - 1.1 MOTION IN SOLIDS - 1 - 1.2 ELASTIC WAVES - 2 - 1.3 BEM AND ANALYTIC BASIS - 3 - 1.4 MOTION IN A THIN PLATE - 4 - 1.5 TIME COMPLEXITY - 5 - 1.6 PARALLEL PROGRAMMING - 6 - CHAPTER II FORMULATION - 9 - 2.1 THE PROBLEM - 9 - 2.2 BEM FORMULATION - 11 - 2.3 DISCRETE APPROXIMATION - 13 - 2.4 TIME STEPPING EQUATIONS - 16 - CHAPTER III PROGRAMMING AND ANALYSIS - 19 - 3.1 OVERVIEW - 19 - 3.2 PARAMETERS - 20 - 3.3 NODES AND SYMMETRY - 22 - 3.4 CODE FLOW - 23 - 3.5 IMPULSE RESPONSE - 24 - 3.6 CONVOLUTION - 27 - CHAPTER IV PARALLEL PROGRAMMING WITH OPENMP - 30 - 4.1 OPENMP DIRECTIVES - 30 - 4.2 OPENMP BASICS - 31 - 4.3 A PARALLEL PARADIGM - 33 - 4.4 SETUP - 37 - 4.5 MEMORY PROBLEM - 38 - 4.6 RESULT AND PROFILING - 39 - 4.7 IMPROVEMENTS - 41 - CHAPTER V DISCUSSION AND CONCLUSION - 47 - 5.1 DISPLACEMENT AT A DISTANCE - 47 - 5.2 TIME INSTABILITY - 51 - 5.3 REMARKS - 52 - 5.4 CONCLUSION - 52 - REFERENCES - 54 -

    [1] Shih-yu Shen. An indirect elastodynamic boundary element method with analytic bases. International Journal for Numerical Methods in Engineering 2003; 57; 767-794.
    [2] http://www.nvidia.com/object/what-is-gpu-computing.html
    [3] https:// software.intel.com/en-us
    [4] Y. C. Fung. Foundations of solid mechanics. Eaglewood Cliffs, N.J. Prentice-Hall, Inc. 1985
    [5] Marc Bonnet. Boundary Integral Equation Methods for Solids and Fluids. John Wiley & Sons Ltd. 1995
    [6] Eringen AC, Suhubi ES. Elastodynamics, vol. II. Academic Press: New York, 1975.
    [7] http://www.openmp.org/mp-documents/OpenMP4.0.0.pdf
    [8] https://software.intel.com/en-us/articles/avoiding-and-identifying-false-sharing-among-threads
    [9] Siebrits E. Crouch SL. Two-dimensional elastodynamics displacement discontinuity method. International Journal for Numerical Methods in Engineering 1994; 37:2229-3250.

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