Overview of Taiwan BEM 1980 2018 Paradise and

Overview of Taiwan BEM (1980 -2018) Paradise and parasite of BIEM/BEM Jeng-Tzong Chen 海洋大學河 系 陳正宗終身特聘教授 Vice president, Tw. SIAM Convener of Civil & Hydraulic Engineering Program, MOST, Taiwan Fellow of STAM, ROC Life-time Distinguished Professor Dept. Harbor and River Engineering Dept. Mechanical and Mechatronic Engineering Taiwan Ocean University 09: 00 -10: 00, August 2, 2018 145報告廰 (中南 2018. ppt)

Outline 1. Overview of Tw. SIAM 2. Overview of Taiwan BEM development 3. Rank deficient systems in BIEM/BEM

TWSIAM • Establish: non-profit academic society established on June 26, 2012 • Aim: – To promote research and education of applied mathematics – To bridge mathematics and industry communities • Members (2018): – Regular members: 102 – Group members: 16 – Student members: 53 • Web address: www. twsiam. org 4

In the sky, there is a paradise In the earth, there is Suchou and Hangzhou 上有天堂 下有蘇杭 BEM always needs fundamental solution or Green function 邊界元素法有格林函數與基本解 天堂(paradise)? ? 寄生蟲(parasite)? ? Fundamental solution BEM Suzhou 2008 Hangzhou 2015 Green function Paradise in the Earth Parasite in the BEM

Paradise of BEM (1984 -2000) 3 D→ 2 D 鄭板橋 刪繁就簡三秋樹 領異標新二月花 Paradise Stress concentration 2020/12/1 Infinite domain Fracture and fatigue Page 6

Overview of numerical methods Numerical Methods Meshless Methods Mesh Methods Finite Difference Method Difference Equation 開刀 operation Finite Element Method PDE- variational 把脈 Take pulse Boundary Element Method Null-field BIEM Degenerate kernels Integral Equation 針 灸 Acupuncture Page 7

How to select melon and how to cook 退化邊界 一般邊界 (ordinary boundary) (degenerate boundary)

History & Background Taiwan BEM workshop (1986 -2018) Year The host unit 1986 NTU IAM Prof. Y H Pao Establishment of NTU IAM 1998 NSC Prof. J T Chen NCHC 2010 NTOU-HRE-MSV Prof. J T Chen NTOU-HRE 50 th anniversary 2011 NCTS(South) Prof. K M Lee NCKU 80 th anniversary 2012 Feng Chia University Prof. Y C Shiah Prof. Hong’s 60 th birthday 2013 National Chung Hsing University Prof. K J Shou Congratulations for Academicain Dean S L Crouch Academician, NAE 2014 National SYS University Prof. T T Lu Prof. Young’s 70 th birthday Prof. D L Young 2015 NCREE (cross strait) Dr. R Z Wang NCREE 2016 NCTS (Japan-Taiwan) Prof. J H Lee NCTS 2017 NIU 2018 ISU The organizer Prof. I L Chern Prof. K H Chen Prof. H T Huang Ceremony Ilan Univ Keynote Prof. F J Rizzo Prof. A H D Cheng Prof. Z C Li NCKU Prof. H-K Hong Cross strait ceremony Prof. H-K Hong Prof. W-W Lin Prof. H-K Hong Prof. W-C Wang

Never escape from te hand of Gauss Why BEM (Advantage) B Gauss 1+2+3+. . . +100=? Area = ? B Planimeter 3 D 2 D BEM Gauss' theorem Green's identities Somigliana identity B 10

Degenerate boundary (-1, 0. 5) geometry node (1, 0. 5) 4 7 N 6 5 8 the Nth constant or linear element 3 (0, 0) 1 2 (-1, -0. 5) (1, -0. 5) 5(+) 6(+) 5(+) 6(-) 5(+) 6(+) dependency 5(+) 6(+) 5(+) 6(-) 15: 27 March 20, 2013 5(+) 6(+) Nonuniqueness BEM 4 -Taiwan, 2013 5(+) 6(-) P. 11

Liggett and Liu (1983) • The singularities that occur when the base point and field point coincide are not integrable ? ? ? Multi-domain BEM, Ingraffea 1981 (before 1983) J C Nedelec 1982 Google citing 1728 15: 27 March 20, 2013 Google citing 574 BEM 4 -Taiwan, 2013 P. 12

How to get an additional constraint The number of constraint equation is not enough to determine coefficients of p and q. Another constraint equation is obtained by differential operator 15: 27 March 20, 2013 BEM 4 -Taiwan, 2013 P. 13 13

Dual Integral Equations by Hong and Chen(1984 -1986) Singular integral equation Cauchy principal value Boundary element method 1969 Hypersingular integral equation Hadamard principal value (Mangler principal value) Dual boundary element method 1986 normal boundary degenerate boundary NTUCE 15: 28 March 20, 2013 BEM 4 -Taiwan, 2013 Ó P. 14

Dual BEM, DDM and Dislocation theory Dual BEM Hong and Chen (ASCE, 1988) -a 0 a Dislocation theory DDM Crouch S. L. (1983) Neuber-Papkovitch function 15: 28 March 20, 2013 ∞ Higher order element by Shou K. J. BEM 4 -Taiwan, 2013 P. 15

裂縫成長 Crack growth FEM Remesh near tip Subdomain BEM Ingraffea, 1981 Dual BEM (MIT) Hong and Chen, 1988 Chen and Hong, 1999

Seepage (sheet pile) A K Chugh, US Bureau of Reclamation (USBR), USA

Seepage with free surface FEM (iteration No. 49) Initial guess After iteration BEM(iteration No. 13) Initial guess After iteration Remesh area Remesh line

Dual BEM results and experiment data by NTOU Thin breakwater (degenerate boundary) d/h = 0. 2 BEM W K Weng and C Y Yueh (1. 7 -mm thick) Dual BEM 19/ 97

Solid rocket motor (Army 蜂火箭) 20

Shong-Fon II missile (Navy) Thin airfoil (degenerate boundary) 21

IDF (Air Force) Thin airfoil (degenerate boundary) 22

V-band structure (Tien-Gen missile) 23

Dual BEM 走過三十年(1984 -2018) Yu D. H. (余德浩) (1983) 中國科學院博士論文 (Chinese) Takakuda K. (高久田) (1985) JSME Chen J. T. (陳正宗) (1986) 台灣大學應力所碩士論文 supervised by Prof. H. –K. Hong Ugodchicoff and Khutoryanskiy (1986) Kazan Univ. Press (Russian) (1986) 中國科學中文版(Chinese) (1987) 中國科學英文版(English) Hong H. -K. and Chen J. T. (洪宏基與陳正宗) (1988) ASCE, EM Aliabadi M. H. (1992) IJNME Chen J T and H K Hong (1999) ASME-AMR Hu H. C. (胡海昌)

Parasite of BEM (2000 -2018) Minimum singular value t(a, 0) Rank-deficient systems 0/0 Mechanics Research Communications Radius Degenerate scale Fictitious frequency Engineering Analysis with Boundary Elements Pitfall Parasite Dependency Spurious eigenvalue International Journal for Numerical Methods in Engineering Degenerate boundary Thermochimita Acta Parasite of BEM. pptx made by York

(Hangzhou: paradise in the world) BEM/BIEM the BEM) (U(x, s): parasite in Match maker (ask for help) (Disadvantage: Failure) Engineering problems Test function PDE and IE are not equivalent PDE model (1) Fundamental sol. (2) Green function IE model(BEM) Existence unique solution (1) (2) (3) (4) 引狼入室 (set a fox to keep geese) Degenerate scale Degenerate boundary Spurious eigenvalues Fictitious frequency Range deficiency Rank deficiency Singular matrix 2015 Master Thesis Oral Defense , MSV, Nonunique solution Fredholm alternative theorem Infinite solution (Not sufficient) No solution (Not necessary) National Taiwan Ocean University , Keelung 26

Citing records of dual BEM (updated June 23, 2018) Hong and Chen, 1988 ASCE-EM WOS: 203 Google: 307 Chen and Hong, 1999 ASME-AMR WOS: 284 Google: 387

New direction 八卦邊界元 Trigram (Bagua) boundary element method Real variable BEM Complex variable BEM 八卦 BEM Clifford algebra valued BEM 2020/12/1 Quaternion valued BEM Page 29

Conclusions 1. Overview of Tw. SIAM 2. Overview of Taiwan BEM development 3. Paradise and parasite of BEM Rank deficient systems in BIEM/BEM

Thanks 鄧又軍教授 to arrange this talk Thanks for your kind attentions Welcome to visit the web site of MSVLAB/NTOU http: //msvlab. hre. ntou. edu. tw/ Since 1999

Welcome to visit NTOU/MSV 窗外

http: //msvlab. hre. ntou. edu. tw/ Since 1999 台灣製造 輸出中國 NTOU/MSV 有您真好 Welcome to visit the web site of MSVLAB/NTOU E mail: jtchen@mail. ntou. edu. tw 台灣天下 捨我其誰 33

臺灣數學與 程互動(Bridge: computational mechanics) Ø Taiwan SIAM 扮演的角色 Ø建立數學與 程的連接橋樑 研 究 強 度 ØMathematics與Engineering並重 數學 程 (由數學界發起的) 研 Mathematics & Engineering 究(Taiwan SIAM) may bridge the gap 強 度 Time Evolution Taiwan BEM 數學 程 series meeting (由 程界發起的) 34 Filename: NTOUMSV交叉. ppt