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研究生:徐懿蕙
研究生(外文):Yi-Hui Hsu
論文名稱:新誤差評估技術應用於正規化無網格法及無因次動力影響函數法求解霍姆荷茲問題
論文名稱(外文):Applications of a New Error Estimation Technique to the Regularized Meshless Method and the Non-dimensional Dynamic Influence Function Method for Solving the Helmholtz Problems
指導教授:陳桂鴻陳桂鴻引用關係
指導教授(外文):Kue-Hong Chen
口試委員:徐文信呂學育
口試日期:2013-11-27
學位類別:碩士
校院名稱:國立宜蘭大學
系所名稱:土木工程學系碩士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:171
中文關鍵詞:邊界節點配置法正規化無網格法基本解法無網格法誤差評估技術最佳數目源點配置點輔助問題水波問題
外文關鍵詞:boundary collocation methodregularized meshless methodmethod of fundamental solutionsmeshless methoderror estimation techniqueoptimal numbersource pointscollocation pointsauxiliary problemwater wave problem
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本論文為了彌補基本解法在物理域外人工邊界的缺陷,引入兩種改良方法,即邊界配置法及正規化無網格法;這兩種數值方法不僅可以將觀測點及源點放置於真實邊界,也可以保有基本解法的精神。我們使用誤差評估技術評估兩種方法的數值誤差,藉由觀察其誤差曲線,我們可獲得最佳配置點的數目;於採取最佳配置點後,在無解析解的情況下,該方法收斂的數值解可以被獲得。此外,我們藉由多重座標系統的概念改良這個誤差評估技術,解決本誤差評估技術於求解內域及外域多孔洞問題。最後,我們舉一些數值算例來驗證誤差評估技術的準確性和穩定性;本論文將多個散射體的水波問題置於最後來驗證此誤差評估技術的應用性及可行性。
In this thesis, two improved approach, called the boundary collocation method (BCM) and the regularized meshless method (RMM) were introduced to remedy the drawback of the controversial artificial boundary outside the physical domain of the method of fundamental solutions (MFS). Not only can both numerical methods retain the spirit of the MFS, but they can also distribute the observation and the source points on the coincident locations of the real boundary. Furthermore, we implemented a proposed error estimation technique to estimate the numerical error of the two methods. By observing the obtained error curve, we derived the optimal number of collocation points. After adopting the optimal number of collocation points, the convergent solution of problem can be obtained in unavailable analytical solution condition. In addition, we improved this error technique by the concept of the multiply coordinate systems when we treat with the interior and exterior problem with multiply holes. Finally, we took the numerical examples to verify the accuracy and stability of the proposed error estimation technique. The water wave problem with multiply scatters was taken in the final numerical example to verify the applicable and practicable of this error technique.
Contents I
Table captions IV
Figure captions V
Notation captions XVI
Abstract XX
摘要 XXI
Chapter 1 Introduction
1.1 Motivation of the research 1
1.2 Organization of the thesis 3
Chapter 2 The method of fundamental solutions
2.1 Introduction 4
2.2 Problems statement 5
2.2.1 Boundary value problem 5
2.2.2 Green’s function problem 6
2.2.3 Water wave problem 7
2.3 Formulation 9
2.4 The proposed error estimation technique 12
2.4.1 Definition of an auxiliary problem 12
2.4.1.1 Defining the G.E., contour and B.C. type 12
2.4.1.2 Giving the exact solution 13
2.4.1.3 Specifying B.C.s 14
2.4.1.4 Difference between the auxiliary problem and the original problem 14
2.4.2 Error analysis in the auxiliary problem 15
2.4.3 Solving the original problem 16
2.5 Illustrative examples and discussions 16
2.6 Conclusions 23
Chapter 3 The boundary collocation method
3.1 Introduction 25
3.2 Problems statement 26
3.3 Formulation 26
3.3.1 Meshless formulation using radial basis function of the imaginary-part kernel 27
3.3.2 Calculation for the diagonal elements in the four influence matrices using the rule and invariant method 28
3.4 The proposed error estimation technique 29
3.5 Illustrative examples and discussions 29
3.6 Conclusions 33
Chapter 4 The regularized meshless method
4.1 Introduction 35
4.2 Problems statement 36
4.3 Formulation 36
4.3.1 Meshless formulation using radial basis functions 36
4.3.2 Derivation of diagonal coefficients of influence matrices 38
4.3.2.1 Diagonal coefficients of interior type 38
4.3.2.2 Diagonal coefficients of exterior type 39
4.4 The proposed error estimation technique 43
4.5 Illustrative examples and discussions 44
4.6 Conclusions 49
Chapter 5 Conclusions and further research
5.1 Conclusions 50
5.2 Further research 51
References
Table 2-1 The complementary solution for the Helmholtz equation 62
Fig. 1-1 The frame of this thesis. 63
Fig. 1-2 History of the proposed error estimation technique. 64
Fig. 2-1 The problem statement of boundary value problem, (a) the interior domain with multiply holes, (b) the exterior domain with multiply holes. 65
Fig. 2-2 The problem statement of Green’s function problem, (a) the interior domain with multiply holes, (b) the exterior domain with multiply holes. 66
Fig. 2-3 The problem statement of water wave problem with multiply holes, (a) x-z plane, (b) x-y plane. 67
Fig. 2-4 The sketch of the concept of the multiply coordinate systems. 68
Fig. 2-5 The flowchart of the formulation in implementing the proposed error estimation technique for MFS. 69
Fig. 2-6 Problem sketch of the case 1 of example 2-1. 70
Fig. 2-7 The error analysis versus the parameter d, for case 1 of example 2-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 71
Fig. 2-8 R.M.S error versus the number of collocation points for case 1 of example 2-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 72
Fig. 2-9 The field solution of original problem for case 1 of example 2-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 73
Fig. 2-10 Problem sketch of the case 2 of example 2-1. 74
Fig. 2-11 The error analysis versus the parameter d, for case 2 of example 2-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 75
Fig. 2-12 R.M.S error versus the number of collocation points for case 2 of example 2-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 76
Fig. 2-13 The field solution of original problem for case 2 of example 2-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 77
Fig. 2-14 Problem sketch of the example 2-2. 78
Fig. 2-15 The error analysis versus the parameter d, for example 2-2, (a) Single-layer potential approach, (b) Double-layer potential approach. 79
Fig. 2-16 R.M.S error versus the number of collocation points for example 2-2, (a) Single-layer potential approach, (b) Double-layer potential approach. 80
Fig. 2-17 The field solution of original problem for example 2-2, (a) Single-layer potential approach, (b) Double-layer potential approach. 81
Fig. 2-18 Problem sketch of the example 2-3. 82
Fig. 2-19 The error analysis versus the parameter d, for example 2-3, (a) Single-layer potential approach, (b) Double-layer potential approach. 83
Fig. 2-20 R.M.S error versus the number of collocation points for example 2-3, (a) Single-layer potential approach, (b) Double-layer potential approach. 84
Fig. 2-21 The field solution of original problem for example 2-3, (a) Single-layer potential approach, (b) Double-layer potential approach. 85
Fig. 2-22 Problem sketch of the example 2-4. 86
Fig. 2-23 The error analysis versus the parameter d, for example 2-4, (a) Single-layer potential approach, (b) Double-layer potential approach. 87
Fig. 2-24 R.M.S error versus the number of collocation points for example 2-4, (a) Single-layer potential approach, (b) Double-layer potential approach. 88
Fig. 2-25 The field solution of original problem for example 2-4, (a) Single-layer potential approach, (b) Double-layer potential approach. 89
Fig. 2-26 Problem sketch of the case 1 of example 2-5. (Lx=Ly=1, x0=y0=0.8) 90
Fig. 2-27 The error analysis versus the parameter d, for case 1 of example 2-5, (a) Single-layer potential approach, (b) Double-layer potential approach. 91
Fig. 2-28 R.M.S error versus the number of collocation points for case 1 of example 2-5, (a) Single-layer potential approach, (b) Double-layer potential approach. 92
Fig. 2-29 The field solution of original problem for case 1 of example 2-5, (a) Actual solution, (b) Single-layer potential approach, (c) Double-layer potential approach. 93
Fig. 2-30 Problem sketch of the case 2 of example 2-5. (Lx=Ly=1, x0=y0=0.8) 94
Fig. 2-31 The error analysis versus the parameter d, for case 2 of example 2-5, (a) Single-layer potential approach, (b) Double-layer potential approach. 95
Fig. 2-32 R.M.S error versus the number of collocation points for case 2 of example 2-5, (a) Single-layer potential approach, (b) Double-layer potential approach. 96
Fig. 2-33 The field solution of original problem for case 2 of example 2-5, (a) FEM, (a) Single-layer potential approach, (b) Double-layer potential approach. 97
Fig. 2-34 Problem sketch of case 1 of example 2-6. (r=1, θinc=0°) 98
Fig. 2-35 The error analysis versus the parameter d, of case 1 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 99
Fig. 2-36 R.M.S error versus the number of collocation points of case 1 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 100
Fig. 2-37 The field solution of original problem of case 1 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 101
Fig. 2-38 Free surface elevation around cylinder of case 1 of example 2-6. 102
Fig. 2-39 Problem sketch of case 2 of example 2-6. (r/l=1/3, θinc=0°) 103
Fig. 2-40 The error analysis versus the parameter d, of case 2 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 104
Fig. 2-41 R.M.S error versus the number of collocation points of case 2 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 105
Fig. 2-42 The field solution of original problem of case 2 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 106
Fig. 2-43 Free surface elevation around cylinder (1) and (2) of case 2 of example 2-6. 107
Fig. 2-44 The resultant forces on the corresponding cylinder for case 2 of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 108
Fig. 2-45 Problem sketch of the case 1 of case 3 of example 2-6. (r/l=0.8) 109
Fig. 2-46 The error analysis versus the parameter d, for case 3(a) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 110
Fig. 2-47 R.M.S error versus the number of collocation points for case 3(a) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 111
Fig. 2-48 The field solution of original problem for case 3(a) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 112
Fig. 2-49 Free surface elevation around cylinder (1), (2), (3) and (4) for case 3(a) of example 2-6. 113
Fig. 2-50 The resultant force on the corresponding cylinder for case 3(a) of example 2-6, (a) D. V. Evans (1997), (b) Single-layer potential approach, (c) Double-layer potential approach. 114
Fig. 2-51 The error analysis versus the parameter d, for case 3(b) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 115
Fig. 2-52 R.M.S error versus the number of collocation points for case 3(b) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 116
Fig. 2-53 The field solution of original problem for case 3(b) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 117
Fig. 2-54 Free surface elevation around cylinder (1), (2), (3) and (4) for case 3(b) of example 2-6. 118
Fig. 2-55 The resultant force on the corresponding cylinder for case 3(b) of example 2-6, (a) Single-layer potential approach, (b) Double-layer potential approach. 119
Fig. 3-1 The flowchart of the formulation in implementing the proposed error estimation technique for BCM. 120
Fig. 3-2 The error analysis versus the number of collocation point for case 1 of example 3-1. 121
Fig. 3-3 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 122
Fig. 3-4 The field solution of original problem for case 1 of example 3-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 123
Fig. 3-5 The error analysis versus the number of collocation point for case 2 of example 3-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 124
Fig. 3-6 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 125
Fig. 3-7 The field solution of original problem for case 2 of example 3-1, (a) Single-layer potential approach, (b) Double-layer potential approach. 126
Fig. 3-8 The error analysis versus the number of collocation point for example 3-2, (a) Single-layer potential approach, (b) Double-layer potential approach. 127
Fig. 3-9 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 128
Fig. 3-10 The field solution of original problem for example 3-2, (a) Single-layer potential approach, (b) Double-layer potential approach. 129
Fig. 3-11 The error analysis versus the number of collocation point for example 3-3, (a) Single-layer potential approach, (b) Double-layer potential approach. 130
Fig. 3-12 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 131
Fig. 3-13 The field solution of original problem for example 3-3, (a) Single-layer potential approach, (b) Double-layer potential approach. 132
Fig. 3-14 The error analysis versus the number of collocation point for example 3-4, (a) Single-layer potential approach, (b) Double-layer potential approach. 133
Fig. 3-15 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 134
Fig. 3-16 The field solution of original problem for example 3-4, (a) Single-layer potential approach, (b) Double-layer potential approach. 135
Fig. 3-17 The error analysis versus the number of collocation point for case 1 of example 3-5, (a) Single-layer potential approach, (b) Double-layer potential approach. 136
Fig. 3-18 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 137
Fig. 3-19 The field solution of original problem for case 1 of example 3-5, (a) Actual solution, (b) Single-layer potential approach, (c) Double-layer potential approach. 138
Fig. 3-20 The error analysis versus the number of collocation point for case 2 of example 3-5, (a) Single-layer potential approach, (b) Double-layer potential approach. 139
Fig. 3-21 The convergence rate of the error analysis versus and computational time, (a) Single-layer potential approach, (b) Double-layer potential approach. 140
Fig. 3-22 The field solution of original problem for case 2 of example 3-5, (a) FEM, (b) Single-layer potential approach, (c) Double-layer potential approach. 141
Fig. 4-1 The flowchart of the formulation in implementing the proposed error estimation technique for RMM. 142
Fig. 4-2 The convergence rate of the error analysis versus and computational time for case 1 of example 4-1. 143
Fig. 4-3 The field solution of original problem for case 1 of example 4-1. 144
Fig. 4-4 The convergence rate of the error analysis versus and computational time for case 2 of example 4-1. 145
Fig. 4-5 The field solution of original problem for case 2 of example 4-1. 146
Fig. 4-6 The convergence rate of the error analysis versus and computational time for example 4-2. 147
Fig. 4-7 The field solution of original problem for example 4-2. 148
Fig. 4-8 The convergence rate of the error analysis versus and computational time for example 4-3. 149
Fig. 4-9 The field solution of original problem for example 4-3. 150
Fig. 4-10 The convergence rate of the error analysis versus and computational time for example 4-4. 151
Fig. 4-11 The field solution of original problem for example 4-4. 152
Fig. 4-12 The convergence rate of the error analysis versus and computational time for case 1 of example 4-5. 153
Fig. 4-13 The field solution of original problem for case 1 of example 4-5. 154
Fig. 4-14 The convergence rate of the error analysis versus and computational time for case 2 of example 4-5. 155
Fig. 4-15 The field solution of original problem for case 2 of example 4-5. 156
Fig. 4-16 The convergence rate of the error analysis versus and computational time for case 1 of example 4-6. 157
Fig. 4-17 The field solution of original problem for case 1 of example 4-6. 158
Fig. 4-18 Free surface elevation around cylinder of case 1 of example 4-6. 159
Fig. 4-19 The convergence rate of the error analysis versus and computational time for case 2 of example 4-6. 160
Fig. 4-20 The field solution of original problem for case 2 of example 4-6. 161
Fig. 4-21 Free surface elevation around cylinder (1) and (2) of case 2 of example 4-6. 162
Fig. 4-22 The resultant forces on the corresponding cylinder for case 2 of example 4-6. 163
Fig. 4-23 The convergence rate of the error analysis versus and computational time for case 3(a) of example 4-6. 164
Fig. 4-24 Free surface elevation around cylinder (1), (2), (3) and (4) for case 3(a) of example 4-6. 165
Fig. 4-25 Free surface elevation around cylinder (1), (2), (3) and (4) for case 3(a) of example 4-6. 166
Fig. 4-26 The resultant force on the corresponding cylinder for case 3(a) of example 4-6, (a) D. V. Evans (1997), (b) RMM. 167
Fig. 4-27 The convergence rate of the error analysis versus and computational time for case 3(b) of example 4-6. 168
Fig. 4-28 The field solution of original problem for case 3(b) of example 4-6. 169
Fig. 4-29 Free surface elevation around cylinder (1), (2), (3) and (4) for case 3(b) of example 4-6. 170
Fig. 4-30 The resultant force on the corresponding cylinder for case 3(b) of example 4-6. 171

[1]A. H. D. Cheng, "Particular solutions of Laplacian, Helmholtz-type, and polyharmonic operators involving higher order radial basis functions," Eng Anal Bound Elem vol. 24, pp. 531-538, 2000.
[2]A. H. D. Cheng, D. L. YoungL, and C. C. Tsai, "The solution of Poisson’s equation by iterative DRBEM using compactly supported, positive definite radial basis function," Eng Anal Bound Elem, vol. 24, pp. 549-575, 2000.
[3]A. N. Williams and W. Li, "Water wave interaction with an array of bottom-mounted surface-piercing porous cylinders," Ocean Eng, vol. 27, pp. 841-866, 2000.
[4]A. Poullikkas, A. Karageorghis, and G. Georgiou, "Methods of fundamental solutions for harmonic and biharmonic boundary value problems," Comput Mech vol. 21, pp. 416-423, 1998.
[5]B. H. Spring and P. L. Monkmeyer, "Interaction of plane waves with vertical cylinders," Proceeding of 14th International Conference on Coastal Engineering, pp. 1828-1845, 1974.
[6]B. Jin and W. Chen, "Boundary knot method based on geodesic distance for anisotropic problems," J Comput Phys, vol. 215, pp. 614-629, 2006.
[7]C. C. Tsai, D. L. Young, C. W. Chen, and C. M. Fan, "The method of fundamental solutions for eigenproblems in domains with and without interior holes," Proc R Soc A, vol. 462, pp. 1443-1466, 2006.
[8]C. F. Liao, "Applications of new error estimation technique in torsion and anti-plane shear problems with multiple inclusions " Master, National Ilan University, Ilan, Taiwan, 2012.
[9]C. M. Linton and D. V. Evans, "The interaction of waves with arrays of vertical circular cylinders," J Fluid Mech, pp. 215, 549-569, 1990.
[10]D. L. Young, K. H. Chen, and C. W. Lee, "Novel meshless method for solving the potential problems with arbitrary domains," Journal of Computational Physics, vol. 209, pp. 290-321, 2005.
[11]D. L. Young, K. H. Chen, and C. W. Lee, "Singular meshless method using double layer potentials for exterior acoustics," Journal of the Acoustical Society of America vol. 119, pp. 96-107, 2006.
[12]D. V. Evans and R. Porter, "Near-trapping of waves by circular arrays of vertical cylinders," Appl Ocean Res, vol. 19, pp. 83-99, 1997.
[13]D. V. Evans and R. Porter, "Trapping and near-trapping by arrays of cylinders in waves," J Eng Math, vol. 35, pp. 149-179, 1999.
[14]F. L. Jhong, "Applications of new error estimation technique to the method of fundamental solutions and Trefftz method for solving the boundary value problems of Helmholtz equation " Master, National Ilan University, Ilan, Taiwan, 2011.
[15]G. Duclos and A. H. Clement, "Wave propagation through arrays of unevenly spaced vertical piles," Ocean Eng, vol. 31, pp. 1655-1668, 2004.
[16]G. Fairweather and A. Karageorghis, "The method of fundamental solutions for elliptic boundary value problems," Adv Comput Math vol. 9, pp. 69-95, 1998.
[17]G. R. Liu and Y. T. Gu, "Meshless local Petrov-Galerkin (MLPG) method in combination with finite element approaches," Computational Mechanics, vol. 26, pp. 536-546, 2000.
[18]C. W. Hon YC, "Boundary knot method for 2D and 3D Helmholtz and convection–diffusion problems under complicated geometry," Int J Numer Methods Eng, 2003.
[19]I. Babuska and T. Strouboulis, The finite element method and its reliability Oxford: Oxford Univ, 2001.
[20]J. Li, H. Liu, and S. K. Tan, "Numerical study of wave trapping within cylinderical arrays," International Offshore and Polar Engineers Conference, 2012.
[21]J. P. Chen, C. X. Huang, and K. H. Chen, "Determination of spurious eigenvalues and multiplicities of true eigenvalues using the real-part dual BEM," Computational Mechanics, vol. 24(1), 41-51, 1999.
[22]J. Sladek, V. Sladek, and S. N. Atluri, "Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties," Computational Mechanics, vol. 24, pp. 456-462, 2000.
[23]J. T. Chen, "An application of new error estimation technique in the meshless method and boundary element method," Master, National Ilan University, Ilan, Taiwan, 2010.
[24]J. T. Chen, I. L. Chen, K. H. Chen, Y. T. Lee, and Y. T. Yeh, "A meshless method for free vibration analysis of circular and rectangular clamped plates using radial basis function," Engineering Analysis with Boundary Elements, vol. 28, pp. 535-545, 2004.
[25]J. T. Chen and K. H. Hong, "Review of dual integral representations with emphasis on hypersingular integrals and divergent series," Transactions of the American Society of Mechanical Engineers, vol. 52, pp. 17-33, 1999.
[26]J. T. Chen, M. H. Chang, K. H. Chen, and I. L. Chen, "Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function," Computational Mechanics, vol. 29, pp. 392-408, 2002.
[27]J. T. Chen, M. H. Chang, K. H. Chen, and S. R. Lin, "The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function," J Sound Vib, vol. 257, pp. 667-711, 2002.
[28]J. T. Chen, S. K. Kao, W. M. Lee, and Y. T. Lee, "Eigensolutions of the Helmholtz equation for a multiply connected domain with circular boundaries using the multipole Trefftz method," Engineering Analysis with Boundary Elements, vol. 34, pp. 463-470, 2009.
[29]J. T. Chen, S. R. Kuo, K. H. Chen, and Y. C. Chenh, "Comment on “vibration analysis of arbitrary shaped membranes using non-dimensional dynamic influence function”," Journal of Sound and Vibration, vol. 235, pp. 156-171, 2000.
[30]J. T. Oden, "Adaptive modeling in solid mechanics," Second European Congress on Computational Mechanics, 2001.
[31]J. T. Oden and K. Vemaganti, "Estimation of local modeling error and goal-oriented modeling of heterogeneous materials; Part I: Error estimates and adaptive algorithms," J Comput Phys, vol. 164, 2000.
[32]J. T. Oden and S. Prudhomme, "Goal-oriented error estimation and adaptivity for the finite element method," Comput Math Appl, vol. 41, 2001.
[33]J. T. Oden and S. Prudhomme, "Estimation of modeling error in computational mechanics," J Comput Phys, vol. 182, pp. 496-515, 2002.
[34]J. T. Oden, S. Prudhomme, D. Hammerand, and M. Kuczma, "Modeling error and adaptivity in nonlinear continuum mechanics," Comput Methods Appl Mech Eng, vol. 190, p. 6663, 2001.
[35]J. T. Oden and T. I. Zohdi, "Analysis and adaptive modeling of highly heterogeneous elastic structures," Comput Methods Appl Mech Eng, vol. 148, p. 367, 1997.
[36]K. H. Chen, J. H. Kao, and J. T. Chen, "Regularized meshless method for antiplane piezoelectricity problems with multiple inclusions," CMC, vol. 9, pp. 253-279, 2009.
[37]K. H. Chen, J. H. Kao, J. T. Chen, D. L. Young, and M. C. Lu, "Regularized meshless method for multiply-connected-domain Laplace problems," Engineering Analysis with Boundary Elements, vol. 30, pp. 822-896, 2006.
[38]K. H. Chen, J. T. Chen, and J. H. Kao, "Regularized meshless method for solving acoustic eigenproblem with multiply-connected domain," Computer Modeling in Engineering & Sciences, vol. 16, pp. 27-39, 2006.
[39]K. H. Chen, M. C. Lu, and H. M. Hsu, "Regularized meshless method analysis of the problem of obliquely incident water wave," Engineering Analysis with Boundary Elements, vol. 35, pp. 355-362, 2011.
[40]K. Vemaganti and J. T. Oden, "Estimation of local modeling error and goal-oriented adaptive modeling of heterogeneous materials. II. A computational environment for adaptive modeling of heterogeneous elastic solids," Comput Methods Appl Mech Eng, vol. 190, p. 6089, 2001.
[41]M. A. Tournour and N. Atalla, "Efficient evaluation of the acoustic radiation using multipole expansion.," Int J Numer Methods Eng, vol. 46, pp. 825-837, 1999.
[42]M. Abramowitz and I. A. Stegun, "Handbook of mathematical functions with formulation graphs and mathematical tablesdover," ed. New York, 1972.
[43]M. Ainsworth, "A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains," Numer Math, vol. 80, p. 325, 1998.
[44]M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis. New York: Wiley, 2000.
[45]M. G. Larson and T. J. Barth, "A posteriori error estimation for adaptive discontinuous Galerkin approximations of hyperbolic systems," Lect Notes Comput Sci Eng, vol. 11, p. 363, 2000.
[46]M. Paraschivoiu, J. Peraire, and A. T. Patera, "A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations," Comput Methods Appl Mech Eng, vol. 150, p. 289, 1997.
[47]O. Z. Mehdizadeh and M. Paraschivoiu, "Investigation of a two-dimensional spectral element method for Helmholtz's equation," J Comput Phys, vol. 189, pp. 111-129, 2003.
[48]P. Houston and B. Suli, "hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems," SIAM J Sci Comput, vol. 23,, p. 1226, 2001.
[49]R. Becker and R. Rannacher, "A feedback approach to error control in finite elements methods: Basic analysis and examples," East-West J Numer Math, vol. 4, p. 237, 1996.
[50]R. C. Maccamy and R. A. Fuchs, "Wave force on piles: A diffraction theory, Technical Memorandum No. 69, US Army Coastal Engineering Research Center (formerly Beach Erosion Board)," 1954.
[51]R. Mclver and D. V. Evans, "Approximation of wave forces on cylinder arrays," Appl Ocean Res, vol. 6, pp. 101-107, 1984.
[52]R. Song and W. Chen, "An investigation on the regularized meshless method for irregular domain problems," CMES, vol. 42, pp. 59-70, 2009.
[53]S. N. Atluri, J. Sladek, V. Sladek, and T. Zhu, "The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity," Computational Mechanics, vol. 25, pp. 180-198, 2000.
[54]S. N. Atluri and T. L. Zhu, "The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics," Computational Mechanics, vol. 25, pp. 169-179, 2000.
[55]S. N. Atluri and T. L. Zhu, "New concept in meshless methods," Int. J. Numer. Meth. Engng., vol. 47, pp. 537-556, 2000.
[56]S. N. Atluri and T. Zhu, "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics," Computational Mechanics, vol. 22, pp. 117-127, 1998.
[57]S. Prudhomme and J. T. Oden, "On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors," Comput Methods Appl Mech Eng, vol. 176, p. 313, 1999.
[58]S. W. Kang, "Free vibration analysis of arbitrarily shaped plates with a mixed boundary condition using non-dimensional dynamic influence function," Journal of Sound and Vibration, vol. 256, pp. 533-549, 2002.
[59]S. W. Kang, I. S. Kim, and J. M. Lee, "Free Vibration Analysis of Arbitrarily Shaped Plates With Smoothly Varying Free Edges Using NDIF Method," Journal of Vibration and Acoustics, vol. 130, pp. 041010-1, 2008.
[60]S. W. Kang and J. M. Lee, "Application of free vibration analysis of membranes using the non-dimensional dynamic influence function," Journal of Sound and Vibration, vol. 234, pp. 455-, 2000.
[61]S. W. Kang and J. M. Lee, "Free vibration analysis of arbitrarily shaped plates with clamped edges using wave-type function," Journal of Sound and Vibration, vol. 242, pp. 9-26, 2001.
[62]S. W. Kang and J. M. Lee, "Free vibration analysis of arbitrarily shaped plates with clamped edges using wave-type functions," J Sound Vib, vol. 242, pp. 9-26, 2001.
[63]S. W. Kang, J. M. Lee, and Y. J. Kang, "Vibration analysis of arbitrarily shaped membranes using non-dimensional dynamic influence function," J Sound Vib, vol. 221, pp. 117-132, 1999.
[64]V. D. Kupradze and M. A. Aleksidze, "The method of functional equations for the approximate solution of certain boundary value problems," USSR Comput Math Math Phys, vol. 4, pp. 199-205, 1964.
[65]V. Sladek, J. Sladek, S. N. Atluri, and R. Van Keer, "Numerical integration of singularities in meshless implementation of local boundary integral equations," Computational Mechanics, vol. 25, pp. 394-403, 200.
[66]V. Twersky, "Multiple scattering of radiation by an arbitrary configuration of parallel cylinders," J Acoust Soc, vol. 24, pp. 42-46, 1952.
[67]W. Chen, "Symmetric boundary knot method," Eng Anal Bound Elem vol. 26, 2002.
[68]W. Chen, J. Lin, and F. Wang, "Regularized meshless method for nonhomogeneous problems," Engineering Analysis with Boundary Elements, vol. 35, pp. 253-257, 2011.
[69]W. Chen, J. Shi, and L. Chen, "Investigation on the spurious eigenvalues of vibration plates by non-dimensional dynamic influence function method," Engineering Analysis with Boundary Elements, vol. 33, pp. 885-889, 2009.
[70]W. Chen and M. Tanaka, "A meshfree integration-free and boundary-only RBF technique," Comput Math Appl, vol. 43, pp. 379-391, 2002.
[71]W. S. Hwang, L. P. Hung, and C. H. Ko, "Non-singular boundary integral formulations for plane interior potential problems," Int J Numer Methods Eng, vol. 53, pp. 1751-1762.
[72]Y. C. Hon and W. Chen, "Boundary knot method for 2D and 3D Helmholtz and the convection-diffusion problems with complicated geometry," Int J Numer Methods Eng, vol. 56, pp. 1931-1948, 2003.
[73]Y. H. Chen, "Wave-induced oscillations in harbors by permeable arc break-waters," Master, National Taiwan Ocean University, Keelung, Taiwan, 2004.

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