Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method

Simulation of Seismic Wave Scattering by Embedded Cavities in an Elastic Half-Plane Using the Novel Singular Boundary Method

Year:    2018

Author:    Ji Lin, Chuanzeng Zhang, Linlin Sun, Jun Lu

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 322–342

Abstract

In the present study, a numerical procedure for analyzing the seismic response of the linear elastic half-plane including buried cavities subjected to incident P and SV waves is proposed by means of the novel singular boundary method (SBM). The SBM is a recently developed boundary-type meshless collocation method, which applies the singular fundamental solutions as basis functions. In order to avoid the singularities of the fundamental solutions, the SBM introduces the concept of origin intensity factors at the origin. With the aid of the origin intensity factors of the Laplace and the plane-strain elastostatic problems, this study first derives the origin intensity factors for the traction boundary condition as well as the origin intensity factors for the flat boundary, in order to form the SBM formulation for wave scattering problems in the linear elastic half-plane including buried cavities. Results obtained with the SBM model are compared with the results obtained with the finite element method, which shows that the method is quite promising for studying seismic wave scattering problems.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2016-0187

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 2 : pp. 322–342

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Singular boundary method (SBM) embedded cavity linear elastic half-plane dynamic displacements fundamental solutions.

Author Details

Ji Lin

Chuanzeng Zhang

Linlin Sun

Jun Lu

  1. A meshless method for solving a class of nonlinear generalized telegraph equations with time-dependent coefficients based on radial basis functions

    Zheng, Bin | Reutskiy, Sergiy | Lu, Jun

    The European Physical Journal Plus, Vol. 135 (2020), Iss. 9

    https://doi.org/10.1140/epjp/s13360-020-00547-w [Citations: 1]
  2. A meshless radial basis function based method for modeling dual-phase-lag heat transfer in irregular domains

    Lin, Ji | Yu, Hao | Reutskiy, Sergiy | Wang, Yuan

    Computers & Mathematics with Applications, Vol. 85 (2021), Iss. P.1

    https://doi.org/10.1016/j.camwa.2020.12.018 [Citations: 4]
  3. A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis

    Sun, Linlin | Fu, Zhuojia | Chen, Zhikang

    Applied Mathematics and Computation, Vol. 439 (2023), Iss. P.127600

    https://doi.org/10.1016/j.amc.2022.127600 [Citations: 10]
  4. An efficient method of approximate particular solutions using polynomial basis functions

    Deng, Cheng | Zheng, Hui | Fu, Mingfu | Xiong, Jingang | Chen, C.S.

    Engineering Analysis with Boundary Elements, Vol. 111 (2020), Iss. P.1

    https://doi.org/10.1016/j.enganabound.2019.10.014 [Citations: 4]
  5. A modified multilevel algorithm for large-scale scientific and engineering computing

    Li, Junpu | Chen, Wen | Qin, Qing-Hua | Fu, Zhuojia

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 8 P.2061

    https://doi.org/10.1016/j.camwa.2018.12.012 [Citations: 33]
  6. Learning solutions to the source inverse problem of wave equations using LS-SVM

    Wu, Ziku | Ding, Chang | Li, Guofeng | Han, Xiaoming | Li, Juan

    Journal of Inverse and Ill-posed Problems, Vol. 27 (2019), Iss. 5 P.657

    https://doi.org/10.1515/jiip-2018-0066 [Citations: 6]
  7. The sample solution approach for determination of the optimal shape parameter in the Multiquadric function of the Kansa method

    Chen, Wen | Hong, Yongxing | Lin, Ji

    Computers & Mathematics with Applications, Vol. 75 (2018), Iss. 8 P.2942

    https://doi.org/10.1016/j.camwa.2018.01.023 [Citations: 52]
  8. Study on the integrated calculation method of fluid–structure interaction vibration, acoustic radiation, and propagation from an elastic spherical shell in ocean acoustic environments

    Huang, He | Zou, Ming-Song | Jiang, Ling-Wen

    Ocean Engineering, Vol. 177 (2019), Iss. P.29

    https://doi.org/10.1016/j.oceaneng.2019.02.032 [Citations: 18]
  9. A review of computational models for underwater acoustic radiation induced by structural vibration in the shallowmarine environment

    Xi, Qiang | Fu, Zhuojia

    Chinese Science Bulletin, Vol. 67 (2022), Iss. 27 P.3269

    https://doi.org/10.1360/TB-2022-0229 [Citations: 0]
  10. The generalized finite difference method for the inverse Cauchy problem in two-dimensional isotropic linear elasticity

    Li, Po-Wei | Fu, Zhuo-Jia | Gu, Yan | Song, Lina

    International Journal of Solids and Structures, Vol. 174-175 (2019), Iss. P.69

    https://doi.org/10.1016/j.ijsolstr.2019.06.001 [Citations: 45]
  11. The adaptive algorithm for the selection of sources of the method of fundamental solutions

    Lin, Ji | Lamichhane, A.R. | Chen, C.S. | Lu, Jun

    Engineering Analysis with Boundary Elements, Vol. 95 (2018), Iss. P.154

    https://doi.org/10.1016/j.enganabound.2018.07.008 [Citations: 15]
  12. General dynamic properties of conduction electron within the first Brillouin zone of graphene

    Suprun, A. D. | Shmeleva, L. V.

    The European Physical Journal Plus, Vol. 134 (2019), Iss. 1

    https://doi.org/10.1140/epjp/i2019-12520-7 [Citations: 2]
  13. Two-level implicit high order method based on half-step discretization for 1D unsteady biharmonic problems of first kind

    Kaur, Deepti | Mohanty, R.K.

    Applied Numerical Mathematics, Vol. 139 (2019), Iss. P.1

    https://doi.org/10.1016/j.apnum.2018.12.015 [Citations: 3]
  14. A dual interpolation boundary face method for three-dimensional potential problems

    Zhang, Jianming | Chi, Baotao | Lin, Weicheng | Ju, Chuanming

    International Journal of Heat and Mass Transfer, Vol. 140 (2019), Iss. P.862

    https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.011 [Citations: 15]
  15. A Hybrid GFDM–SBM Solver for Acoustic Radiation and Propagation of Thin Plate Structure Under Shallow Sea Environment

    Xi, Qiang | Fu, Zhuojia | Li, Yudong | Huang, He

    Journal of Theoretical and Computational Acoustics, Vol. 28 (2020), Iss. 02 P.2050008

    https://doi.org/10.1142/S2591728520500085 [Citations: 12]
  16. Singular boundary method based on time‐dependent fundamental solutions for active noise control

    Li, Junpu | Chen, Wen

    Numerical Methods for Partial Differential Equations, Vol. 34 (2018), Iss. 4 P.1401

    https://doi.org/10.1002/num.22263 [Citations: 10]
  17. A wideband fast multipole accelerated singular boundary method for three-dimensional acoustic problems

    Qu, Wenzhen | Zheng, Changjun | Zhang, Yaoming | Gu, Yan | Wang, Fajie

    Computers & Structures, Vol. 206 (2018), Iss. P.82

    https://doi.org/10.1016/j.compstruc.2018.06.002 [Citations: 12]
  18. Simulation of heat conduction problems in layered materials using the meshless singular boundary method

    Zheng, Bin | Lin, Ji | Chen, Wen

    Engineering Analysis with Boundary Elements, Vol. 100 (2019), Iss. P.88

    https://doi.org/10.1016/j.enganabound.2018.02.003 [Citations: 5]
  19. Parallel and vectorized implementation of analytic evaluation of boundary integral operators

    Zapletal, Jan | Of, Günther | Merta, Michal

    Engineering Analysis with Boundary Elements, Vol. 96 (2018), Iss. P.194

    https://doi.org/10.1016/j.enganabound.2018.08.015 [Citations: 11]
  20. Application of modified Fourier law in von Kármán swirling flow of Maxwell fluid with chemically reactive species

    Khan, Masood | Ahmed, Jawad | Ahmad, Latif

    Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40 (2018), Iss. 12

    https://doi.org/10.1007/s40430-018-1490-0 [Citations: 15]
  21. The improved backward substitution method for the simulation of time-dependent nonlinear coupled Burgers’ equations

    Zhang, Yuhui | Lin, Ji | Reutskiy, Sergiy | Sun, Hongguang | Feng, Wenjie

    Results in Physics, Vol. 18 (2020), Iss. P.103231

    https://doi.org/10.1016/j.rinp.2020.103231 [Citations: 15]
  22. A regularized approach evaluating origin intensity factor of singular boundary method for Helmholtz equation with high wavenumbers

    Li, Junpu | Fu, Zhuojia | Chen, Wen | Qin, Qing-Hua

    Engineering Analysis with Boundary Elements, Vol. 101 (2019), Iss. P.165

    https://doi.org/10.1016/j.enganabound.2019.01.008 [Citations: 12]
  23. Thermal analysis of heat transfer in pipe cooling concrete structure by a meshless RBF-FD method combined with an indirect model

    Hong, Yongxing | Lin, Ji | Cheng, Alex H.-D. | Wang, Yuan | Chen, Wen

    International Journal of Thermal Sciences, Vol. 152 (2020), Iss. P.106296

    https://doi.org/10.1016/j.ijthermalsci.2020.106296 [Citations: 10]
  24. A Discontinuous Dual Reciprocity Method in Conjunction with a Regularized Levenberg–Marquardt Method for Source Term Recovery in Inhomogeneous Anisotropic Materials

    Ellabib, Abdellatif | El Madkouri, Abdessamad

    International Journal of Computational Methods, Vol. 17 (2020), Iss. 10 P.2050002

    https://doi.org/10.1142/S0219876220500024 [Citations: 1]
  25. Research on Error Estimations of the Interpolating Boundary Element Free-Method for Two-Dimensional Potential Problems

    Wang, Jufeng | Sun, Fengxin | Xu, Ying

    Mathematical Problems in Engineering, Vol. 2020 (2020), Iss. P.1

    https://doi.org/10.1155/2020/6378745 [Citations: 1]
  26. Evaluation of soil-nail pullout resistance using mesh-free method

    Oliaei, M. | Norouzi, B. | Binesh, S.M.

    Computers and Geotechnics, Vol. 116 (2019), Iss. P.103179

    https://doi.org/10.1016/j.compgeo.2019.103179 [Citations: 11]
  27. Boundary moving least square method for 2D elasticity problems

    Huang, Zhentian | Lei, Dong | Huang, Dianwu | Lin, Ji | Han, Zi

    Engineering Analysis with Boundary Elements, Vol. 106 (2019), Iss. P.505

    https://doi.org/10.1016/j.enganabound.2019.06.005 [Citations: 16]
  28. Numerical solutions of the coupled unsteady nonlinear convection-diffusion equations based on generalized finite difference method

    Fu, Zhuo-Jia | Tang, Zhuo-Chao | Zhao, Hai-Tao | Li, Po-Wei | Rabczuk, Timon

    The European Physical Journal Plus, Vol. 134 (2019), Iss. 6

    https://doi.org/10.1140/epjp/i2019-12786-7 [Citations: 32]
  29. Forced Vibration Analysis of Isotropic Thin Circular Plate Resting on Nonlinear Viscoelastic Foundation

    Salawu, Saheed Afolabi | Sobamowo, Gbeminiyi Musibau | Sadiq, Obanishola Mufutau

    Iranian Journal of Science and Technology, Transactions of Civil Engineering, Vol. 44 (2020), Iss. S1 P.277

    https://doi.org/10.1007/s40996-020-00368-y [Citations: 4]
  30. A reproducing kernel Hilbert space approach in meshless collocation method

    Azarnavid, Babak | Emamjome, Mahdi | Nabati, Mohammad | Abbasbandy, Saeid

    Computational and Applied Mathematics, Vol. 38 (2019), Iss. 2

    https://doi.org/10.1007/s40314-019-0838-0 [Citations: 7]
  31. Localized method of fundamental solutions for interior Helmholtz problems with high wave number

    Qu, Wenzhen | Fan, Chia-Ming | Gu, Yan

    Engineering Analysis with Boundary Elements, Vol. 107 (2019), Iss. P.25

    https://doi.org/10.1016/j.enganabound.2019.06.018 [Citations: 15]
  32. A hybrid meshless method for the solution of the second order hyperbolic telegraph equation in two space dimensions

    Zhou, Yunxu | Qu, Wenzhen | Gu, Yan | Gao, Hongwei

    Engineering Analysis with Boundary Elements, Vol. 115 (2020), Iss. P.21

    https://doi.org/10.1016/j.enganabound.2020.02.015 [Citations: 21]
  33. Multiple reciprocity singular boundary method for 3D inhomogeneous problems

    Wei, Xing | Huang, Ai | Sun, Linlin | Chen, Bin

    Engineering Analysis with Boundary Elements, Vol. 117 (2020), Iss. P.212

    https://doi.org/10.1016/j.enganabound.2020.04.015 [Citations: 5]
  34. The semi‐analytical method for time‐dependent wave problems with uncertainties

    Bartual, Maria Consuelo Casabán | López, Juan Carlos Cortés | Sánchez, Lucas Jódar

    Mathematical Methods in the Applied Sciences, Vol. 43 (2020), Iss. 14 P.7977

    https://doi.org/10.1002/mma.5813 [Citations: 1]
  35. Analytical modeling of solution-phase diffusion in porous composite electrodes under time-dependent flux boundary conditions using Green’s function method

    Parhizi, Mohammad | Jain, Ankur

    Ionics, Vol. 27 (2021), Iss. 1 P.213

    https://doi.org/10.1007/s11581-020-03777-1 [Citations: 6]
  36. Two-dimensional analysis of interlaminar stresses in thin anisotropic composites subjected to inertial loads by regularized boundary integral equation

    Shiah, Y.C. | Hsu, Kuo-Wei

    Composites Part B: Engineering, Vol. 159 (2019), Iss. P.105

    https://doi.org/10.1016/j.compositesb.2018.09.088 [Citations: 3]
  37. On the sources placement in the method of fundamental solutions for time-dependent heat conduction problems

    Grabski, Jakub Krzysztof

    Computers & Mathematics with Applications, Vol. 88 (2021), Iss. P.33

    https://doi.org/10.1016/j.camwa.2019.04.023 [Citations: 17]
  38. Determination of elastic resonance frequencies and eigenmodes using the method of fundamental solutions

    Alves, Carlos J.S. | Antunes, Pedro R.S.

    Engineering Analysis with Boundary Elements, Vol. 101 (2019), Iss. P.330

    https://doi.org/10.1016/j.enganabound.2019.01.014 [Citations: 9]
  39. The method of particular solutions for solving nonlinear Poisson problems

    Dou, Fangfang | Liu, Yanshan | Chen, C.S.

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 2 P.501

    https://doi.org/10.1016/j.camwa.2018.09.053 [Citations: 9]
  40. A novel radial basis function method for 3D linear and nonlinear advection diffusion reaction equations with variable coefficients

    Tian, Xia | Lin, Ji

    Engineering with Computers, Vol. 38 (2022), Iss. S1 P.475

    https://doi.org/10.1007/s00366-020-01161-1 [Citations: 5]
  41. Learning solutions to a Cauchy problem for the modified Helmholtz equations using LS-SVM

    Wu, Ziku | Han, Xiaoming | Li, GuoFeng

    Engineering Computations, Vol. 38 (2021), Iss. 2 P.1024

    https://doi.org/10.1108/EC-04-2019-0168 [Citations: 2]
  42. Three-dimensional transient heat conduction analysis by boundary knot method

    Fu, Zhuo-jia | Shi, Jin-hong | Chen, Wen | Yang, Li-wen

    Mathematics and Computers in Simulation, Vol. 165 (2019), Iss. P.306

    https://doi.org/10.1016/j.matcom.2018.11.025 [Citations: 9]
  43. A kernel‐based method for solving the time‐fractional diffusion equation

    Fardi, Mojtaba

    Numerical Methods for Partial Differential Equations, Vol. 39 (2023), Iss. 3 P.2719

    https://doi.org/10.1002/num.22984 [Citations: 9]
  44. A dual-level method of fundamental solutions for three-dimensional exterior high frequency acoustic problems

    Li, Junpu | Qin, Qinghua | Fu, Zhuojia

    Applied Mathematical Modelling, Vol. 63 (2018), Iss. P.558

    https://doi.org/10.1016/j.apm.2018.07.002 [Citations: 31]
  45. Two-dimensional simulation of the damped Kuramoto–Sivashinsky equation via radial basis function-generated finite difference scheme combined with an exponential time discretization

    Dehghan, Mehdi | Mohammadi, Vahid

    Engineering Analysis with Boundary Elements, Vol. 107 (2019), Iss. P.168

    https://doi.org/10.1016/j.enganabound.2019.06.007 [Citations: 25]
  46. An effective semi-analytical method for solving telegraph equation with variable coefficients

    Lin, Ji | He, Yuxin | Reutskiy, S. Y. | Lu, Jun

    The European Physical Journal Plus, Vol. 133 (2018), Iss. 7

    https://doi.org/10.1140/epjp/i2018-12104-1 [Citations: 12]
  47. A cubic B-spline semi-analytical algorithm for simulation of 3D steady-state convection-diffusion-reaction problems

    Lin, Ji | Reutskiy, Sergiy

    Applied Mathematics and Computation, Vol. 371 (2020), Iss. P.124944

    https://doi.org/10.1016/j.amc.2019.124944 [Citations: 13]
  48. Effect of cooling water temperature and space between cooling pipes of post-cooling system on temperature and thermal stress in mass concrete

    Tasri, Adek | Susilawati, Anita

    Journal of Building Engineering, Vol. 24 (2019), Iss. P.100731

    https://doi.org/10.1016/j.jobe.2019.100731 [Citations: 28]
  49. Numerical simulation of wave propagation by using a hybrid method with an arbitrary order accuracy in both spatial and temporal approximations

    Ma, Haodong | Sun, Wenxiang | Qu, Wenzhen | Gu, Yan | Li, Po-Wei

    Engineering Analysis with Boundary Elements, Vol. 167 (2024), Iss. P.105873

    https://doi.org/10.1016/j.enganabound.2024.105873 [Citations: 1]
  50. A non-excavation detection method for buried PE pipelines based on 3D time-domain stacking focusing of elastic wave reflection

    Qi, Yongsheng | Wang, Xinhua | Yang, Lin | Wang, Yuexin | Guo, Zisheng

    Measurement Science and Technology, Vol. 35 (2024), Iss. 2 P.025120

    https://doi.org/10.1088/1361-6501/ad04b9 [Citations: 0]
  51. A meshless method for solving three-dimensional time fractional diffusion equation with variable-order derivatives

    Gu, Yan | Sun, HongGuang

    Applied Mathematical Modelling, Vol. 78 (2020), Iss. P.539

    https://doi.org/10.1016/j.apm.2019.09.055 [Citations: 81]
  52. A local radial basis function collocation method for band structure computation of 3D phononic crystals

    Zheng, H. | Zhang, Ch. | Yang, Z.

    Applied Mathematical Modelling, Vol. 77 (2020), Iss. P.1954

    https://doi.org/10.1016/j.apm.2019.09.006 [Citations: 29]
  53. Current Trends and Perspectives of Detection and Location for Buried Non-Metallic Pipelines

    Ge, Liang | Zhang, Changpeng | Tian, Guiyun | Xiao, Xiaoting | Ahmed, Junaid | Wei, Guohui | Hu, Ze | Xiang, Ju | Robinson, Mark

    Chinese Journal of Mechanical Engineering, Vol. 34 (2021), Iss. 1

    https://doi.org/10.1186/s10033-021-00613-z [Citations: 21]
  54. The MAPS with polynomial basis functions for solving axisymmetric time-fractional equations

    Xi, Qiang | Chen, C.S. | Fu, Zhuojia | Comino, Eva

    Computers & Mathematics with Applications, Vol. 88 (2021), Iss. P.78

    https://doi.org/10.1016/j.camwa.2019.11.014 [Citations: 5]
  55. Study of integrated calculation method of fluid-structure coupling vibrations, acoustic radiation, and propagation for axisymmetric structures in ocean acoustic environment

    Huang, He | Zou, Ming-Song | Jiang, Ling-Wen

    Engineering Analysis with Boundary Elements, Vol. 106 (2019), Iss. P.334

    https://doi.org/10.1016/j.enganabound.2019.05.013 [Citations: 10]
  56. An efficient boundary collocation scheme for transient thermal analysis in large-size-ratio functionally graded materials under heat source load

    Xi, Qiang | Fu, Zhuo-Jia | Rabczuk, Timon

    Computational Mechanics, Vol. 64 (2019), Iss. 5 P.1221

    https://doi.org/10.1007/s00466-019-01701-7 [Citations: 34]
  57. A point-to-point convolutional neural network for reconstructing electromagnetic parameters of multiple cavities scattering with inhomogeneous anisotropic media

    Zhao, Meiling | Zhang, Yunwei | Yuan, Zhanbin | Wang, Liqun

    Engineering Analysis with Boundary Elements, Vol. 155 (2023), Iss. P.281

    https://doi.org/10.1016/j.enganabound.2023.06.005 [Citations: 0]
  58. A novel space–time meshless method for nonhomogeneous convection–diffusion equations with variable coefficients

    Yue, Xingxing | Wang, Fajie | Hua, Qingsong | Qiu, Xiang-Yun

    Applied Mathematics Letters, Vol. 92 (2019), Iss. P.144

    https://doi.org/10.1016/j.aml.2019.01.018 [Citations: 48]
  59. Simulation of two-dimensional steady-state heat conduction problems by a fast singular boundary method

    Li, Weiwei | Xu, Shaoqiang | Shao, Mingyu

    Engineering Analysis with Boundary Elements, Vol. 108 (2019), Iss. P.149

    https://doi.org/10.1016/j.enganabound.2019.06.020 [Citations: 6]
  60. A Novel Triangular Element with Continuous Nodal Acoustic Pressure Gradient for Acoustic Scattering Problems

    Chai, Yingbin | Li, Wei | Zhang, Yong-Ou | Arpino, Fausto

    Mathematical Problems in Engineering, Vol. 2019 (2019), Iss. 1

    https://doi.org/10.1155/2019/7436472 [Citations: 0]
  61. A fast singular boundary method for 3D Helmholtz equation

    Li, Weiwei

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 2 P.525

    https://doi.org/10.1016/j.camwa.2018.09.055 [Citations: 29]
  62. A truly meshfree method for solving acoustic problems using local weak form and radial basis functions

    You, Xiangyu | Li, Wei | Chai, Yingbin

    Applied Mathematics and Computation, Vol. 365 (2020), Iss. P.124694

    https://doi.org/10.1016/j.amc.2019.124694 [Citations: 24]
  63. Study on calculation methods for acoustic radiation of axisymmetric structures in finite water depth

    Huang, He | Zou, Ming-Song | Jiang, Ling-Wen

    Journal of Fluids and Structures, Vol. 98 (2020), Iss. P.103115

    https://doi.org/10.1016/j.jfluidstructs.2020.103115 [Citations: 5]
  64. Implementation of Different Types of Meshfree Technique in Computational Solid Mechanics: A Comprehensive Review Across Nano, Micro, and Macro Scales

    Al Mahmoud, Zummurd | Safaei, Babak | Sahmani, Saeid | Asmael, Mohammed | Shahzad, Muhammad Atif | Zeeshan, Qasim | Qin, Zhaoye

    Archives of Computational Methods in Engineering, Vol. (2023), Iss.

    https://doi.org/10.1007/s11831-023-09999-6 [Citations: 3]
  65. The convergence and stability analysis of a numerical method for solving a mathematical model of language competition

    Eslahchi, M.R. | Esmaili, Sakine

    Applied Numerical Mathematics, Vol. 151 (2020), Iss. P.119

    https://doi.org/10.1016/j.apnum.2019.12.015 [Citations: 1]
  66. A high accurate simulation of thin plate problems by using the method of approximate particular solutions with high order polynomial basis

    Xiong, Jingang | Jiang, Pengfei | Zheng, Hui | Chen, C.S.

    Engineering Analysis with Boundary Elements, Vol. 94 (2018), Iss. P.153

    https://doi.org/10.1016/j.enganabound.2018.06.009 [Citations: 11]
  67. A novel B-spline method to analyze convection-diffusion-reaction problems in anisotropic inhomogeneous medium

    Reutskiy, Sergiy | Zhang, Yuhui | Lin, Ji | Lu, Jun | Xu, Haifeng | He, Yongjun

    Engineering Analysis with Boundary Elements, Vol. 118 (2020), Iss. P.216

    https://doi.org/10.1016/j.enganabound.2020.06.013 [Citations: 5]
  68. The Laplace equation in three dimensions by the method of fundamental solutions and the method of particular solutions

    Zhang, Li-Ping | Li, Zi-Cai | Chen, Zhen | Huang, Hung-Tsai

    Applied Numerical Mathematics, Vol. 154 (2020), Iss. P.47

    https://doi.org/10.1016/j.apnum.2020.03.008 [Citations: 6]
  69. Meshless singular boundary method for two-dimensional pseudo-parabolic equation: analysis of stability and convergence

    Aslefallah, Mohammad | Abbasbandy, Saeid | Shivanian, Elyas

    Journal of Applied Mathematics and Computing, Vol. 63 (2020), Iss. 1-2 P.585

    https://doi.org/10.1007/s12190-020-01330-x [Citations: 7]
  70. Simulation of the band structure for scalar waves in 2D phononic crystals by the singular boundary method

    Li, Weiwei | Chen, Wen

    Engineering Analysis with Boundary Elements, Vol. 101 (2019), Iss. P.17

    https://doi.org/10.1016/j.enganabound.2018.11.017 [Citations: 7]
  71. Domain-decomposition generalized finite difference method for stress analysis in multi-layered elastic materials

    Wang, Yuanyuan | Gu, Yan | Fan, Chia-Ming | Chen, Wen | Zhang, Chuanzeng

    Engineering Analysis with Boundary Elements, Vol. 94 (2018), Iss. P.94

    https://doi.org/10.1016/j.enganabound.2018.06.006 [Citations: 26]
  72. Meshless simulation of anti-plane crack problems by the method of fundamental solutions using the crack Green’s function

    Ma, Ji | Chen, Wen | Zhang, Chuanzeng | Lin, Ji

    Computers & Mathematics with Applications, Vol. 79 (2020), Iss. 5 P.1543

    https://doi.org/10.1016/j.camwa.2019.09.016 [Citations: 7]
  73. Localized boundary knot method and its application to large-scale acoustic problems

    Wang, Fajie | Gu, Yan | Qu, Wenzhen | Zhang, Chuanzeng

    Computer Methods in Applied Mechanics and Engineering, Vol. 361 (2020), Iss. P.112729

    https://doi.org/10.1016/j.cma.2019.112729 [Citations: 66]
  74. Dispersion Reduction for the Wave Propagation Problems Using a Coupled “FE-Meshfree” Triangular Element

    Chai, Yingbin | You, Xiangyu | Li, Wei

    International Journal of Computational Methods, Vol. 17 (2020), Iss. 09 P.1950071

    https://doi.org/10.1142/S0219876219500713 [Citations: 32]
  75. A Numerical Method for Filtering the Noise in the Heat Conduction Problem

    Sun, Yao | Wei, Xiaoliang | Zhuang, Zibo | Luan, Tian

    Mathematics, Vol. 7 (2019), Iss. 6 P.502

    https://doi.org/10.3390/math7060502 [Citations: 2]
  76. Regularized formulation of potential field gradients in singular boundary method

    Qu, Wenzhen | Chen, Wen

    Engineering Analysis with Boundary Elements, Vol. 95 (2018), Iss. P.167

    https://doi.org/10.1016/j.enganabound.2018.07.007 [Citations: 1]
  77. The modified method of fundamental solutions for exterior problems of the Helmholtz equation; spurious eigenvalues and their removals

    Zhang, Li-Ping | Li, Zi-Cai | Huang, Hung-Tsai | Wei, Yimin

    Applied Numerical Mathematics, Vol. 145 (2019), Iss. P.236

    https://doi.org/10.1016/j.apnum.2019.06.008 [Citations: 6]
  78. Higher order meshless schemes applied to the finite element method in elliptic problems

    Milewski, Sławomir | Putanowicz, Roman

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 3 P.779

    https://doi.org/10.1016/j.camwa.2018.10.016 [Citations: 5]
  79. Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE–BE solver

    Zheng, Chang-Jun | Bi, Chuan-Xing | Zhang, Chuanzeng | Gao, Hai-Feng | Chen, Hai-Bo

    Journal of Computational Physics, Vol. 359 (2018), Iss. P.183

    https://doi.org/10.1016/j.jcp.2018.01.018 [Citations: 28]
  80. A frequency domain formulation of the singular boundary method for dynamic analysis of thin elastic plate

    Sun, Linlin | Wei, Xing

    Engineering Analysis with Boundary Elements, Vol. 98 (2019), Iss. P.77

    https://doi.org/10.1016/j.enganabound.2018.10.010 [Citations: 37]
  81. Meshless formulation to two‐dimensional nonlinear problem of generalized Benjamin–Bona–Mahony–Burgers through singular boundary method: Analysis of stability and convergence

    Aslefallah, Mohammad | Abbasbandy, Saeid | Shivanian, Elyas

    Numerical Methods for Partial Differential Equations, Vol. 36 (2020), Iss. 2 P.249

    https://doi.org/10.1002/num.22426 [Citations: 10]
  82. An efficient meshless boundary point interpolation method for acoustic radiation and scattering

    Chen, Linchong | Li, Xiaolin

    Computers & Structures, Vol. 229 (2020), Iss. P.106182

    https://doi.org/10.1016/j.compstruc.2019.106182 [Citations: 13]
  83. An overview of the method of fundamental solutions—Solvability, uniqueness, convergence, and stability

    Cheng, Alexander H.D. | Hong, Yongxing

    Engineering Analysis with Boundary Elements, Vol. 120 (2020), Iss. P.118

    https://doi.org/10.1016/j.enganabound.2020.08.013 [Citations: 95]
  84. Adaptive Analysis of Acoustic‐Elastodynamic Interacting Models Considering Frequency Domain MFS‐FEM Coupled Formulations

    Soares, D. | Godinho, L. | Yang, Mijia

    Mathematical Problems in Engineering, Vol. 2019 (2019), Iss. 1

    https://doi.org/10.1155/2019/4834521 [Citations: 0]
  85. LIE SYMMETRY ANALYSIS TO THE WEAKLY COUPLED KAUP–KUPERSHMIDT EQUATION WITH TIME FRACTIONAL ORDER

    WANG, ZHENLI | ZHANG, LIHUA | LI, CHUANZHONG

    Fractals, Vol. 27 (2019), Iss. 04 P.1950052

    https://doi.org/10.1142/S0218348X1950052X [Citations: 8]
  86. RETRACTED: A hybrid Finite element-Meshfree method based on partition of unity for transient wave propagation problems in homogeneous and inhomogeneous media

    Chai, Yingbin | Cheng, Cong | Li, Wei | Huang, Yu

    Applied Mathematical Modelling, Vol. 85 (2020), Iss. P.192

    https://doi.org/10.1016/j.apm.2020.03.026 [Citations: 9]
  87. Simulation of thermal field in mass concrete structures with cooling pipes by the localized radial basis function collocation method

    Hong, Yongxing | Lin, Ji | Chen, Wen

    International Journal of Heat and Mass Transfer, Vol. 129 (2019), Iss. P.449

    https://doi.org/10.1016/j.ijheatmasstransfer.2018.09.037 [Citations: 36]
  88. Optimization of ICCP Anode Configuration Based on Multi Objective Genetic Algorithm

    Zhang, Qizhi | Lei, Jia | Li, Lin

    2019 International Conference on Computer Network, Electronic and Automation (ICCNEA), (2019), P.46

    https://doi.org/10.1109/ICCNEA.2019.00019 [Citations: 3]
  89. Solving biharmonic equation as an optimal control problem using localized radial basis functions collocation method

    Boudjaj, Loubna | Naji, Ahmed | Ghafrani, Fatima

    Engineering Analysis with Boundary Elements, Vol. 107 (2019), Iss. P.208

    https://doi.org/10.1016/j.enganabound.2019.07.007 [Citations: 6]
  90. Equivalent inclusion method for arbitrary cavities or cracks in an elastic infinite/semi-infinite space

    Yang, Wanyou | Zhou, Qinghua | Wang, Jiaxu | Khoo, Boo Cheong | Phan-Thien, Nhan

    International Journal of Mechanical Sciences, Vol. 195 (2021), Iss. P.106259

    https://doi.org/10.1016/j.ijmecsci.2020.106259 [Citations: 12]
  91. Singular boundary method for 3D time-harmonic electromagnetic scattering problems

    Wei, Xing | Sun, Linlin

    Applied Mathematical Modelling, Vol. 76 (2019), Iss. P.617

    https://doi.org/10.1016/j.apm.2019.06.039 [Citations: 17]
  92. A symplectic procedure for two-dimensional coupled elastic wave equations using radial basis functions interpolation

    Zhang, Shengliang

    Computers & Mathematics with Applications, Vol. 76 (2018), Iss. 9 P.2167

    https://doi.org/10.1016/j.camwa.2018.08.014 [Citations: 11]
  93. Optimizing anode location in impressed current cathodic protection system to minimize underwater electric field using multiple linear regression analysis and artificial neural network methods

    Kim, Y.-S. | Seok, S. | Lee, J.-S. | Lee, S.K. | Kim, J.-G.

    Engineering Analysis with Boundary Elements, Vol. 96 (2018), Iss. P.84

    https://doi.org/10.1016/j.enganabound.2018.08.012 [Citations: 20]
  94. A boundary collocation method for anomalous heat conduction analysis in functionally graded materials

    Fu, Zhuo-Jia | Yang, Li-Wen | Xi, Qiang | Liu, Chein-Shan

    Computers & Mathematics with Applications, Vol. 88 (2021), Iss. P.91

    https://doi.org/10.1016/j.camwa.2020.02.023 [Citations: 48]
  95. A typical backward substitution method for the simulation of Helmholtz problems in arbitrary 2D domains

    Hong, Yongxing | Lin, Ji | Chen, Wen

    Engineering Analysis with Boundary Elements, Vol. 93 (2018), Iss. P.167

    https://doi.org/10.1016/j.enganabound.2018.05.004 [Citations: 25]
  96. Coupling of the improved singular boundary method and dual reciprocity method for multi-term time-fractional mixed diffusion-wave equations

    Safari, Farzaneh | Chen, Wen

    Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 5 P.1594

    https://doi.org/10.1016/j.camwa.2019.02.001 [Citations: 28]
  97. A novel homogenization function method for inverse source problem of nonlinear time-fractional wave equation

    Qiu, Lin | Hu, Chao | Qin, Qing-Hua

    Applied Mathematics Letters, Vol. 109 (2020), Iss. P.106554

    https://doi.org/10.1016/j.aml.2020.106554 [Citations: 13]
  98. Meshless Method for Analysis of Permeable Breakwaters in the Proximity of A Vertical Wall

    Chioukh, Nadji | Ouazzane, Karim | Yüksel, Yalçın | Hamoudi, Benameur | Çevik, Esin

    China Ocean Engineering, Vol. 33 (2019), Iss. 2 P.148

    https://doi.org/10.1007/s13344-019-0015-7 [Citations: 8]
  99. The generalized finite difference method for long-time transient heat conduction in 3D anisotropic composite materials

    Gu, Yan | Hua, Qingsong | Zhang, Chuanzeng | He, Xiaoqiao

    Applied Mathematical Modelling, Vol. 71 (2019), Iss. P.316

    https://doi.org/10.1016/j.apm.2019.02.023 [Citations: 69]
  100. Experimental study on comprehensive detection technology of shallow gas in deep soft soil layer

    Liu, Mingqing | Sun, Fuxue

    Heliyon, Vol. 10 (2024), Iss. 15 P.e35544

    https://doi.org/10.1016/j.heliyon.2024.e35544 [Citations: 0]
  101. A RBF-based technique for 3D convection–diffusion–reaction problems in an anisotropic inhomogeneous medium

    Reutskiy, Sergiy | Lin, Ji

    Computers & Mathematics with Applications, Vol. 79 (2020), Iss. 6 P.1875

    https://doi.org/10.1016/j.camwa.2019.10.010 [Citations: 11]
  102. Meshless generalized finite difference method for water wave interactions with multiple-bottom-seated-cylinder-array structures

    Fu, Zhuo-Jia | Xie, Zhuo-Yu | Ji, Shun-Ying | Tsai, Chia-Cheng | Li, Ai-Lun

    Ocean Engineering, Vol. 195 (2020), Iss. P.106736

    https://doi.org/10.1016/j.oceaneng.2019.106736 [Citations: 99]
  103. Analysis of three-dimensional heat conduction in functionally graded materials by using a hybrid numerical method

    Qu, Wenzhen | Fan, Chia-Ming | Zhang, Yaoming

    International Journal of Heat and Mass Transfer, Vol. 145 (2019), Iss. P.118771

    https://doi.org/10.1016/j.ijheatmasstransfer.2019.118771 [Citations: 31]
  104. Integrated radial basis functions (IRBFs) to simulate nonlinear advection–diffusion equations with smooth and non-smooth initial data

    Ebrahimijahan, Ali | Dehghan, Mehdi | Abbaszadeh, Mostafa

    Engineering with Computers, Vol. 38 (2022), Iss. 2 P.1071

    https://doi.org/10.1007/s00366-020-01039-2 [Citations: 4]
  105. Novel numerical method based on cubic B-splines for a class of nonlinear generalized telegraph equations in irregular domains

    Reutskiy, Sergiy | Zhang, Yuhui | Lin, Ji | Sun, Hongguang

    Alexandria Engineering Journal, Vol. 59 (2020), Iss. 1 P.77

    https://doi.org/10.1016/j.aej.2019.12.009 [Citations: 9]
  106. Kalman filter-based force estimation in a clamped plate using reduced order model and noisy measurements

    Shrivastava, Akash | Mohanty, Amiya Ranjan

    Inverse Problems in Science and Engineering, Vol. 27 (2019), Iss. 8 P.1170

    https://doi.org/10.1080/17415977.2018.1503657 [Citations: 4]
  107. A stable SPH discretization of the elliptic operator with heterogeneous coefficients

    Lukyanov, Alexander A. | Vuik, Cornelis

    Journal of Computational and Applied Mathematics, Vol. 374 (2020), Iss. P.112745

    https://doi.org/10.1016/j.cam.2020.112745 [Citations: 3]
  108. A meshless singular boundary method for transient heat conduction problems in layered materials

    Qiu, Lin | Wang, Fajie | Lin, Ji

    Computers & Mathematics with Applications, Vol. 78 (2019), Iss. 11 P.3544

    https://doi.org/10.1016/j.camwa.2019.05.027 [Citations: 53]
  109. The boundary element-free method for 2D interior and exterior Helmholtz problems

    Chen, Linchong | Liu, Xin | Li, Xiaolin

    Computers & Mathematics with Applications, Vol. 77 (2019), Iss. 3 P.846

    https://doi.org/10.1016/j.camwa.2018.10.022 [Citations: 34]
  110. A boundary element approach for solving plane elastostatic equations of anisotropic functionally graded materials

    Ang, Whye‐Teong

    Numerical Methods for Partial Differential Equations, Vol. 35 (2019), Iss. 4 P.1396

    https://doi.org/10.1002/num.22356 [Citations: 7]
  111. Meshless analysis of parabolic interface problems

    Ahmad, Masood |

    Engineering Analysis with Boundary Elements, Vol. 94 (2018), Iss. P.134

    https://doi.org/10.1016/j.enganabound.2018.06.008 [Citations: 18]
  112. The approximate solution of nonlinear Volterra integral equations of the second kind using radial basis functions

    Assari, Pouria | Dehghan, Mehdi

    Applied Numerical Mathematics, Vol. 131 (2018), Iss. P.140

    https://doi.org/10.1016/j.apnum.2018.05.001 [Citations: 23]
  113. Simulating thin plate bending problems by a family of two-parameter homogenization functions

    Liu, Chein-Shan | Qiu, Lin | Lin, Ji

    Applied Mathematical Modelling, Vol. 79 (2020), Iss. P.284

    https://doi.org/10.1016/j.apm.2019.10.036 [Citations: 20]
  114. Simulation of linear and nonlinear advection–diffusion–reaction problems by a novel localized scheme

    Lin, Ji | Xu, Yi | Zhang, Yuhui

    Applied Mathematics Letters, Vol. 99 (2020), Iss. P.106005

    https://doi.org/10.1016/j.aml.2019.106005 [Citations: 47]
  115. A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems

    Li, Wei | Zhang, Qifan | Gui, Qiang | Chai, Yingbin

    International Journal of Computational Methods, Vol. 18 (2021), Iss. 03 P.2041002

    https://doi.org/10.1142/S0219876220410029 [Citations: 57]
  116. The electromagnetic scattering from multiple arbitrarily shaped cavities with inhomogeneous anisotropic media

    Zhao, Meiling | Zhu, Na | Wang, Liqun

    Journal of Computational Physics, Vol. 489 (2023), Iss. P.112274

    https://doi.org/10.1016/j.jcp.2023.112274 [Citations: 3]
  117. Analysis of three-dimensional interior acoustic fields by using the localized method of fundamental solutions

    Qu, Wenzhen | Fan, Chia-Ming | Gu, Yan | Wang, Fajie

    Applied Mathematical Modelling, Vol. 76 (2019), Iss. P.122

    https://doi.org/10.1016/j.apm.2019.06.014 [Citations: 35]
  118. A high accuracy method for long-time evolution of acoustic wave equation

    Qu, Wenzhen

    Applied Mathematics Letters, Vol. 98 (2019), Iss. P.135

    https://doi.org/10.1016/j.aml.2019.06.010 [Citations: 53]
  119. A modified dual-level fast multipole boundary element method based on the Burton–Miller formulation for large-scale three-dimensional sound field analysis

    Li, Junpu | Chen, Wen | Qin, Qinghua

    Computer Methods in Applied Mechanics and Engineering, Vol. 340 (2018), Iss. P.121

    https://doi.org/10.1016/j.cma.2018.05.016 [Citations: 32]
  120. An improved boundary point interpolation method for exterior acoustic radiation problem

    Chen, Linchong | Li, Xiaolin

    Engineering Analysis with Boundary Elements, Vol. 103 (2019), Iss. P.11

    https://doi.org/10.1016/j.enganabound.2019.02.002 [Citations: 10]
  121. Method of fundamental solutions for a Cauchy problem of the Laplace equation in a half-plane

    Chen, Bo | Sun, Yao | Zhuang, Zibo

    Boundary Value Problems, Vol. 2019 (2019), Iss. 1

    https://doi.org/10.1186/s13661-019-1151-y [Citations: 6]
  122. A semi-analytical boundary collocation solver for the inverse Cauchy problems in heat conduction under 3D FGMs with heat source

    Xi, Qiang | Fu, Zhuojia | Alves, Carlos | Ji, Hongli

    Numerical Heat Transfer, Part B: Fundamentals, Vol. 76 (2019), Iss. 5 P.311

    https://doi.org/10.1080/10407790.2019.1665386 [Citations: 7]
  123. A semi-analytical collocation Trefftz scheme for solving multi-term time fractional diffusion-wave equations

    Fu, Zhuo-Jia | Yang, Li-Wen | Zhu, Hui-Qing | Xu, Wen-Zhi

    Engineering Analysis with Boundary Elements, Vol. 98 (2019), Iss. P.137

    https://doi.org/10.1016/j.enganabound.2018.09.017 [Citations: 43]
  124. An Edge-Based Smoothed Finite Element Method for Analyzing Stiffened Plates

    Li, Wei | Chai, Yingbin | You, Xiangyu | Zhang, Qifan

    International Journal of Computational Methods, Vol. 16 (2019), Iss. 06 P.1840031

    https://doi.org/10.1142/S0219876218400315 [Citations: 3]
  125. High-performance practical stiffness analysis of high-rise buildings using superfloor elements

    Torky, Ahmed A | Rashed, Youssef F

    Journal of Computational Design and Engineering, Vol. 7 (2020), Iss. 2 P.211

    https://doi.org/10.1093/jcde/qwaa018 [Citations: 3]
  126. Optimality of the Boundary Knot Method for Numerical Solutions of 2D Helmholtz-Type Equations

    Wang, Fuzhang | Zheng, Kehong | Li, Congcong | Zhang, Juan

    Wuhan University Journal of Natural Sciences, Vol. 24 (2019), Iss. 4 P.314

    https://doi.org/10.1007/s11859-019-1402-x [Citations: 3]
  127. An efficient MAPS for solving fourth order partial differential equations using trigonometric functions

    Wang, Dan | Chen, C.S. | Li, Wen

    Computers & Mathematics with Applications, Vol. 79 (2020), Iss. 4 P.934

    https://doi.org/10.1016/j.camwa.2019.08.005 [Citations: 3]
  128. A meshless numerical method for time harmonic quasi-periodic scattering problem

    Luan, Tian | Sun, Yao | Zhuang, Zibo

    Engineering Analysis with Boundary Elements, Vol. 104 (2019), Iss. P.320

    https://doi.org/10.1016/j.enganabound.2019.03.034 [Citations: 2]
  129. Application of the singular boundary method to the two-dimensional telegraph equation on arbitrary domains

    Aslefallah, Mohammad | Rostamy, Davood

    Journal of Engineering Mathematics, Vol. 118 (2019), Iss. 1 P.1

    https://doi.org/10.1007/s10665-019-10008-8 [Citations: 19]
  130. A localized RBF-MLPG method for numerical study of heat and mass transfer equations in elliptic fins

    Safarpoor, Mansour | Shirzadi, Ahmad

    Engineering Analysis with Boundary Elements, Vol. 98 (2019), Iss. P.35

    https://doi.org/10.1016/j.enganabound.2018.09.016 [Citations: 9]
  131. A meshless singular boundary method for elastic wave propagation in 2D partially saturated poroelastic media

    Sun, Linlin | Wei, Xing | Chen, Bin

    Engineering Analysis with Boundary Elements, Vol. 113 (2020), Iss. P.82

    https://doi.org/10.1016/j.enganabound.2019.12.019 [Citations: 9]
  132. An accurate meshless collocation technique for solving two-dimensional hyperbolic telegraph equations in arbitrary domains

    Lin, Ji | Chen, Fen | Zhang, Yuhui | Lu, Jun

    Engineering Analysis with Boundary Elements, Vol. 108 (2019), Iss. P.372

    https://doi.org/10.1016/j.enganabound.2019.08.012 [Citations: 25]
  133. The singular boundary method for unilateral contact problems

    Chen, Bin | Zhang, Lei | Shu, Kaiou

    Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 44 (2022), Iss. 5

    https://doi.org/10.1007/s40430-022-03486-y [Citations: 1]
  134. Thermal Analysis of 2D FGM Beam Subjected to Thermal Loading Using Meshless Weighted Least‐Square Method

    Zhou, H. M. | Zhang, X. M. | Wang, Z. Y. | Shaat, Mohamed

    Mathematical Problems in Engineering, Vol. 2019 (2019), Iss. 1

    https://doi.org/10.1155/2019/2541707 [Citations: 6]
  135. A modified dual-level fast multipole boundary element method for large-scale three-dimensional potential problems

    Li, Junpu | Chen, Wen | Qin, Qinghua | Fu, Zhuojia

    Computer Physics Communications, Vol. 233 (2018), Iss. P.51

    https://doi.org/10.1016/j.cpc.2018.06.024 [Citations: 8]
  136. A Smoothing Scheme for Seismic Wave Propagation Simulation with a Mixed FEM of Diffusionized Wave Equation

    Imai, Ryuta | Kasui, Naoki | Yamada, Masayuki | Hada, Koji | Fujiwara, Hiroyuki

    International Journal of Computational Methods, Vol. 19 (2022), Iss. 02

    https://doi.org/10.1142/S0219876221500614 [Citations: 0]