Evaluation of regular and singular domain integrals with boundary-only discretization-theory and Fortran code. A set of boundary integrals is derived based on a radial integration technique to accurately evaluate two dimensional and three dimensional, regular and singular domain integrals. A self-contained Fortran code is listed and described for numerical implementation of these boundary integrals. The main feature of the theory is that only the boundary of the integration domain needs to be discretized into elements. This feature cannot only save considerable efforts in discretizing the integration domain into internal cells (as in the conventional method), but also make computational results for singular domain integrals more accurate since the integrals have been regularized. Some examples are provided to verify the correctness of the presented formulations and the included code.

References in zbMATH (referenced in 36 articles , 1 standard article )

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  1. Liu, Biao; Wang, Qiao; Zhou, Wei; Chang, Xiaolin: NURBS-enhanced line integration BEM for thermo-elastic problems considering the gravity load (2021)
  2. Ramos, Caio C. R.; Daros, C. H.: Stacking sequence optimization of laminated plate structures using the boundary element method (2021)
  3. Wang, Zihao; Yao, Weian; Zuo, Chong; Hu, Xiaofei: Solving phase change problems via a precise time-domain expanding boundary element method combined with the level set method (2021)
  4. Bołtuć, Agnieszka: Automatic generating and spread of a plastic region in PIES (2020)
  5. Guo, Shuaiping; Fan, Xinming; Gao, Kuidong; Li, Hongguang: Precision controllable Gaver-Wynn-Rho algorithm in Laplace transform triple reciprocity boundary element method for three dimensional transient heat conduction problems (2020)
  6. Narváez, A.; Useche, J.: The kriging integration method applied to the boundary element analysis of Poisson problems (2020)
  7. Wang, Qiao; Zhou, Wei; Cheng, Yonggang; Ma, Gang; Chang, Xiaolin: NURBS-enhanced line integration boundary element method for 2D elasticity problems with body forces (2019)
  8. Wang, Qiao; Zhou, Wei; Cheng, Yonggang; Ma, Gang; Chang, Xiaolin: Line integration method for treatment of domain integrals in 3D boundary element method for potential and elasticity problems (2017)
  9. Wang, Qiao; Zhou, Wei; Cheng, Yonggang; Ma, Gang; Chang, Xiaolin: A line integration method for the treatment of 3D domain integrals and accelerated by the fast multipole method in the BEM (2017)
  10. Wang, Qiao; Zhou, Wei; Cheng, Yonggang; Ma, Gang; Chang, Xiaolin; Huang, Qiang: The boundary element method with a fast multipole accelerated integration technique for 3D elastostatic problems with arbitrary body forces (2017)
  11. Bołtuć, Agnieszka: Parametric integral equation system (PIES) for 2D elastoplastic analysis (2016)
  12. Bołtuć, Agnieszka: Elastoplastic boundary problems in PIES comparing to BEM and FEM (2016)
  13. Zhou, Wei; Wang, Qiao; Cheng, Yonggang; Ma, Gang: A fast multipole method accelerated adaptive background cell-based domain integration method for evaluation of domain integrals in 3D boundary element method (2016)
  14. Niu, Zhongrong; Hu, Zongjun; Cheng, Changzheng; Zhou, Huanlin: A novel semi-analytical algorithm of nearly singular integrals on higher order elements in two dimensional BEM (2015)
  15. Qu, Wenzhen; Chen, Wen; Fu, Zhuojia: Solutions of 2D and 3D non-homogeneous potential problems by using a boundary element-collocation method (2015)
  16. Yang, Kai; Feng, Wei-Zhe; Li, Jun; Gao, Xiao-Wei: New analytical expressions in radial integration BEM for stress computation with several kinds of variable coefficients (2015)
  17. Yang, Kai; Peng, Hai-Feng; Cui, Miao; Gao, Xiao-Wei: New analytical expressions in radial integration BEM for solving heat conduction problems with variable coefficients (2015)
  18. Yao, Wei-An; Yao, Hong-Xiao; Yu, Bo: Radial integration BEM for solving non-Fourier heat conduction problems (2015)
  19. Hu, Jin-Xiu; Peng, Hai-Feng; Gao, Xiao-Wei: Numerical evaluation of arbitrary singular domain integrals using third-degree B-spline basis functions (2014)
  20. Peng, Hai-Feng; Liu, Jian; Zhu, Qiang-Hua; Zhang, Ch.: Evaluation of strongly singular domain integrals for internal stresses in functionally graded materials analyses using RIBEM (2014)

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