Article
Engineering, Multidisciplinary
Guizhong Xie, Ke Li, Yudong Zhong, Hao Li, Bing Hao, Wenliao Du, Chunya Sun, Haoqi Wang, Xiaoyu Wen, Liangwen Wang
Summary: When using boundary element analysis for thin walled structures, special considerations on the singular and nearly singular integrals are essential for computational accuracy. The method uses coordinate transformations to handle singularities and near singularities separately, and the results are validated through three numerical examples in good agreement with analytical and FEM solutions.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Yudong Zhong, Guizhong Xie, Junjian Hou, Wenbin He, Liangwen Wang, Shuguang Wang
Summary: This paper proposes a method for the numerical discretization of multilayer thin structures to eliminate weak singularities, accurately calculate integrals through coordinate transformation and sinh transformation method. The proposed method shows promising numerical accuracy in several examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Zhilin Han, Wei Pan, Changzheng Cheng, Zongjun Hu, Zhongrong Niu
Summary: This paper proposes a semi-analytical approach for handling nearly singular integrals in 3D potential problems. By expanding kernel items using Taylor series and transforming the coordinates to polar coordinates, the integrals are separated into near-singular parts and regular parts using the subtraction technique. Through this method, the nearly singular integrals can be efficiently dealt with, resulting in accurate close-boundary potentials and flux densities.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Yudong Zhong, Junjian Hou, Shizhe Feng, Guizhong Xie, Xinsheng Wang, Wenbin He, Liangwen Wang, Zhiqiang Chen, Hongwei Hao
Summary: A composite transformation method was developed to evaluate singular and nearly singular boundary integrals in boundary element analysis for multilayer thin structures. The method uses sinh transformation to eliminate nearly singular integrals and improves complex transformation to handle weakly singular integrals. By combining (alpha, beta) coordinate transformation and sinh transformation, the method removes weak singularity in the radial direction and potentially near singularity in the circumferential direction. The proposed transformation formulations were used to analyze multi-domain elasticity problems for multilayer thin structures, with numerical results demonstrating computational accuracy.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
Weiyu Zhou, Xiangjuan Yang, Yongqiang Chen
Summary: A novel integration scheme, adaptive sinh transformation Gaussian quadrature (ASTGQ), is proposed based on deep learning, which can determine the number of Gaussian points according to the required accuracy. Compared to the adaptive Gaussian quadrature (AGQ) method, the proposed scheme can significantly improve the computational efficiency.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mathematics, Applied
Rongjie Huang, Guizhong Xie, Yudong Zhong, Hongrui Geng, Hao Li, Liangwen Wang
Summary: This paper proposes a dual transformation method for accurately calculating weakly singular integrals with considerations for near singularity. The method demonstrates good applicability in the context of thin structural problems.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Baotao Chi, Fushun Wang, Qianjian Guo, Yaoming Zhang, Chuanming Ju, Wei Yuan
Summary: This paper presents an adaptive element subdivision method (APSM) based on affine transformation and partitioning techniques for efficient evaluation of nearly singular integrals. APSM has advantages such as adaptive subdivision, improved accuracy, and simplicity of implementation.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Multidisciplinary
Xuan Peng, Haojie Lian
Summary: This article presents some numerical aspects of isogeometric boundary element methods (IGABEM). The behavior of hyper-singular and nearly-singular integration on distorted NURBS surfaces is explored, and several numerical treatments are proposed. The numerical implementation of IGABEM on trimmed NURBS is detailed, and the surface crack problem is modeled using the phantom element method, allowing the crack to intersect with the boundary of the body while preserving the original parametrization of the NURBS-based CAD geometry.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2022)
Article
Mathematics, Applied
Andrew Gibbs, David Hewett, Andrea Moiola
Summary: This article presents and analyzes numerical quadrature rules for evaluating regular and singular integrals on self-similar fractal sets. The article focuses on composite quadrature rules and composite barycentre rules to improve the accuracy of the calculations.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Multidisciplinary
Yoshihiro Ochiai
Summary: This paper introduces a new technique based on the boundary element method for evaluating weak singular integrals in the solution of the three-dimensional Laplace's equation. The method utilizes the formulation of the boundary element method and a two-dimensional interpolation method for direct numerical integration of arbitrary shape surfaces. It also uses Green's second identity to transform two-dimensional integration into one-dimensional integration. Numerical examples are provided to demonstrate the efficiency of the proposed method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
Aaron D. Brovont, Steven D. Pekarek
Summary: Closed-form solutions are derived for regular and adjacent-singular integrals associated with the two-dimensional Laplacian's Green's function and its normal derivative in the Galerkin BEM. By comparing accuracy and computation time to traditional numerical integration, it is demonstrated that using closed-form solutions can reduce computation time for influence matrices by approximately 95% relative to Gauss quadrature, while maintaining similar accuracy. Furthermore, all elements of the matrices are expressed in a convenient form for implementation.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Computer Science, Interdisciplinary Applications
Chuanming Ju, J. Zhang, Yudong Zhong, Xianfeng Du, Jun Li, Baotao Chi
Summary: This paper presents an adaptive binary-tree element subdivision method for evaluating nearly singular integrals in three-dimensional boundary element method. The proposed method allows for automatic and high-quality patch generation.
ENGINEERING COMPUTATIONS
(2023)
Article
Engineering, Multidisciplinary
Baotao Chi, Qianjian Guo, Liguo Zhang, Wei Yuan, Yaoming Zhang
Summary: This study introduces an adaptive binary-tree element subdivision method for evaluating volume integrals to facilitate automatic and high-quality patch generation. The method improves integration accuracy and reduces sensitivity to element shape. The implementation of geometry-adaptive projection cavity construction algorithm and comprehensive cavity projection techniques enhances the efficiency and accuracy of the proposed method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2022)
Article
Engineering, Multidisciplinary
Damir Latypov
Summary: This paper presents a closed-form solution for singular and near-singular double surface integrals on arbitrary coplanar polygonal surfaces, as well as an evaluation method extendable to non-coplanar and non-polygonal surfaces. The evaluation method constructs exact differential forms for integration via the Stokes' theorem, providing advantages over traditional singularity subtraction methods. Numerical tests show that the proposed method maintains accuracy for triangles with aspect ratios tending to infinity, unlike existing methods.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Luiz M. Faria, Carlos Perez-Arancibia, Marc Bonnet
Summary: This paper introduces a general high-order kernel regularization technique that can be applied to linear elliptic PDEs in two and three spatial dimensions. By interpolating the density function and solutions of the underlying homogeneous PDE, singular and nearly singular integrals are converted into bounded integrands without explicit computation of high-order derivatives. The proposed approach is kernel- and dimension-independent, showing accuracy, flexibility, efficiency, and compatibility with fast solvers through large-scale three-dimensional numerical examples.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
