A binary-tree element subdivision method for evaluation of nearly singular domain integrals with continuous or discontinuous kernel

Zhang, Jianming; Chi, Baotao; Singh, Krishna M.; Zhong, Yi; Ju, Chuanming

doi:10.1016/j.cam.2019.04.027

Cited by 10 publications

(2 citation statements)

References 21 publications

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“…At present, there are many methods have been developed to handle the weak singular integrals, such as integral simplification method [24], element subdivision methods [25][26] and polar coordinate transformation methods [20,[27][28][29][30][31]. When the position of the source point is close to the boundaries of the element, the computational accuracy cannot be guaranteed only by using the coordinate transformation method [32].…”

Section: Introductionmentioning

confidence: 99%

A Subdivision Transformation Method for Weakly Singular Boundary Integrals in Thin-structural Problem

Hou

Zeng

Zhong

et al. 2023

mech

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Accurate and effective calculation of weakly singular integral in the boundary integral equation of the thin-structural problem is the key to the numerical implementation of the boundary element method. In this paper, a subdivision transformation method evaluated for weakly singular integrals is proposed, and the method is implemented as follows: based on the position of the source points, the shape information of the elements and the nearest distance from the source point to the integral element, a subdivision technology is constructed at first. With this subdivision technology, the integral element can be divided into several integral blocks with good shapes. And then, a simpler coordinate transformation method is constructed to remove the weak singularities of the integral blocks obtained by the subdivision technology. Compared with the conventional polar coordinate transformation method, the present transformation method does not need to calculate their integral interval, which is more simple and effective to implement. Finally, the paper gives three numerical examples to verify the accuracy and validity of the present method.

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Section: Introductionmentioning

confidence: 99%

A Subdivision Transformation Method for Weakly Singular Boundary Integrals in Thin-structural Problem

Hou

Zeng

Zhong

et al. 2023

mech

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show abstract

“…The subdivision scheme can be considered as the generalization of discrete modeling by spline representation, such as the Catmull-Clark subdivision [17], Doo-Sabin subdivision [18], Loop subdivision [19], and other classes of interpolatory subdivision schemes. The adaptive subdivision algorithm [20][21][22][23] is less cumbersome by defining the refinement rules to add new points as linear combinations of old ones. The process continues until the given terminating criteria for all discrete segments or patches are not met.…”

Section: Introductionmentioning

confidence: 99%

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

et al. 2023

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The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation curve is mainly applied to solve the difficult geometry defeaturing problems for curve modeling in existing computer-aided technology. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual interpolation curve is flexible and convenient for characterizing a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of characterizing the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

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An adaptive element subdivision method based on the affine transformations and partitioning techniques for evaluating the weakly singular integrals

Chi

Jia

et al. 2024

Journal of Computational and Applied Mathematics

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A binary-tree element subdivision method for evaluation of nearly singular domain integrals with continuous or discontinuous kernel

Cited by 10 publications

References 21 publications

A Subdivision Transformation Method for Weakly Singular Boundary Integrals in Thin-structural Problem

A Subdivision Transformation Method for Weakly Singular Boundary Integrals in Thin-structural Problem

A New Definition of the Dual Interpolation Curve for CAD Modeling and Geometry Defeaturing

An adaptive element subdivision method based on the affine transformations and partitioning techniques for evaluating the weakly singular integrals

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