Numerical calculation of regular and singular integrals in boundary integral equations using Clenshaw–Curtis quadrature rules

Chen, Linchong; Li, Xiaolin

doi:10.1016/j.enganabound.2023.05.047

Cited by 2 publications

(1 citation statement)

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“…In the BEM, the numerical techniques for the singular integrals are key research focuses and challenges. In recent years, many scholars have investigated singular integral problems in various applied fields, as referenced in [19][20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Structural Shape Optimization Based on Multi-Patch Weakly Singular IGABEM and Particle Swarm Optimization Algorithm in Two-Dimensional Elastostatics

Chen,

Xie

2024

Mathematics

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In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method is based on the weakly singular boundary integral equation, quadrature techniques, dedicated to the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take full advantage of the multi-patch technique. The generated collocation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by simple examples with analytical solutions. The features of the present multi-patch WSIGABEM are investigated by comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner, and the arch bridge are verified to be effective.

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Section: Introductionmentioning

confidence: 99%

Structural Shape Optimization Based on Multi-Patch Weakly Singular IGABEM and Particle Swarm Optimization Algorithm in Two-Dimensional Elastostatics

Chen,

Xie

2024

Mathematics

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A boundary point interpolation method for acoustic problems with particular emphasis on the calculation of Cauchy principal value integrals

Chen,

2024

Computers & Structures

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Numerical calculation of regular and singular integrals in boundary integral equations using Clenshaw–Curtis quadrature rules

Cited by 2 publications

References 38 publications

Structural Shape Optimization Based on Multi-Patch Weakly Singular IGABEM and Particle Swarm Optimization Algorithm in Two-Dimensional Elastostatics

Structural Shape Optimization Based on Multi-Patch Weakly Singular IGABEM and Particle Swarm Optimization Algorithm in Two-Dimensional Elastostatics

A boundary point interpolation method for acoustic problems with particular emphasis on the calculation of Cauchy principal value integrals

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