Analytical method for the evaluation of singular integrals arising from boundary element method in electromagnetism

Oueslati, Soumaya; Balloumi, Imen; Daveau, Christian; Khelifi, Abdessatar

doi:10.1002/jnm.2792

Cited by 3 publications

(2 citation statements)

References 9 publications

(22 reference statements)

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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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“…The problem of electromagnetic scattering by conducting objects (PEC) coated with dielectric materials has been of considerable and growing interest due to its significance in radar prediction of targets, stealth technology, geophysics, and antennas 1–3 . This significance is also fortified by the need to enhance the computational efficiency of the existing techniques.…”

Section: Introductionmentioning

confidence: 99%

New approximation method for high order impedance boundary condition with surface integral equations for the scattering problem

Daveau,

Oueslati,

Kacem

2024

Int J Numerical Modelling

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In this paper, we propose a new method to approximate operators resulted from solving the scattering Problem in electromagnetism by dielectrically coated conducting bodies, using integral equations and high order impedance boundary condition. We introduce the variational Problem and we prove its well‐posedness. After discretization, we find that operators arising from the high‐order impedance boundary conditions are not well‐defined. We present the new theoretical approach and highlight its potential through numerical experiments.

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Analytical Galerkin Boundary Integrals of Laplace Kernel Layer Potentials in \(\boldsymbol{\mathbb{R}^3}\)

Gumerov,

Kaneko,

Duraiswami

2024

SIAM J. Sci. Comput.

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Analytical method for the evaluation of singular integrals arising from boundary element method in electromagnetism

Abstract: We present a new method for the explicit evaluation of single and double layers involved in a boundary element method to solve Maxwell's equations in the harmonic regime. This is an analytical method.

Cited by 3 publications

References 9 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

New approximation method for high order impedance boundary condition with surface integral equations for the scattering problem

Analytical Galerkin Boundary Integrals of Laplace Kernel Layer Potentials in \(\boldsymbol{\mathbb{R}^3}\)

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