• Journal of electromagnetic engineering and science
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• v.17 no.2
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• pp.91-97
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• 2017

An accurate and efficient evaluation for hypersingular integrals (HIs), strongly singular integrals (SSIs), and weakly singular integrals (WSIs) plays an essential role in the numerical solutions of 3D electromagnetic scattering problems. We derive analytic formulas for WSIs based on Stokes' theorem, which can be expressed in elementary functions. Several numerical examples are presented to validate these analytic formulas. Then, to show the feasibility of the proposed formulations for numerical methods, these formulations are used with the existing analytical expressions of HIs and SSIs to correct the near-field interaction in an iterative physical optics (IPO) scheme. Using IPO, the scattering caused by a dihedral reflector is analyzed and compared with the results of the method of moments and measurement data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.85-97
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• 2000

A quadrature rule for the solution of Cauchy singular integral equation is constructed and investigated. This method to calculate numerically singular integrals uses classical Jacobi quadratures adopting Hunter's method. The proposed method is convergent under a reasonable assumption on the smoothness of the solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.81-95
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• 1998

The superconvergence of the Sloan iterate obtained from a Galerkin method for the approximate solution of the singular integral equation based on the use of two sets of orthogonal polynomials is investigated. The discrete Sloan iterate using Gaussian quadrature to evaluate the integrals in the equation becomes the Nystr$\ddot{o}$m approximation obtained by the same rules. Consequently, it is impossible to expect the faster convergence of the Sloan iterate than the discrete Galerkin approximation in practice.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.71-79
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• 2017

In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.

• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.108-114
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• 2022

Most studies on the shape of the steady vortex ring have been based on the Stokes stream function approach. In this study, the velocity approach is introduced as a trial approach. A contour dynamics method for fluid velocity is used to analyze the Norbury-Fraenkel family of vortex rings. Analytic integration is performed over the logarithmic-singular segment. A system of nonlinear equations for the discretized shape of the vortex core is formulated using the material boundary condition of the core. An additional condition for the velocities of the vortical and impulse centers is introduced to complete the system of equations. Numerical solutions are successfully obtained for the system of nonlinear equations using the iterative scheme. Specifically, the evaluation of the kinetic energy in terms of line integrals is examined closely. The results of the proposed method are compared with those of the stream function approaches. The results show good agreement, and thereby, confirm the validity of the proposed method.

• Geophysics and Geophysical Exploration
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• v.3 no.1
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• pp.13-18
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• 2000

We describe the concept of the singularity in the integral equation of electromagnetic (EM) modeling in comparison with that in the integral representation of electric fields in EM theory, which would clarify the singular integral problems of the Green's tensor. We have also derived and classified the singular integrals of the Green's tensors in 3-D, 2.5-D and 2-D as well as in the thin sheet integral equations of the EM scattering problem, which have the most important effect on the accuracy of the numerical solution of the problems.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.10
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• pp.89-101
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• 1995

선형 탄성 등방성 물체 내에 있는 일반적인 복합모드 크랙 문제들을 해석하기 위한 이중 경계적분방정식의 일반식과 계산해법이 제시되었다. 크랙면이 포함된 물체 해석에 있어서 유일한 해를 얻기 위하여, 한 면상의 점에는 변위 경계적분방정식이 적용되었고 마주하고 있는 상대면 상의 점에는 인력 경계적분방정식이 적용되었다. 인력 및 변위 경계적분방정식의 강특이해 및 초특이해 적분항들은 수치해법을 적용하기 전에 정상화되었다. 정상화과정 중 보정되는 강특이적분항이 상대 크랙면 상의 특이해 요소를 따라 직접 적분되는 것을 격리시키기 위하여, 특이해 적분 경로를 완만한 곡면으로 우회시킨 가상의 비특이해 보조경계로 대치하여 적분값을 계산하였다. 제시된 해법의 정확성과 효율성을 예시하기 위하여, 2차원 및 3차원 크랙 문제의 변형 후 모습과 응력강도계수 계산 결과를 보였다.