• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.757-769
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• 2019

A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a $H{\ddot{o}}lder$ continuous function, regularity of the resulting solution is in line with the standard parabolic theory.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.15 no.8
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• pp.765-774
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• 2004

In this paper, a novel approximate solution for scattering by a very thin planar homogeneous dielectric scatterer with an arbitrary shape is formulated. This solution is based on a volumetric integral equation and is expressed in terms of Fourier transform. It is shown that the obtained solution is reduced to an exact solution for an infinite dielectric slab. For 2D, or 3D scatterers, the formulation is verified numerically. Especially fur edge-on TM polarized wave incidence a closed-form solution of backscattering from a thin dielectric half-plane is formulated, which is very accurate for wide range of normalized surface impedance except very low impedances(│η│〈0.5).

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.463-475
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• 2012

In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1994.10a
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• pp.38-45
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• 1994

P-version finite element model for the computation of stress intensity factors in two dimensional cracked panels by J-integral method is presented. The proposed model is based on high order theory and hierarchical shape function. The displacements fields are defined by integrals of Legendre polynomials which can be classified into three part such as basic mode, side mode, integral mode. The stress intensity factors are computed by J-integral method. The example models for validating the proposed p-version model are centrally cracked panel, single and double edged crack in a rectangular panel under pure Mode I. And the analysis results are compared with those by the h-version of FEM and empirical solutions in literatures. Very good agreement with the existing solution are shown.

• Journal of Industrial Technology
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• v.20 no.A
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• pp.203-209
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• 2000

The fluctuation integrals which give useful information in the structure of solution are associated with the mixed direct correlation integral ($C_{12}$) known. Using its weighted arithmetic mean of $C_{11}$ and $C_{22}$ and the activity coefficient model, the fluctuation integrals on solute-solute, solvent-solute, and solvent-solvent can be calculated in the function of mole fraction. In this work, several binary mixtures containing c-hexane were tested and the results on the fluctuation integrals were rather good.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.51 no.11
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• pp.559-566
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• 2002

In this paper, we present an accurate and stable method for the solution of the transient electromagnetic response from the conducting wire structures using the time domain integral equation. By using an implicit scheme with the central finite difference approximation for the time domain electric field integral equation, we obtain the transient response from a wire scatterer illuminated by a plane wave and a conducting wire antenna with an impressed voltage source. Also, we consider a wire above a 3-dimensional conducting object. Numerical results are presented, which show the validity of the presented methodology, and compared with a conventional method using backward finite difference approximation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.2
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• pp.125-136
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• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.121-126
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• 1994

A mutual integral, which has the conservation property, is applied to the problem of a crack in an isotropic elastic material. The stress intensity factors $K_{I}, K_{II}, K_{III}$ and T-stress for the problem in an infinite medium are easily obtained by using the mutual integral without solving the boundary value problem. The auxiliary solutions necessary in the proposed method are taken from the known asymptotic solutions. This method is amenable to numerical evaluation of the stress intensity factors and T-stress if the crack in a finite medium is considered.

• Advances in Computational Design
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• v.9 no.1
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• pp.73-80
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• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.479-489
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• 1989

The $J_{k}$ integral method for determining mixed mode stress intensity factors separately in the cracked anisotropic plate is developed. Stress intensity factors are indirectly determined from the values of $J_{1}$ and $J_{2}$. The $J_{2}$ integral can be evaluated efficiently from a finite element solution, neglecting the contribution from the portion of the integration contour along the crack faces, by selecting the integration contour in the vicinity of the crack tip. Using functions of a complex variable, the complete relations between $J_{1}$, $J_{2}$ and $K_{I}$ , $K_{II}$ for anisotropic materials are derived conveniently by selecting narrow rectangular contours shrinking to the crack tip. Compared to the existing path independent integral methods, the present method does not involve calculating the auxiliary solution and hence numerical procedures become quite simple. Numerical results to various problems are given and demonstrate the accuracy, stability and versatility of the method.