• 지구물리와물리탐사
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• 제3권1호
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• pp.13-18
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• 2000

적분방정식 전자탐사 모델링에서 종종 애매모호하게 받아 들여온 특이 요소에 대한 Green 텐서 적분을 명확히 해결하고자, 전자탐사 적분방정식에서의 특이치의 개념을 전자기 이론에서 사용되는 전기장의 적분식 표현에서의 특이치 문제와의 비교를 통해 설명하였다. 또한 적분방정식 전자탐사 모델링에서 수치해의 정확도를 좌우하는 가장 중요한 요소인 특이 적분을 3차원, 2.5차원 및 2차원, 그리고 얇은 판 적분방정식의 경우에 대해 유도하고 정리하였다.

• 전자공학회논문지D
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• 제35D권1호
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• pp.8-15
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• 1998

An analysis of the microstripline is started as an assumption of the axial & transveral current distribution. Applying the boundary conditions to the scalar wave equations of a electric & magnetic potential, the two simultaneous coupled integral equations are produced. The electronmagnetic fields in microstrip line can be obtained by solving these two coupled integral equaltion. In general, either a numerical analysis method or a Galerkin method was used to solve them. In this paper, a residue theorem is proposed to solve them. The electromagnetic fields are expressed as integral equations for LSE and LSM mode in the spectral domain. Applying a residue theorem to the Fourier transformed equation and Fourier inverse transformed equation which is necessary for interchanging the space domain and the spectral domain, the electromagnetic fields are expressed as algebraic equations whichare relatively easier to handle. the distributions of the electromagnetic field are shown at the range of -5w/2.leq.x.leq.5w/2, 0.lep.y.leq.4h for z=0. It agrees well with the results of the Quasi-TEM mode analysis.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• Structural Engineering and Mechanics
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• 제15권5호
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• pp.535-550
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• 2003

In this paper, a boundary-type meshfree method, the boundary radial point interpolation method (BRPIM), is presented for solving boundary value problems of two-dimensional solid mechanics. In the BRPIM, the boundary of a problem domain is represented by a set of properly scattered nodes. A technique is proposed to construct shape functions using radial functions as basis functions. The shape functions so formulated are proven to possess both delta function property and partitions of unity property. Boundary conditions can be easily implemented as in the conventional Boundary Element Method (BEM). The Boundary Integral Equation (BIE) for 2-D elastostatics is discretized using the radial basis point interpolation. Some important parameters on the performance of the BRPIM are investigated thoroughly. Validity and efficiency of the present BRPIM are demonstrated through a number of numerical examples.

• 한국전자파학회논문지
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• 제15권8호
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• pp.765-774
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• 2004

본 논문에서 얇은 균질 유전체의 산란해석을 위한 근사식이 유도된다. 이 해는 volumetric integral equation을 바탕으로 Fourier transform형식으로 나타내어진다. 얇은 무한 평면구조에서는 구한 식은 정확한 해로 떨어지며 다른 2D 또는 3D 구조에 대해서는 수치해석 결과와 비교하여 구한 식의 유용성을 보였다. 특히 TM파가 edge-on 방향으로 입사할 경우 반 무한 평면 구조에서의 산란에 대한 closed-form식을 구했다. 구한 식은 넓은 범위의 유전률에 대해 정확한 결과를 예측한다.

• Structural Engineering and Mechanics
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• 제26권5호
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• pp.591-615
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• 2007

An improvement is introduced to solve the plane problems of linear elasticity by reciprocal theorem for orthotropic materials. This method gives an integral equation with complex kernels which will be solved numerically. An artificial boundary is defined to eliminate the singularities and also an algorithm is introduced to calculate multi-valued complex functions which belonged to the kernels of the integral equation. The chosen sample problem is a plate, having a circular or elliptical hole, stretched by the forces parallel to one of the principal directions of the material. Results are compatible with the solutions given by Lekhnitskii for an infinite plane. Five different orthotropic materials are considered. Stress distributions have been calculated inside and on the boundary. There is no boundary layer effect. For comparison, some sample problems are also solved by finite element method and to check the accuracy of the presented method, two sample problems are also solved for infinite plate.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2006년도 Proceedings of ISRS 2006 PORSEC Volume I
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• pp.520-523
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• 2006

Whereas it is well known that the surface roughness parameters, the RMS height and the correlation length, of a natural soil surface are underestimated with a short surface profile, it is not clear how much the underestimated surface parameters affect the backscattering coefficients of the surface for various incidence angles and polarizations. The backscattering coefficients of simulated and measured surface profiles are computed using the integral equation method (IEM) and analyzed in this paper to answer this question. It is shown that the RMS error of the backscattering coefficients between 5-m- and 1-m-long measured surface profiles is 1.7 dB for vv-polarization and 0.5 dB for hh-polarization at a medium range of incidence angle ($15^{\circ}{\leq}{\theta}{\leq}70^{\circ}$), while the surface roughness parameters are significantly reduced; from 2.4 cm to 1.5 cm for the RMS height s and from 35.1 cm to 10.0 cm for the autocorrelation length l. This result is verified with numerous simulations with various roughness conditions and various wavelengths.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.473-485
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• 2010

We consider the differential equation $$(x^2\;-\;1)u_{xx}\;+\;2xyu_{xy}\;+\;(y^2\;-\;1)u_{yy}\;+\;gxu_x\;+\;gyu_y\;=\;\lambda_nu,\;(*)$$ where $\lambda_n\;=\;n(n\;+\;9\;-\;1)$. We show that the differential equation (*) has a polynomial set as solutions if $g\;{\neq}\;-1$, -3, -5, $\cdots$. Also, we construct an orthogonalizing distributional weight for g < 1 and $g\;{\neq}\;1$, 0, -1, $\cdots$ by regularizing a one-dimensional integral with a singularity on the endpoint of the interval.

• 대한기계학회논문집A
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• 제27권11호
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• pp.1986-1996
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• 2003

Methodology based on the elastic-plastic fracture mechanics has been widely accepted in predicting the critical crack length(CCL) of pressure tubes of CANDU nuclear plants. A conservative estimate of CCL is obtained by employing the J-resistance curves measured with the specimens satisfying plane strain condition as suggested in the ASTM standard. Due to limited thickness of the pressure tubes the curved compact tension(CT) specimens taken out from tile pressure tube have been used in obtaining J-resistance curves. The curved CT specimen inevitably introduce slant fatigue crack during precracking. Hence, effect of specimen geometry and slant crack on J-resistance curve should be explored. In this study, the difference of J integral values between the standard CT specimens satisfying plane strain condition and the nonstandard curved CT with limited thickness (4.2mm) is estimated using finite element analysis. The fracture resistance curves of Zr-2.5Nb obtained previously by other authors are critically discussed. Various finite element analysis were conducted such as 2D analysis under plane stress and plane strain conditions and 3D analysis for flat CT, curved CT with straight crack and curved CT with slant crack front. J-integral values were determined by local contour integration near the crack tip, which was considered as accurate J-values. J value was also determined from the load versus load line displacement curve and the J estimation equation in the ASTM standard. Discrepancies between the two values were shown and suggestion was made for obtaining accurate J values from the load line displacement curves obtained by the curved CT specimens.

• 지구물리와물리탐사
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• 제1권2호
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• pp.127-135
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• 1998

전자탐사에서 Born 근사는 이상체내에서의 전기장을 이상체가 없는 균질 매질에서의 일차장으로 대치하는 방법으로 복잡한 전자기 산란(EM scattering)문제를 근사하는데 널리 사용되고 있는 방법이다. 그러나 Born 근사는 이상체의 전도도가 주변 매질에 비하여 너무 크거나, 이상체의 크기가 클 때는 상당히 부정확한 결과를 나타낸다. 확장된 Born근사법은 이러한 Born근사의 문제점을 해결하기 위하여 제안된 방법으로 이상체내의 전기장을 탈분극 텐서와 일차 전기장의 곱으로 근사하는 방법이다. 한편 전자탐사에 3차원 송신원을 사용하는 2차원 모델링은 주로 유한차분법과 유한요소법이 이용되었다. 일반적으로 이들 미분 방정식을 이용하는 2차원 전자탐사 모델링에서 3차원 송신원 문제의 해결을 위하여 Fourier변환을 통해 파수영역(wavenumber domain)으로 이동하는 방법이 사용되어 왔다. 또한 파수영 역에서 계산된 결과는 Fourier 역변환을 통하여 다시 공간영역(space domain)으로 이동해야 하는 번거로움이 있다. 따라서 이들 방법은 계산시간이 많이 걸리고 이상체가 없는 지역도 미소체로 분할해야 하므로 수치계산시 대량의 기억용량이 필요하다. 본 연구에서는 Born근사의 문제점 및 전자탐사 2차원 모델링시 3차원 송신원 문제를 해결할 수 있는 확장된 Born 근사법에 근거한 전자탐사 2.5차원 모델링 프로그램을 개발하였다. 이 모델링 프로그램을 이용하여 수직 자기 쌍극자를 송신원으로 하는 시추공간 전자탐사법에 대한 2차 자기 장을 계산하고 적분 방정식에 의한 3차원 모델링 결과와 비교, 분석하였다. 모든 주파수 대역에서 확장된 Born근사에 의한 2.5차원 모델링 결과가 3차원 모델링 결과와 잘 일치하고 있다. 그러나 이상체의 전도도와 모암의 전도도 차이가 10배 이상의 경우일 때는 두 반응은 상당한 차이를 보인다. 따라서 본 연구에서 개발된 확장된 Born 근사에 의한 2.5차원 모델링은 이상체와 모암의 전도도 차이가 너무 크지 않을 경우 이상체의 위치 및 형상을 파악하는데 효과적일 것으로 기대된다.