• Title/Summary/Keyword: green integral equation

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A B-Spline Higher Order Panel Method Applied to the Radiation Wave Problem for a 2-D Body Oscillating on the Free Surface

  • Hong, D.C.;Lee, C.-S.
    • Journal of Ship and Ocean Technology
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    • v.3 no.4
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    • pp.1-14
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    • 1999
  • The improved Green integral equation using the Kelvin-type Green function in known free of irregular frequencies where the integral over the inner free surface integral is removed from the integral equation, resulting in an overdetermined integral equation. The solution of the overdetermined Green integral equation is shown identical with the solution of the improved Green integral equation Using the B-spline higher order panel method, the overdetermined equation is discretized in two different ways; one of the resulting linear system is square and the other is redundant. Numerical experiments show that the solutions of both are identical. Using the present methods, the exact values and higher derivatives of the potential at any place over the wetted surface of the body can be found with much fewer panels than low order panel method.

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Application of the Improved Green Integral Equation to the Radiation-Diffraction Problem for a Floating Ocean Structure in Waves and Current

  • Hong, Do-Chun
    • International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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    • v.3 no.1
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    • pp.14-22
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    • 2000
  • The improved Green integral equation for the calculation of time-harmonic potentials in the radiation diffraction problem about a freely floating body in the presence of moderate or weak current is presented. The forward-speed Green function presented by Brard is used. The correct free surface boundary conditions on the physical free surface are employed as well as an appropriate boundary conditions on the non-physical inner free surface. The default in the existing Green integral equation as well as in the source integral equation is discussed in detail.

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The Exact Formulation of the Green Integral Equation Applied to the Radiation-Diffraction Problem for a Surface Ship Advancing in Waves (파중 전진하는 선체에 의한 방사파-산란파 문제의 해법에 적용되는 Green 적분방정식의 정확한 도출)

  • 홍도천
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2000.04a
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    • pp.23-28
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    • 2000
  • The Green integral equation for the calculation of the forward-speed time-harmonic radiation-diffraction potentials IS derived. The forward-speed Green function presented by Brard is used and the correct free surface boundary condition for the Green function is imposed. The cause of the mistakes in the existing Green integral equation is also pointed out.

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Numerical Solution of the Radiation Problem by the B-Spline Higher Order Kelvin Panel Method for a Half-Immersed Cylinder in Wave and Current

  • Hong, Do-Chun
    • Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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    • 2000.10a
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    • pp.184-188
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    • 2000
  • The improved Green integral equation of overdetermined type applied to the radiation problem for an oscillating cylinder in the presence of weak current is presented. A two-dimensional Green function for the weak current is also presented. The present numerical solution of the Improved Green integral equation by the B-spline higher order Kelvin panel method is shown to be free of irregular frequencies which are present in the usual Green integral equation.

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Solution of the Radiation Problem by the B-Spline Higher Order Kelvin Panel Method for an Oscillating Cylinder Advancing in the Free Surface

  • Hong, Do-Chun;Lee, Chang-Sup
    • Journal of Ship and Ocean Technology
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    • v.6 no.1
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    • pp.34-53
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    • 2002
  • Numerical solution of the forward-speed radiation problem for a half-immersed cylinder advancing in regular waves is presented by making use of the improved Green integral equation in the frequency domain. The B-spline higher order panel method is employed stance the potential and its derivative are unknown at the same time. The present numerical solution of the improved Green integral equation by the B-spline higher order Kelvin panel method is shown to be free of irregular frequencies which are present in the Green integral equation using the forward-speed Kelvin-type Green function.

Singular Cell Integral of Green's tensor in Integral Equation EM Modeling (적분방정식 전자탐사 모델링에서 Green 텐서의 특이 적분)

  • Song Yoonho;Chung Seung-Hwan
    • 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.

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Prediction of Sound Field Inside Duct with Moving Medium by using one Dimensional Green's function (평균 유동을 고려한 1차원 그린 함수를 이용한 덕트 내부의 음장 예측 방법)

  • Jeon, Jong-Hoon;Kim, Yang-Hann
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11a
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    • pp.915-918
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    • 2005
  • Acoustic holography uses Kirchhoff·Helmholtz integral equation and Green's function which satisfies Dirichlet boundary condition Applications of acoustic holography have been taken to the sound field neglecting the effect of flow. The uniform flow, however, changes sound field and the governing equation, Green's function and so on. Thus the conventional method of acoustic holography should be changed. In this research, one possibility to apply acoustic holography to the sound field with uniform flow is introduced through checking for the plane wave in a duct. Change of Green's function due to uniform flow and one method to derive modified form of Kirchhoff·Heimholtz integral is suggested for 1-dimensional sound field. Derivation results show that using Green's function satisfying Dirichlet boundary condition, we can predict sound pressure in a duct using boundary value.

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Prediction of Wave Energy Absorption Efficiency of a Flp-Harbour Device by a Hybrid Integral Equation (Hybrid 적분방정식을 사용한 Flap-Harbour 복합체 파 에너지 흡수효율 추정)

  • 김현주
    • Journal of Ocean Engineering and Technology
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    • v.14 no.2
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    • pp.1-6
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    • 2000
  • Wave energy absorption by a flap equipped with a harbor in a water of finite depth is studied. The wave potential is calculated by a hybrid integral equation consisting of Green integral equations associated with Rankine and Kelvin Green functions. The absorbed wave energy is calculated by both the near-field and far-field methods. The present methods can be used for the design of a flap-harbor wave energy absorber since the numerical results by the two methods are in good agreement.

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Calculation of Stress Intensity Factors Using the Mixed Volume and Boundary Integral Equation Method (혼합 체적-경계 적분방정식법을 이용한 응력확대계수 계산)

  • Lee, Jung-Ki;Lee, Hyeong-Min
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.7
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    • pp.1120-1131
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    • 2003
  • A recently developed numerical method based on a mixed volume and boundary integral equation method is applied to calculate the accurate stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks subject to external loads. Firstly, it should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. Secondly, this method takes full advantage of the capabilities developed in FEM and BIEM. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and volume integral equation method. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

Elastic Analysis of Unbounded Solids Using a Mixed Numerical Method (혼합 수치해석 방법을 이용한 무한고체의 탄성해석)

  • Lee , Jung-Ki;Heo, Kang-Il
    • Proceedings of the KSME Conference
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    • 2001.11a
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    • pp.341-348
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    • 2001
  • A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions.

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