• Title/Summary/Keyword: Galerkin' method

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Development of 2-D Water Quality Management Model by Using Reliability Analysis (신뢰도 해석기법을 이용한 2차원 수질관리모형의 개발)

  • Kim, Sang-Ho;Han, Kun-Yeun;Kim, Won;Choi, Hung-Sik
    • Journal of Korea Water Resources Association
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    • v.35 no.5
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    • pp.463-474
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    • 2002
  • A two-dimensional water quality management model, Unsteady/Uncertainty Water Quality Model(UUWQM), is developed for a hydrodynamic analysis, an advection-diffusion analysis, and a reliability analysis by using uncertainty technique. The model is applied to the 35 km reach of Sungju to Hyunpoong in the midstream of Nakdong River. 2-D hydrodynamic and water quality analyses are peformed in this reach. Important input variables are decided by sensitivity analysis and verified by Monte Carlo method. Frequency distributions of water quality concentrations are computed from MFOSM method and Monte Carlo method at several locations in this study area. A water quality management system is constructed by calculating the violation probabilities of existing water quality standards.

Resonance Characteristics and Radiation Characteristics of a Spherical Patch on a Dielectric Sphere (구형 유전체 위에 있는 구형 패치의 공진 특성과 방사 특성)

  • Jeong, Yi-Ru;Hong, Ic-Pyo;Lee, Myung-Gun;Chun, Hueng-Jae;Yook, Jong-Gwan
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.23 no.4
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    • pp.515-523
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    • 2012
  • In this paper, the resonance characteristics and radiation characteristics of a spherical patch on a dielectric sphere are analyzed. Resonance characteristics can be obtained from the resonant frequency and the quality factor. Radiation characteristics can be also analyzed from the E-field in the far region. In order to calculate these parameters, spectral domain analysis method is applied. Algebraic equation can be obtained in spectral domain through Vector Legendre transform pair and Galerkin's method. So, efficient calculation is possible numerically. It is investigated that radius, curvature of a spherical patch, and dielectric constant of a dielectric sphere have an effect on characteristics of a spherical patch.

Solution of TM Scattering Applying FGMM and PMM for Conductive Strip Grating Between a Grounded Double Dielectric Layers (접지된 2중 유전체층 사이의 도체띠 격자에 대해FGMM과 PMM을 적용한 TM 산란 해)

  • Uei-Joong Yoon
    • The Journal of the Convergence on Culture Technology
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    • v.9 no.3
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    • pp.721-726
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    • 2023
  • In this paper, TM electromagnetic scattering problems for conductive strip grating between grounded double dielectric layers are analyzed by applying the FGMM(fourier galerkin moment method) and PMM(point matching method) known as a numerical method of electromagnetic field. The boundary conditions are applied to obtain the unknown field coefficients. In order to deal with the problem of grounded double dielectric layers, numerical calculation was performed only when the thickness and relative permittivity of the dielectric layers had the same value. As the thickness of the dielectric layer and the relative permittivity increased, the overall reflected power increased, and the minimum values of the reflected power shifted in the direction of increasing the strip width. The numerical results obtained by applying the numerical methods of FGMM and PMM to the structure proposed in this paper agree very well.

Analysis of H-polarized Electromagnetic Scattering by a Conductive Strip Grating Between a Grounded Double Dielectric Layer Using FGMM (FGMM을 이용한 접지된 2중 유전체층 사이의 완전도체띠 격자구조에 의한 H-분극 전자파 산란 해석)

  • Yoon, Uei-Joong
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.20 no.1
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    • pp.83-88
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    • 2020
  • In this paper, H-polarized electromagnetic scattering problems by a conductive strip grating between a grounded double dielectric layer are analyzed by applying the FGMM(Fourier-Galerkin Moment Method) known as a numerical method of electromagnetic fileld. The boundary conditions are applied to obtain the unknown field coefficients, and the conductive boundary condition is applied to analysis of the conductive strip. The numerical results for normalized reflected power are analyzed by according as the width and spacing of conductive strip, the relative permittivity and thickness of the grounded double dielectric layers, and incident angles. Generally, as the value of the dielectric constant and dielectric thickness of a grounded double dielectric layer increases, the reflected power increased. And as dielectric thickness of a grounded double dielectric layer increases, the current density induced in the strip center increases. The numerical results for the presented structure of this paper are shown in good agreement compared to those of the existing papers using the PMM(Point Matching Method).

Development of Depth-averaged Mixing Length Turbulence Model and Assessment of Eddy Viscosity (수심평균 혼합거리 난류 모형의 개발 및 와점성계수의 평가)

  • Choi, Seung-Yong;Han, Kun-Yeun;Hwang, Jae-Hong
    • Journal of Wetlands Research
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    • v.13 no.3
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    • pp.395-409
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    • 2011
  • The objective of this study is to develop an accurate and robust two-dimensional finite element method for turbulence simulation in open channels. The model is based on Streamline Upwind/Petrov-Galerkin finite element method and Boussinesq's eddy viscosity theory. The method developed in the study is depth-averaged mixing length model which assumes anisotropic and local equilibrium state of turbulence. The model calibration and validation were performed by comparing with analytical solutions and observed data. Several numerical simulations were carried out, which examined the performance of the turbulence model for the purpose of sensitivity analysis. The uniform channels that appear horizontal flow and vertical flow were carried out. The model was also applied to the Han river was in for the applicability test. The results were compared with the observed data. The suggested model displayed reasonable flow distribution compare to the observed data in natural river flow. As a result of this study, the two-dimensional finite element model provides a reliable results for flow distribution based on the turbulence simulation in open channels.

Numerical Experiments of Shallow Water Eqs. by FEM (유한요소법을 이용한 천수방정식의 수치실험)

  • Choi, Sung Uk;Lee, Kil Seong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.10 no.4
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    • pp.141-150
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    • 1990
  • Numerical experiments of sballow water equations are performed under various boundary conditions by finite element method to simulate the circulation in estuaries and coastal areas. Galerkin method is employed to discretize spatial domain, and for time integration, finite difference method (Crank-Nicolson scheme) is used. This method is tested in five problems, in which first four cases have analytic solutions. The computed values are well in agreement with the analytic solutions in four experiments and the result of the last 2-dimensional ease is resonable. Implicit and two step Lax-Wendroff schemes in time domain are compared, and the results when using four node bilinear and triangular elements are presented. Consequently it takes very long time for complex problems requiring many elements to integrate all the time steps using the implicit schemes. And the explicit scheme requires careful consideration in selecting the time step and the grid size to obtain the desired accuracy.

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Solution of TE Scattering by a Resistive Strip Grating Over Grounded Dielectric Multilayers (접지된 다층 유전체위의 저항띠 격자구조에 의한 TE 산란의 해)

  • Yoon Uei-Joong
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.31 no.9A
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    • pp.913-919
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    • 2006
  • In this paper, TE(transverse electric) scattering problems by a resistive strip grating over grounded dielectric multilayers according to the strip width and grating period, the relative permittivity and thickness of dielectric multilayers, and incident angles of a TE plane wave are analyzed by applying the FGMM(Fourier-Galerkin Moment Method) known as a numerical procedure. The induced surface current density is simply expanded in a Fourier series by using the exponential function as a simple function. Generally, the relected power gets increased according as the relative permittivity and thickness of dielectric multilayers gets increased, the sharp variations of the reflected power are due to resonance effects that take place and were previously called wood's anomallies$^{[7]}$. To verify the validity of the proposed method, the numerical results of normalized reflected power for the uniform resistivity R = 0 as a conductive strip case show in good agreement with those in the existing paper.

Dynamic Characteristics Analysis Considering the Effect of the Vortexes of Flux in a LIM for Railway Propulsion System (맴돌이 자속의 영향을 고려한 철도추진용 선형유도전동기의 동특성 연구)

  • Park, Chan-Bae;Lee, Byung-Song;Lee, Ju
    • Journal of the Korean Society for Railway
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    • v.12 no.3
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    • pp.437-442
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    • 2009
  • In the case of a Linear Induction Motor (LIM), numerical analysis method like Finite Element Method (FEM) has been mainly used to analyze the travelling magnetic field problem which includes the velocity-induced electromotive force. If the problem including the velocity-induced electromotive force is analyzed by FEM using the Galerkin method, the solution can be oscillated according to the Peclet Number, which is determined by conductivity, permeability, moving velocity and size of mesh. Consequently, the accuracy of the solution can be low and the vortexes of flux can be occurred at the secondary back-iron. These vortexes of the flux occurred at the secondary back-iron does not exist physically, but it can be occurred in the analysis. In this case, the vortexes of the flux can be generally removed by using Up-Wind method which is impossible to apply a conventional S/W tool (Maxwell 2D). Therefore, in this paper, authors examined the vortexes of the flux occurred at the secondary back-iron of the LIM according to variations of the Peclet Number, and analyzed whether these vortexes of the flux affect on the dynamic force characteristics of the LIM or not.

Solution of TE Scattering by a Resistive Strip Grating Between a Double Dielectric Layer Using FGMM (FGMM을 이용한 2중 유전체층 사이의 저항띠 격자구조에 의한 TE 산란 해)

  • Uei-Joong Yoon
    • The Journal of the Convergence on Culture Technology
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    • v.9 no.3
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    • pp.619-624
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    • 2023
  • In this paper, TE(transverse electric) scattering problems by a resistive strip grating between a double dielectric layer are analyzed by using the FGMM(fourier galerkin moment method) known as a numerical method of electromagnetic fileld. The boundary conditions are applied to obtain the unknown field coefficients, the scattered electromagnetic fields are expanded in a series of Floquet mode functions, and the resistive boundary condition is applied to analysis of the resistive strip. In order to deal with the problem of the double dielectric layer, numerical calculation was performed only when the thickness and relative permittivity of the dielectric layers had the same value. Overall, as the resistivity of the uniform resistivity increased, the current density induced in the resistive strip decreased, the reflected power decreased, and the transmitted power relatively increased. The numerical results of the structure proposed in this paper are shown in good agreement compared to the results of PMM, a numerical analysis method of the existing paper.

Solution of E-polarized Scattering by a Resistive Strip Grating Between a Double Dielectric Layer Using FGMM (FGMM을 이용한 2중 유전체층 사이의 저항띠 격자구조에 의한 TM 산란 해)

  • Uei-Joong Yoon
    • The Journal of the Convergence on Culture Technology
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    • v.9 no.3
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    • pp.641-646
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    • 2023
  • In this paper, TM(transverse magnetic) scattering problems by a resistive strip grating between a double dielectric layer are analyzed by using the FGMM(fourier galerkin moment method) known as a numerical method of electromagnetic fileld. The boundary conditions are applied to obtain the unknown field coefficients, the scattered electromagnetic fields are expanded in a series of Floquet mode functions, and the resistive boundary condition is applied to analysis of the resistive strip. Overall, as the uniform resistivity of the resistive strip increased, the size of the current density induced in the resistance band decreased, the reflected power decreased, and the transmitted power increased. In addition, As the thickness of the dielectric layer increased, the reflected power increased and the transmitted power relatively decreased. The numerical results of the structure proposed in this paper are shown in good agreement compared to the results of PMM, a numerical analysis method of the existing paper.