• Water Engineering Research
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• 제2권3호
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• pp.171-178
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• 2001

There are three methods for analyzing flow and pressure distribution in looped water distribution networks (the loop method, the node method, the element method) taking into consideration hydraulic parameters chosen as unknown. For all these methods the non-linear system of equations can be solved by iterative procedures. The paper presents a different approach to this problem by using the method of variational formulations for hydraulic analysis of water distribution networks. This method has the advantage that it uses a specialized optimization algorithm which minimizes directly an objective multivariable function without constraints, implemented in a computer program. The paper compares developed method to the classic Hardy-Cross method. This shows the good performance of the new method.

• 한국군사과학기술학회지
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• 제14권5호
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• pp.957-964
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• 2011

New time schemes based on the FEM were developed and their performances were tested with 2D wave equation. The least-squares and weighted residual methods are used to construct new time schemes based on traditional residual minimization method. To overcome some drawbacks that time schemes based on the least-squares and weighted residual methods have, ad-hoc method is considered to minimize residuals multiplied by others residuals as a new approach. And variational method is used to get necessary conditions of ad-hoc minimization. A-stability was chosen to check the stability of newly developed time schemes. Specific values of new time schemes are presented along with their numerical solutions which were compared with analytic solution.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• 한국전자파학회지:전자파기술
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• 제3권1호
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• pp.33-41
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• 1992

본 논문에서는 변분 유한요소법을 통하여 임의의 유전율 텐서를 포함하는 비등방성 매질에 수직으로 입사한 전자파의 전파특성을 고찰하였다. 먼저 유기정리, 리액션 정리, 가역정리 둥에 기초한 새로운 접근 방볍을 통해 변분수식을 유도하였다. 그 다음 유한요소볍을 이용하여 구해진 범함수로부터 여러 전파특성 에 대해 해석하였다. 특히 냉 자기 플라즈마 슬랩과 같은 균질 및 비균질 비둥방성 매질에 평면파가 수직 으로 입사한 경우에 대해 반사계수, 투과계수 및 축비율을 구하였다. 그리고 이 결과들은 기존의 방법과 비교하여 잘 일치함을 보였다.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• 한국멀티미디어학회논문지
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• 제22권4호
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• pp.491-501
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• 2019

Variational methods, which cast deformation as an energy-minimization problem, are known to provide a good trade-off between practicality and speed. However, the time required to deform a fully detailed shape means that these methods are largely unsuitable for real-time applications. We simplify a 2D shape into a curve skeleton, which can be deformed much more rapidly than the original shape. The curve skeleton also provides a simplified control for the user, utilizing a small number of control handles. Our system deforms the curve skeleton using an energy-minimization method and then applies the resulting deformation to the original shape using linear blend skinning. This approach effectively reduces the size of the variational optimization problem while producing deformations of a similar quality to those obtained from full-scale nonlinear variational methods.

• Steel and Composite Structures
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• 제27권1호
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• pp.1-12
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• 2018

This paper presents a semi-analytical solution of simply supported horizontally composite curved I-beam by trigonometric series. The flexibility of the interlayer connectors between layers both in the tangential direction and in the radial direction is taken into account in the proposed formulation. The governing differential equations and the boundary conditions are established by applying the variational approach, which are solved by applying the Fourier series expansion method. The accuracy and efficiency of the proposed formulation are validated by comparing its results with both experimental results reported in the literature and FEM results.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.215-228
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• 2007

By using the variational calculus of fractional order, one derives a Hamilton-Jacobi equation and a Lagrangian variational approach to the optimal control of one-dimensional fractional dynamics with fractional cost function. It is shown that these two methods are equivalent, as a result of the Lagrange's characteristics method (a new approach) for solving non linear fractional partial differential equations. The key of this results is the fractional Taylor's series $f(x+h)=E_{\alpha}(h^{\alpha}D^{\alpha})f(x)$ where $E_{\alpha}(.)$ is the Mittag-Leffler function.

• 대한화학회지
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• 제14권1호
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• pp.127-131
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• 1970

The variational approach for the direct evaluation of the energy difference ${\Delta}$E is studied. The method is based on the differential equation corresponding to the integral Hellmann-Feynman formula. The ${\Delta}$E is given by the expectation value of the Hermitian operator which does not involve the 1/$r_{ij}$ term. Because of its variational nature of the method, the coupling problem of the differential equations which are encountered in perturbation treatment does not occur. The method is applied to the evaluation of the electric polarizabilities of the Helium isoelectronic series atoms. The result is in good agreement with the experiment. The method is compared with the recent works of Karplus et al.

• 대한전자공학회논문지SP
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• 제48권5호
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• pp.10-15
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• 2011

히스토그램 평활화 방법은 영상의 대조비를 개선시키는 효과적인 방법이다. 하지만 이 방법은 과도한 대조비 향상이나 잡음을 증폭시키는 것과 같은 의도하지 않은 결함을 발생시킬 수 있다. 이러한 결함은 히스토그램 평활화 방법에서 사용되는 명암도 변환 함수를 조절함으로써 감소시킬 수 있다. 본 논문에서는 명암도 변환 함수를 조절하는 문제를 변분법을 사용하여 접근하였다. 이를 위하여 범함수를 정의하고 그 범함수를 최소화하여 명암도 변환 함수를 계산한다. 제안하는 방법을 적용하여 얻은 명암도 변환 함수를 사용하면 눈에 보이는 결함 없이 영상의 대조비를 개선시킬 수 있음을 실험결과로부터 확인할 수 있다.