• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.238-243
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• 1999

Minimum-fuel and -time orbit transfer are two major goals of the satellite trajectory optimization. In this paper, we consider satellites in two coplanar elliptic orbits when the apsidal lines coincide, and analytically find the conditions for the two-impulse minimum-time transfer orbit using Lambert's theorem. The transfer time is a decreasing function of a variable related to the transfer orbit's semimajor axis in the minimum-time case. In the minimum-time case, there is no unique minimum-time solution, but there is a limiting solution. However, there exists a unique solution in the case of minimum-fuel transfer, fur which we find analytically the necessary and sufficient conditions. As a special case, we consider when the transfer angle is one hundred and eighty degrees. In this case, we show that we obtain the classical fuel-optimal Hohmann transfer orbit. We also derive the Hohmann transfer rime and delta-velocity equations from more general equations, which are obtained using Lambert's theorem. We note the tradeoff between minimum-time and - fuel transfer. An optimal coplanar orbit maneuver algorithm to trade off the minimum-time goal against the minimum-fuel goal is proposed. Finally, the numerical simulation results are given to demonstrate the derived theory and the algorithm.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.173-195
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• 2021

A new implicit discontinuous Galerkin spectral element method (DGSEM) based on the first order hyperbolic system(FOHS) is presented for solving elliptic type partial different equations, such as the Poisson problems. By utilizing the idea of hyperbolic formulation of Nishikawa[1], the original Poisson equation was reformulated in the first-order hyperbolic system. Such hyperbolic system is solved implicitly by the collocation type DGSEM. The steady state solution in pseudo-time, which is the solution of the original Poisson problem, was obtained by the implicit solution of the global linear system. The optimal polynomial orders of 𝒪(𝒽^𝑝+1)) are obtained for both the solution and gradient variables from the test cases in 1D and 2D regular grids. Spectral accuracy of the solution and gradient variables are confirmed from all test cases of using the uniform grids in 2D.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.87-95
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• 1997

In general, the positive solution to biological reaction-diffusion equations is not unique. In this paper, we state the sufficient and necessary conditions of the existence of positive solutions, and give and the proof for the uniqueness of positive solutions for a certain elliptic interacting system.

• Water for future
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• v.23 no.3
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• pp.319-328
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• 1990

The Parameter Identification of 2-demensional estuarine model was carried out using new output ADI-FDM numerical semi-implicit schem transformed in boundary fitted(BF) - coordinate. The hydrodynamic equations which is coupled with the transport equations were used as basic equations in the model. Thompson's equations were used to transform governing equations into rectangular plane equations and his elliptic grid generation scheme was used to generate curvilinear grid system. in BF - coordinates. The parameters to be identified are friction coefficient and disperse coefficient embedded in the governing equations. The numerical output scheme is tidally averaged salinity model in BF - coordinates. The algorithm to optimize norm of error between observations and calculations is the influence coefficinet algorithm associated with least square criterion. The lumped model is conssidered in identification. This paper was concetrated on checking whether the new output scheme might be useful to identify parameters in estuarine salinity model or not. The proposed method was tested through experimental application with hypothetical simple model. The result of the test shows that the proposed method can be used for parameter identification in estuarine model.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.293-294
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• 2015

This work considers the elliptic restricted three-body problem under effects of radiation of the bigger primary, and an oblate spheroid for the smaller primary to mimic an exoplanetary system with a gas giant planet. Under the influences of both effects we look for the existence of the triangular equilibrium points and the influences of the radiation and oblateness on the locations and motion of the points. We set the system in a normalized rotating coordinate system and derive equations of motion for the third infinitesimal object. Our study shows that the effects modify the equilateral/isosceles triangle shape with respect to the primaries. The triangular points also have non-planar motion with period depending on the value of the planet oblateness.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.563-578
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• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.93-115
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• 2024

In this paper, the Gauge-Uzawa methods for the Darcy-Brinkman equations driven by temperature and salt concentration (DBTC) are proposed. The first order backward difference formula is adopted to approximate the time derivative term, and the linear term is treated implicitly, the nonlinear terms are treated semi-implicit. In each time step, the coupling elliptic problems of velocity, temperature and salt concentration are solved, and then the pressure is solved. The unconditional stability and error estimations of the first order semi-discrete scheme are derived, at the same time, the unconditional stability of the first order fully discrete scheme is obtained. Some numerical experiments verify the theoretical prediction and show the effectiveness of the proposed methods.

• Nuclear Engineering and Technology
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• v.29 no.1
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• pp.58-67
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• 1997

A numerical study has been peformed to investigate the flow and mixing characteristics of a chemical injection tank in the chemical and volume control system (CVCS) of Yonggwang 5&6 (YGN 5&6). This study was undertaken to provide a basis for modification of the previous design (YGN 3&4) which gave a lot of difficulties in installation and operation of the chemical injection system during the start-up test because it needs a special reciprocating pump with a high actual head. For the tank of length-to-diameter ratios (L/D) of 1,2 and 3, each with and without a baffle inside, calculation results were obtained by solving the unsteady laminar two-dimensional elliptic forms of governing equations for the mass, momentum and species concentration. Finite-difference method was used to obtain discretized equations, and the SIMPLER solution algorithm, which was developed based on the staggered grid control volume, was employed for the calculation procedure. Results showed that the baffle is very effective in enhancing the mixing in the tank and that a baffle should be installed near the tank entrance in order to 110 chemicals into the reactor coolant system (RCS) within the operating time required.

• Korean Journal of Mathematics
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• v.12 no.1
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• pp.77-90
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• 2004

The purpose of this paper is to give a sufficient condition for the existence, nonexistence and uniqueness of coexistence of positive solutions to a rather general type of elliptic competition system of the Dirichlet problem on the bounded domain ${\Omega}$ in $R^n$. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations. This result yields an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

• Journal of Ocean Engineering and Technology
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• v.25 no.2
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• pp.62-66
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• 2011

In this paper, a liquid-filled long membrane container resting on a horizontal foundation is considered. All of the quantities are normalized to obtain similarity solutions. A system of nonlinear ordinary differential equations with undetermined boundary conditions is solved analytically. The integration of the curvature gives the solutions, which are expressed in terms of the elliptic integrals. A method for finding the shape and characteristic values is proposed for a given cross-sectional volume. The validity of these solutions is confirmed, and some results are shown for characteristic values and shapes.