• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권4호
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• pp.272-280
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• 2023

We study the numerical analysis for the Cahn-Hilliard (CH) equation using the decoupled projection (DP) method. The CH equation is a fourth order nonlinear partial differential equation that is hard to solve. Therefore, various of numerical schemes have been proposed to solve the CH equation. To verify the relation of each existing scheme for the CH equation, we consider the DP method for linear convex splitting schemes. We present the numerical experiments to demonstrate our analysis. Throughout this study, it is expected to construct a novel numerical scheme using the relation with existing numerical schemes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권2호
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• pp.103-121
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• 2015

In this paper, we briefly review and describe a projection algorithm for numerically computing the two-dimensional time-dependent incompressible Navier-Stokes equation. The projection method, which was originally introduced by Alexandre Chorin [A.J. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput., 22 (1968), pp. 745-762], is an effective numerical method for solving time-dependent incompressible fluid flow problems. The key advantage of the projection method is that we do not compute the momentum and the continuity equations at the same time, which is computationally difficult and costly. In the projection method, we compute an intermediate velocity vector field that is then projected onto divergence-free fields to recover the divergence-free velocity. Numerical solutions for flows inside a driven cavity are presented. We also provide the source code for the programs so that interested readers can modify the programs and adapt them for their own purposes.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.171-180
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• 1998

In this paper we analyze the convergence of the semidis-crete solution of the Roseneau equation. We introduce the auxiliary projection of the solution and derive the optimal convergence of the semidiscrete solution as well as the auxiliary projection in L2 normed space.

• 대한수학회보
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• 제46권4호
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• pp.627-644
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• 2009

The gauge-Uzawa method which has been constructed in [11] is a projection type method to solve the evolution Navier-Stokes equations. The method overcomes many shortcomings of projection methods and displays superior numerical performance [11, 12, 15, 16]. However, we have obtained only suboptimal accuracy via the energy estimate in [11]. In this paper, we study semi-discrete gauge-Uzawa method to prove optimal accuracy via energy estimate. The main key in this proof is to construct the intermediate equation which is formed to gauge-Uzawa algorithm. We will estimate velocity errors via comparing with the intermediate equation and then evaluate pressure errors via subtracting gauge-Uzawa algorithm from Navier-Stokes equations.

• 한국측량학회지
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• 제31권3호
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• pp.183-192
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• 2013

최근 전 세계적으로 국가별, 기관별, 목적별로 다양하게 구축된 공간정보를 단일한 위치기반으로 하는 데이터로 통합함으로써 각 자료 간 연계성 및 활용성을 높이고 있다. 본 연구에서는 새로운 국가측지기준의 도입에 따른 위치기준의 변화와 공간정보 분야의 seamless 데이터 서비스 요구에 효율적으로 대응할 수 있도록 새로운 국가 단일원점 평면직각좌표에 대한 연구를 수행하였다. 이를 위해 한반도 전역을 투영영역으로 설정하고 투영영역 내 발생하는 투영왜곡을 분석함으로써 이를 균질화 및 최소화할 수 있는 투영파라미터를 정의하였으며, 이에 대한 표준화 및 국제기구 등록방안을 제시하였다. 연구의 결과, 국가 단일원점 평면직각좌표계를 위한 최적의 투영식은 Hooijberg 투영식으로 분석되었으며, TM 투영을 위한 5가지 투영파라미터는 위도(${\Phi}$) $38^{\circ}N$, 경도(${\lambda}$) $128^{\circ}E$, 축척계수(K) 0.99924로 각각 분석되었다. 또한, 투영원점(${\Phi}$, ${\lambda}$)에 대한 가수값(false Northing & Easting)은 국가지점번호제도의 도입을 고려하여 북쪽방향 700,000m, 동쪽방향 400,000m로 각각 설정하는 것이 적합하였다.

• International Journal of Automotive Technology
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• 제2권3호
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• pp.117-122
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• 2001

For a dynamic analysis of a constrained multibody system, it is necessary to have a routine for satisfying kinematic constraints. LU decomposition scheme, which is used to divide coordinates into dependent and independent coordinates, is efficient but has great difficulty near the singular configuration. Other method such as the projection matrix, which is more stable near a singular configuration, takes longer simulation time due to the large amount of calculation for decomposition. In this paper, the row space and the null space of the Jacobian matrix are proposed by using the pseudo-inverse method and the projection matrix. The equations of the motion of a system are replaced with independent acceleration components using the null space of the Jacobian matrix. Also a new hybrid method is proposed, combining the LU decomposition and the projection matrix. The proposed hybrid method has following advantages. (1) The simulation efficiency is preserved by the LU method during the simulation. (2) The accuracy of the solution is also achieved by the projection method near the singular configuration.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.839-853
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• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• 한국운동역학회지
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• 제13권3호
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• pp.117-131
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• 2003

This study simulated the range of golf ball with different projection angles using a drive swing condition. For the simulation purpose, the differential equation of dynamics was induced by using Bernoulli's principle and average back spin frequency, instant velocity, and dimple of golf ball from amateur group, professional group, and Tiger Woods were chosen as the initial condition. The study result indicated that lift coefficient($C_{lift}$) relative to drag coefficient ($C_d$), 0.3 of differential equation was applied differently in terms of back spin Sequency, and when $C_{lift}$ was 0.4 for amateur, 0.5 for professional, and 0.7 for Tiger Woods the projection ranges of ball were closely matched with initial condition. With selected $C_{lift}$ and back spin frequency of initial condition, the ranges with different projection angle was measured as 193m ($13-17^{\circ}$) for amateur, 240m ($9-13^{\circ}$), professional and 273m ($9^{\circ}$)Tiger Woods, respectively. For the range in terms of back spin frequency and projection angle, the amateur group indicated relatively high spin frequency (70 RPS) and showed the maximal range (195m) with $13^{\circ}$ of projection angle. The tendency of longer range with higher projection angle was also found under the different conditions of spin frequency in this group. The professional group showed their maximal range (245m) with conditions of 60RPS of spin frequency and $9^{\circ}$ of projection angle. Their range was decreased dramatically when the spin frequency was reduced to 40-50 RPS. For Tiger Woods, the maximal range was found with 40RPS of spin frequency and the range was decreased notably when the spin frequency was above 40RPS.

• 한국산업융합학회 논문집
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• 제4권1호
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• pp.87-94
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• 2001

In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve this equation, coordinate partitioning method and constraint stabilization method are commonly used. The coordinate partitioning method divides the coordinate into independent and dependent coordinates. The most typical coordinate partitioning method arc LU decomposition, QR decomposition, projection method and SVD(sigular value decomposition).The objective of this research is to find a efficient coordinate partitioning method in flexible multibody systems and a hybrid decomposition algorithm which employs both LU and projection methods is proposed. The accuracy of the solution algorithm is checked with a slider-crank mechanism.

• 한국자동차공학회논문집
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• 제5권1호
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• pp.154-161
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• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.