• Korean Journal of Mathematics
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• 제22권4호
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• pp.645-658
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• 2014

Many projection methods have been progressively constructed to find more accurate and efficient solution of the Navier-Stokes equations. In this paper, we consider most recently constructed projection methods: the pressure correction method, the gauge method, the consistent splitting method, the Gauge-Uzawa method, and the stabilized Gauge-Uzawa method. Each method has different background and theoretical proof. We prove equivalentness of the pressure correction method and the stabilized Gauge-Uzawa method. Also we will obtain that the Gauge-Uzawa method is equivalent to the gauge method and the consistent splitting method. We gather theoretical results of them and conclude that the results are also valid on other equivalent methods.

• 한국전산유체공학회지
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• 제4권2호
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• pp.39-46
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• 1999

The FVM(Finite Volume Method) have been used mainly for the flow analyses in the piston-cylinder. The objective of the present study is to analyze numerically the piston-driven intake flows using the FEM(Finite Element Method). The FEM algorithm used in this study is 4-step time-splitting method which requires much less execution time and computer storage than the velocity-pressure integrated method and the penalty method. And the explicit Lax-Wendroff scheme is applied to nonlinear convective term in the momentum equations to prevent checkerboard pressure oscillations. Also, the ALE(arbitrary Lagrangian Eulerian) method is adopted for the moving grids. The calculated results show good agreement in comparison with those by the FVM and the experimental results by the LDA.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제6권1호
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• pp.1-15
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• 2002

Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

• Structural Engineering and Mechanics
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• 제11권5호
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• pp.535-546
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• 2001

A new p-adaptive analysis scheme for hp-clouds method is presented. In the scheme, refined global equations are resolved into two parts, one of them being related to the newly appended dof's. The solution obtained in previous analysis step is reflected in the force vector. The size of the p-adaptive equation consisting of the newly appended dof's is much smaller than the original equation. Consequently, the computational cost is drastically decreased. Through numerical examples, the efficiency and efficacy of the method in comparison with the existing p-refinement scheme of the hp-clouds have been demonstrated.

• 방사성폐기물학회지
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• 제10권4호
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• pp.237-246
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• 2012

본 연구에서는 콜로이드와 핵종의 복합이동에 관한 수치모델을 개발하였다. 콜로이드와 핵종의 반응-이동 지배방정식을 풀기 위하여 Operator Splitting Method 중 Strang의 분리 SNI 방식을 수치해석 방법으로 채택하였고 이는 MATLAB을 이용하여 코드화 되었다. 개발된 수치모델은 용질의 이동 및 분산만을 고려한 해석해를 통한 검증과정에서 피어슨 상관계수의 제곱값($r^2$)이 0.99 이상으로 나타나 모델의 정확성이 입증되었다.

• 한국정보과학회논문지:정보통신
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• 제29권1호
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• pp.48-56
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• 2002

본 연구는 IP(Internet Protocol) 망에서 복수 트리경로에 의한 멀티캐스팅 방법을 제시한다. 트래픽 양에 대해 아크 비용이 비선형 함수이고 멀티캐스트 트래픽 수요가 대용량일 때, 단일의 트리경로 대신에 트래픽을 분할하여 복수개의 트리경로로 전송하는 것이 멀티캐스트 서비스 품질을 향상시킬 수 있다. 제시하는 멀티캐스팅 방법은 원하는 수준까지 트리경로를 추가하며, 주어진 트리경로 집합에 대해서 트래픽을 분할한다. 트래픽 분할을 위한 수학적 모형과 최적조건을 도출하였으며, 여러 개의 멀티캐스팅 트래픽을 동시에 전송하고자 할 때도 적용 가능하다. 적용 결과는 제안한 복수 트리경로에 의한 IP 멀티캐스팅 방법이 단-대-단 서비스 품질을 보장하는 데도 상당한 효과를 있음을 보인다.

• 한국수학사학회지
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• 제28권4호
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• pp.167-179
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• 2015

We study the solution of truncated series of Lee Sang-hyeog with the aspect of visualization. Lee Sang-hyeog solved a problem of truncated series by 4 ways: Shen Kuo' series method, splitting method, difference sequence method, and Ban Chu Cha method. As the structure and solution of truncated series in tertiary number is already clarified with algebraic symbols in some previous research, we express and explain it by visual representation. The explanation and proof of algebraic symbols about truncated series is clear in mathematical aspects; however, it has a lot of difficulties in the aspects of understanding. In other words, it is more effective in the educational situations to provide algebraic symbols after the intuitive understanding of structure and solution of truncated series with visual representation.

• 한국콘텐츠학회논문지
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• 제7권8호
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• pp.13-20
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• 2007

의사결정나무는 대량의 데이터를 몇 개의 집단으로 분류하고, 미래상황을 예측하기 위해 자주 사용되는 분석기법 중의 하나이며, 각 노드에서 분할이 일어나면서 자라게 되고, 각 노드에 속하는 자료의 순수도가 효과적으로 증가하도록 진행된다. 또한 의사결정나무를 생성하는 과정에서 필요 이상의 가지(leaves)를 갖게 되면 노드의 분할을 정지하거나, 분류성능 향상에 큰 도움이 되지 못하는 가지를 잘라내게 된다. 이러한 가지치기의 결과로 의사결정나무의 형태가 변하게 되는데 이는 기존의 가지분할이 효율적이지 않았음을 의미하는 것이다. 본 연구에서는 가지치기의 교정뿐 아니라 새로운 분할과정을 혼합한 우수한 의사결정나무 추출 방법을 제안한다. 특히, 새로운 분할 노드의 선택에 있어 퍼지이론을 적용하여 분할의 효과성을 제고할 수 있는 방법을 제시하고자 한다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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• pp.75-89
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• 2018

This paper presents the numerical valuation of the arithmetic Asian option by using the operator-splitting method (OSM). Since there is no closed-form solution for the arithmetic Asian option, finding a good numerical algorithm to value the arithmetic Asian option is important. In this paper, we focus on a two-dimensional PDE. The OSM is famous for dealing with plural-dimensional PDE using finite difference discretization. We provide a detailed numerical algorithm and compare results with MCS method to show the performance of the method.

• 한국통신학회논문지
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• 제30권10C호
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• pp.976-982
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• 2005

In this paper, a channel-adaptive beamforming method is proposed for OFDMA (Orthogonal Frequency Division Multilexing Access) systems with smart antenna, in which the size of a cluster is determined adaptively depending on the frequency selectivity of the channel. The proposed method consists of 4 steps: initial channel estimation, refinement of channel estimates, region-splitting, and computation of weight vector for each region. In the proposed method, the size of a cluster for resource unit is determined adaptively according to a region-splitting criterion. It is shown by simulation that the proposed method shows good performances in both frequency-flat and frequency-selective channels.