• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.343-357
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• 1996

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.453-464
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• 2007

A computationally efficient numerical scheme is presented for the phase-field model of two-phase systems for anisotropic interfacial energy. The scheme is solved by using a nonlinear multigrid method. When the coefficient for the anisotropic interfacial energy is sufficiently high, the interface of the system shows corners or missing crystallographic orientations. Numerical simulations with high and low anisotropic coefficients show excellent agreement with exact equilibrium shapes. We also present spinodal decomposition, which shows the robustness of the pro-posed scheme.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.243-248
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• 1997

A full multigrid scheme was used in computing some eigenvalues of the Laplace eigenvalues problem with the Dirichlet bound-ary condition. We get a system of algebraic equations with an aid of finite difference method and apply subspace iteration method to the system to compute first some eigenvalues. The result shows that this is very effective in calculating some eigenvalues of this problem.

• 한국가시화정보학회:학술대회논문집
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• 2003.11a
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• pp.63-66
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• 2003

A new algorithm, CBIR (Correlation Based Image Registration) was proposed to improve the resolution of image registration for PSP (Pressure Sensitive Paint). The local displacement vectors were obtained by finding the displacement which maximizes the cross-correlation between two interrogation windows of 'wind-off' and 'wind-on' images. A recursive multigrid processing was employed to increase the non-linear spatial resolutions. The variations of image were precisely measured without identifying the control points.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.10a
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• pp.151-159
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• 1998

디젤 엔진의 푸쉬로드 타입의 밸브 트레인에서의 힘의 전달 과정을 기구학적 응용을 통하여 구하였다. 이러한 힘의 최종 전달 단계인 캠과 평판 종동물의 접촉에서의 작용하중과 상대 운동 속도를 계산하였고 접촉면에서의 유막 두께를 고체면의 탄성변형을 고려하여 계산하였다. 특히 탄성 유체 윤활의 해석을 하는데 있어서 안정성과 수렴성이 우수한 멀티그리드 멀티레벨 기법을 사용하였으며 동하중 상태를 고려하여 유막 두께를 계산하고 기존의 정상상태의 해석해와 비교하였다.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.19-35
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• 2004

We develop in this paper some preconditioners for sparse non-symmetric M-matrices, which combine a recursive two-level block I LU factorization with multigrid method, we compare these preconditioners on matrices arising from discretized convection-diffusion equations using up-wind finite difference schemes and multigrid orderings, some comparison theorems and experiment results are demonstrated.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.49-54
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• 1998

3-dimensional Euler solver is parallelized. The spatial discretization method is the 2nd order TVD scheme and DADI method with multigrid is used as a time integration. In order to parallelize this solver, the domain decomposition method with overlapped grid and message passing techniques are used. The informations on the each inter-processor bound-aries are communicated with MPI library. Finally, the parallel performance repsented by calculating the ONERA M6 wing at transonic flow condition using CRAY T3E and C90.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.245-269
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• 1999

Multigrid method and acceleration by conjugate gradient method for first-order system least squares (FOSLS) using bilinear finite elements are developed for various boundary value problems of planar linear elasticity. They are two-stage algorithms that first solve for the displacement flux variable, then for the displacement itself. This paper focuses on solving for the displacement flux variable only. Numerical results show that the convergence is uniform even as the material becomes nearly incompressible. Computations for convergence factors and discretization errors are included. Heuristic arguments to improve the convergences are discussed as well.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1778-1782
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• 2004

A new algorithm, CBIR (Correlation-Based Image Registration) was proposed to improve the resolution of image registration for PSP (Pressure-Sensitive Paint). The local displacement vectors were obtained by finding the displacement which maximizes the cross-correlation between two interrogation windows of 'wind-off' and 'wind-on' images. A recursive multigrid processing was employed to increase the non-linear spatial resolutions. The variations of image were precisely measured without identifying the control points.

• Journal of Korea Multimedia Society
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• v.7 no.12
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• pp.1680-1691
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• 2004

One of the representative methods of optical flow is a gradient method which estimates the movement of an object based on the differential of image brightness. However, the method is ineffective for large displacement of the object and many improved methods have been proposed to copy with such limitations. One of these improved techniques is the multigrid processing, which is used in many optical flow algorithms. As an alternative novel technique we have been proposing an orthogonal functional expansion method, where whole displacements are expanded from low frequency terms. This method is expected to be applicable to flow estimation with large displacement and deformation including expansion and contraction, which are difficult to cope with by conventional optical flow methods. In the orthogonal functional expansion method, the apparent displacement field is calculated iteratively by a projection method which utilizes derivatives of the invariant constraint equations of brightness constancy. One feature of this method is that differentiation of the input image is not necessary, thereby reducing sensitivity to noise. In this paper, we apply our method to several real images in which the objects undergo large displacement and/or deformation including expansion. We demonstrate the effectiveness of the orthogonal functional expansion method by comparing with conventional methods including our optimally scaled multigrid optical flow algorithm.