• Title/Summary/Keyword: uniform grid

### Modification of MUSCL Scheme for Application of Non-uniform Grid (비정형격자의 적용을 위한 MUSCL 기법의 수정)

• Kim, Byung-Hyun;Han, Kun-Yeon
• Journal of Korea Water Resources Association
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• v.43 no.1
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• pp.105-117
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• 2010
• This paper presents a new and simple technique to perform MUSCL reconstruction for solving 2D shallow water equations. The modified MUSCL scheme uses weighted area ratio to apply non-uniform grid in stead of the previous method that equally distributed the difference of conservation variables to each interface. The suggested method can physically reconstruct conservation variables in case of uniform grid as well as non-uniform grid. In this study, Unsplit scheme applicable to unstructured grid is used and efficient slope limiter of TVD scheme is used to control numerical oscillation which can be occurred in modified MUSCL scheme. For accurate and efficient treatment of bed slope term, the modified MUSCL scheme is coupled with the surface gradient method. The finite volume model applied to suggested scheme is verified through a comparison between numerical solution and laboratory measurements data such as the simulations of isolated building test case and Bellos's dam break test case.

### A New Approach for the Derivation of a Discrete Approximation Formula on Uniform Grid for Harmonic Functions

• Kim, Philsu;Choi, Hyun Jung;Ahn, Soyoung
• Kyungpook Mathematical Journal
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• v.47 no.4
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• pp.529-548
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• 2007
• The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

### FDTD를 이용한 Suspended Membrane Microstrip(SMM) Line의 해석

• 남윤권
• Proceedings of the Korea Electromagnetic Engineering Society Conference
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• pp.345-346
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• 2001
• 그림 1에서 볼 수 있는 것처럼 신호선을 지지하고 있는 membrane은 SMM line의 전체 크기에 비해 아주 작다. 따라서 uniform grid를 ㅣ용해서 이러한 구조를 해석하게 되면 해석점이 너무 많아져서 많은 메모리를 필요로 하게 되어 일반적인 컴퓨터로는 해석이 어려워지며, non-uniform grid를 사용한다 해도 해석점의 수는 줄일 수 있느나 가장 작은 grid의 크기가 membrane의 크기에 의해서 정해지므로 FDTD 해석에 사용되는 time-step이 아주 작아져서 해석하는데 시간이 오래 걸린게 된다.

### Study of Facial Expression Recognition using Variable-sized Block (가변 크기 블록(Variable-sized Block)을 이용한 얼굴 표정 인식에 관한 연구)

• Cho, Youngtak;Ryu, Byungyong;Chae, Oksam
• Convergence Security Journal
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• v.19 no.1
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• pp.67-78
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• 2019
• Most existing facial expression recognition methods use a uniform grid method that divides the entire facial image into uniform blocks when describing facial features. The problem of this method may include non-face backgrounds, which interferes with discrimination of facial expressions, and the feature of a face included in each block may vary depending on the position, size, and orientation of the face in the input image. In this paper, we propose a variable-size block method which determines the size and position of a block that best represents meaningful facial expression change. As a part of the effort, we propose the way to determine the optimal number, position and size of each block based on the facial feature points. For the evaluation of the proposed method, we generate the facial feature vectors using LDTP and construct a facial expression recognition system based on SVM. Experimental results show that the proposed method is superior to conventional uniform grid based method. Especially, it shows that the proposed method can adapt to the change of the input environment more effectively by showing relatively better performance than exiting methods in the images with large shape and orientation changes.

### SURFACE RECONSTRUCTION FROM SCATTERED POINT DATA ON OCTREE

• Park, Chang-Soo;Min, Cho-Hon;Kang, Myung-Joo
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.31-49
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• 2012
• In this paper, we propose a very efficient method which reconstructs the high resolution surface from a set of unorganized points. Our method is based on the level set method using adaptive octree. We start with the surface reconstruction model proposed in [20]. In [20], they introduced a very fast and efficient method which is different from the previous methods using the level set method. Most existing methods[21, 22] employed the time evolving process from an initial surface to point cloud. But in [20], they considered the surface reconstruction process as an elliptic problem in the narrow band including point cloud. So they could obtain very speedy method because they didn't have to limit the time evolution step by the finite speed of propagation. However, they implemented that model just on the uniform grid. So they still have the weakness that it needs so much memories because of being fulfilled only on the uniform grid. Their algorithm basically solves a large linear system of which size is the same as the number of the grid in a narrow band. Besides, it is not easy to make the width of band narrow enough since the decision of band width depends on the distribution of point data. After all, as far as it is implemented on the uniform grid, it is almost impossible to generate the surface on the high resolution because the memory requirement increases geometrically. We resolve it by adapting octree data structure[12, 11] to our problem and by introducing a new redistancing algorithm which is different from the existing one[19].

### UNIFORM MESH METHOD FOR A MAXWELL'S EQUATION WITH DISCONTINUOUS COEFFICIENTS

• KIM, JI HYUN
• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.123-131
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• 2019
• In this paper, we introduce a uniform mesh method for a Maxwell's equation with discontinuous coefficients. We observe optimal O(h) order for the electric field and O(h) order for the curl.

### The Thermal Response of Biological Tissue Subjected to Short-Pulsed Irradiation Train (초단파 펄스 트레인 레이저 조사시 생체 조직의 열반응)

• Kim, K.H.;Suh, J.;Lee, J.H.
• Proceedings of the Korean Society of Precision Engineering Conference
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• pp.947-948
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• 2009

### Development of Delaunay Triangulation Algorithm Using Subdivision (분할 Delaunay 삼각화 알고리즘 개발)

• 박시형;이성수
• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.248-253
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• 2002
• Delaunay triangulation is well balanced in the sense that the triangles tend toward equiangularity. And so, Delaunay triangulation hasn't some slivers triangle. It's commonly used in various field of CAD applications, such as reverse engineering, shape reconstruction, solid modeling and volume rendering. For Example, In this paper, an improved Delaunay triangulation is proposed in 2-dimensions. The suggested algorithm subdivides a uniform grids into sub-quad grids, and so efficient where points are nonuniform distribution. To get the mate from quad-subdivision algorithm, the area where triangulation-patch will be most likely created should be searched first.

### Dynamics of disconnected risers under rigid and compliant hang-off (강성 및 컴플라이언트 행오프 하에서의 미연결송유관의 동력학)

• Yoon, D. Y.
• Journal of Ocean Engineering and Technology
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• v.1 no.2
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• pp.39-51
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• 1987
• 석유시추 보호관의 비선형 운동을 시뮬레이트하는 유효한 해법이 non-uniform grid 유한차분법과 implicit time 적분법에 근거하여 제시되었다. 극한 상태에 있는 지지 플랫폼의 상승 가속도에 의해 생기는 보호관의 동적 좌굴형 반응에 관하여 상세히 연구되었고, 이 반응에 미치는 중요 변수가 규명되었다. 운동의 현저한 감소와 이에 따른 응력들이 컴플라이언트 행오프(hang-off)를 적용시킴으로써 얻어졌다.

### STABILITY AND ERROR OF THE VARIABLE TWO-STEP BDF FOR SEMILINEAR PARABOLIC PROBLEMS

• EMMRICH ETIENNE
• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.33-55
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• 2005
• The temporal discretisation of a moderate semilinear parabolic problem in an abstract setting by the two-step backward differentiation formula with variable step sizes is analysed. Stability as well as optimal smooth data error estimates are derived if the ratios of adjacent step sizes are bounded from above by 1.91.