• Honam Mathematical Journal
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• v.40 no.4
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.1-13
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• 2002

In this paper we present numerical methods fur computations of nonequilibrium hypersonic flow of air around bodies including chemical reaction effects and present numerical result of the flow over concave corners. We developed implicit finite difference method to overcome numerical difficulties with the lack of resolution behind the shock and near the body. Using our method we were able to find details of the flow properties near the shock and body and were able to continue the computation of the flow for a long distance from the corner of the body.

• Journal of the Korean Vacuum Society
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• v.13 no.3
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• pp.120-126
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• 2004

A damage-reduced trench was investigated in view of the defect distribution along trench sidewall and bottom using high resolution transmission electron microscopy, which was formed by HBr plasma and additive gases in magnetically enhanced reactive ion etching system. Adding $O_2$ and other additive gases into HBr plasma makes it possible to eliminate sidewall undercut and lower surface roughness by forming the passivation layer of lateral etching. To reduce the RIE induced damage and obtain the fine shape trench corner rounding, we investigated the hydrogen annealing effect after trench formation. Silicon atomic migration on trench surfaces using high temperature hydrogen annealing was observed with atomic scale view. Migrated atoms on crystal surfaces formed specific crystal planes such as (111), (113) low index planes, instead of fully rounded comers to reduce the overall surface energy. We could observe the buildup of migrated atoms against the oxide mask, which originated from the surface migration of silicon atoms. Using this hydrogen annealing, more uniform thermal oxide could be grown on trench surfaces, suitable for the improvement of oxide breakdown.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.281-292
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• 2009

The solution of the interface problem or Poisson problem with concave corner has singular perturbation at the interface corners or singular corners. The decoupled dual singular function method (DDSFM) which exploits the singular representations of the solutions was suggested in [3, 9] and estimated optimal accuracy in [10]. The convergence rates consist with theoretical results even for the problems with very strong singularity, with the efficiency depending on parameters used in the methods. Furthermore the errors in $L^2$ and $L^\infty$-spaces display some oscillation, in the cases with meshsize not small enough. In this paper, we present an answer to remove the oscillation via numerical experiments. We observe the effects of parameters in DDSFM, and show the consisting efficiency of the method over the strong singularity.

• Bulletin of the Society of Naval Architects of Korea
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• v.18 no.4
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• pp.13-20
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• 1981

The hydrodynamic added mass of two dimensional cylinders oscillating vertically at high frequencies in the free surface is of interest to ship vibration problems. Conformal transformation is one of the methods commonly in use for computing the inertia coefficient. Especially, Schwarz-Christoffel transformation has been employed to evaluate the inertia coefficient for the cylinders of straight frames and chines. In this paper, the inertia coefficient for the cylinders with round corners in vertical oscillation at high frequencies are evaluated by employing the Schwarz-Christoffel transformation for the concave corner. The results of calculation by employing the Schwarz-Christoffel transformation are found to be well within the expected range of values compared to Lewis form and the results obtained by source distribution method.

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1416-1428
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• 2021

Pebble flow characteristics can be significantly affected by the configuration of pebble bed, especially for HTGR pebble beds. How to achieve a desired uniform flow pattern without stagnation is the top priority for reactor design. Pebbles flows inside some specially designed pebble bed with arc-shaped contraction configurations at the bottom, including both concave-inward and convex-outward shapes are explored based on discrete element method. Flow characteristics including pebble retention, residence-time frequency density, flow uniformity as well as axial velocity are investigated. The results show that the traditionally designed pebble bed with cone-shape bottom is not the most preferred structure with respect to flow pattern for reactor design. By improving the contraction configuration, the flow performance can be significantly enhanced. The flow in the convex-shape configuration featured by uniformity, consistency and less stagnation, is much more desirable for pebble bed design. In contrast, when the shape is from convex-forward to concave-inward, the flow shows more nonuniformity and stagnation in the corner although the average cross-section axial velocity is the largest due to the dominant middle pebbles.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.547-552
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• 2003

In mold machining, there are many concave machining regions where chatter and tool deflection occur since MRR (material removal rate) increases as curvature increases even though cutting speed and depth of cut are constant. Boolean operation between stock and tool model is widely used to compute MRR in NC milling simulation. In finish cutting, the side step is reduced to about 0.3mm and tool path length is sometimes over 300m. so Boolean operation takes long computation time and includes much error if the resolution of stock and tool model is larger than the side step. In this paper, curvature of CL(cutter location) surface and side step of tool path is used to compute the feedrate for constant MRR machining. The data structure of CL surface is Z-map generated from NC tool path. The algorithm to get local curvature from discrete data was developed and applied to compute local curvature of CL surface. The side step of tool path was computed by point density map which includes cutter location point density at each grid element. The feedrate computed from curvature and side step is inserted to new tool path to regulate MRR. The resultants wire applied to feedrate optimization system which generates new tool path with feedrate from NC codes for finish cutting. The system was applied to speaker mold machining. The finishing time was reduced to 12.6%. tool wear was reduced from 2mm to 1.1mm and chatter marks and over cut on corner were removed.

• Proceedings of the Korea Water Resources Association Conference
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• 2012.05a
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• pp.727-727
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• 2012

최근 제체 설치수심의 대수심화로 인해 직립 케이슨제의 건설이 주를 이루고 있으며, 외곽시설의 경우 평면배치에 의하여 곡면부 구간이 형성된다. 이와 같은 구간에서는 파랑 증폭이 발생할 수 있다. 특히 우각부 구간에서의 파랑증폭에 의한 월파량 산정은 기존 직각으로 입사하는 조건에 대한 월파량 산정 방법과는 다른 해석이 필요하다. 본 연구에서는 직립제 우각부에 대한 월파량 분포를 검토 및 분석하고자 한다. 그림 1과 같이 우각부의 각도를 $10^{\circ}{\sim}30^{\circ}$로 제작했으며, 각각 발생시킨 파랑의 주기는 1.18초, 1.38초, 1.57초, 1.77초, 1.98초, 파고는 7.5cm, 10cm, 12.5cm이다. 또한 그림 2와 같이 각 월파가 일어나는 직립제 모형의 여유고를 7.5cm, 10cm, 12.5cm, 15cm를 적용하였다. 우각부 구간에서 월파의 공간적인 분포를 수리모형 실험을 통하여 검토하였다. 월파의 공간적인 분포를 검토하기 위하여 월파량 영향계수( )를 도입하였다. 우각부가 없는 직각으로 입사하는 조건의 월파량 실험을 통해 그 월파량의 값이 영향계수의 $r_x=1.0$이며, 우각부 중심을 기준으로 구조물을 따라서 공간적인 월파량 영향계수를 산정하였다.

• Computers and Concrete
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• v.31 no.2
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• pp.163-171
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• 2023

Face gear transmission is widely used in aerospace shunt-confluence transmission system. Tooth wear is one of the main factors affecting its bearing transmission performance. Furthermore, the installation errors of face gear are inevitable. In order to study the wear mechanism of face gear tooth surface with installation errors, based on tooth contact analysis numerical method and Archard wear theory, the UMESHMOTION subroutine in ABAQUS is developed.Combining with Arbitrary Lagrangian-Eulerian adaptive mesh technology, the finite element mesh wear model of abraded face gear pair is established.The preprocessing conditions are set to generate the inp files.Then,the inp files for each corner are imported and batch processed in ABAQUS.The loading tooth contact problem at each rotation angle is solved and the load distribution coefficient among gear tooth, tooth root bending stress, tooth surface contact stress and loaded transmission error are obtained. Results show that the tooth root wear is the most serious and the wear at the pitch cone is close to 0.The wear law of tooth surface along tooth width direction is convex parabola and the wear law along tooth height direction is concave parabola.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.11 no.3
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• pp.75-81
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• 2011

Protein molecules are combined with another ones which have similar shapes at pocket positions. The pocket positions can be good references to describe the shapes of protein molecules. Harris corner detector is commonly used to detect feature points of 2 or 3D objects. Feature points can be found on the pocket areas and the points which have high derivatives. Generally speaking, the densities of feature points are relatively high at pocket areas because the shapes of pockets are concave. The pocket areas can be decided by the subdivision of voxel cubes which include feature points. The Euclidean distances between feature points and the central coordinate of the decided pocket area are calculated and sorted. The graph of sorted distances describes the shape of a protein molecule and the distribution of feature points. Therefore, it can be used to classify protein molecules by their shapes. Even though the shapes of protein molecules have been distorted with noises, they can be recognized with the accuracy more than 95 %. The accurate shape recognition provides the information to predict the binding properties of protein molecules.