• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.591-612
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• 2021

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Journal of ILASS-Korea
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• v.16 no.4
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• pp.186-194
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• 2011

This study performed the numerical analysis of the internal nozzle flows including cavitation phenomena by using the automated body-fitted grid generator and the multi-fluid model. The effect of grid refinement and the validation of multifluid model were investigated using four computational meshes under two test conditions. The mesh #3 was chosen as the optimum which can reduce the computational time and have good prediction ability to identify the cavitation region simultaneously. In addition, the computed results using multi-fluid model were compared with the reference experimental observations and numerical simulation results using homogeneous equilibrium model. From the distribution of volume fraction and velocity field, the multi-fluid model predicted the internal nozzle flows well when the liquid quality parameters were selected as $1.0{\times}10^{12}$ for initial number density and 25 ${\mu}m$ for bubble diameter.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.113-132
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• 2020

In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2005.11a
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• pp.123-126
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• 2005

Wireless Sensor Networks will revolutionize applications such as environmental monitoring, home automation, and logistics. We developed forest fire surveillance system. In this paper, Considering the fact that in Korea, during November to May, forest fires occur very frequently causing catastrophic damages on the valuable environment, Although exists other forest fire surveillance system such as surveillance camera tower, infrared ray sensor system and satellite system. Preexistence surveillance system can't real-time surveillance, monitoring, database and automatic alarm. But, forest fire surveillance system(FFSS) support above. In this paper, we describes a system development approach for a wireless sensor network based FFSS that is to be used to measure temperature and humidity as well as being fitted with a smoke detector. Such a device can be used as an early warning fire detection system and real-time surveillance in the area of a bush fire or endangered public infrastructure. Once the system has being development, a mesh network topology will be implemented with the chosen sensor node with the aim of developing a sophisticated mesh network.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.20 no.5
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• pp.116-124
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• 2006

No matter how the equally spaced grounding grid is designed there are many problem. The best-fitted design for unequally spaced grounding grid is a part that must be considered. This paper Suggest a new way of calculation for grounding grid space of ground conductor by an algebraic function control(The first-order function, Root function, Polynomial function etc.) and on the optimal spaced grounding conductor that make the under 2[%] between maximum potential and minimum potential.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Journal of the Korea Computer Graphics Society
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• v.15 no.2
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• pp.1-8
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• 2009

This paper introduces a virtual dress up system, according to user's input model and garment image. At first step, we deform the garment image by using skeleton structures and ARAP method. Next step, sampling the boundary points and find their matching vertices which are used for optimizing the boundary fitting. In 2D rendering of the dress up, they have some unrealistic results, so we reconstruct the garment mesh to the 3D mesh. Rendering from the reconstructed 3D mesh, we can get the final dress up result. We present that our system produce a visually plausible and well-fitted virtual dress up results.

• 한국정보디스플레이학회:학술대회논문집
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• 2002.08a
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• pp.388-391
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• 2002

We report our CAB system on thermal analysis for mould designer who is not expert of numerical simulation. Our mathematical model of thermal analysis is axi-symmetrically. It has an automatic mesh-generator that is based on Delaunay method, by using CAD data. And boundary conditions are also fitted automatically.