• ETRI Journal
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• v.31 no.1
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• pp.42-50
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• 2009

A new method for simulating voltage and current distributions in transmission lines is described. It gives the time domain solution of the terminal voltage and current as well as their line distributions. This is achieved by treating voltage and current distributions as distributed state variables (DSVs) and turning the transmission line equation into an ordinary differential equation. Thus the transmission line is treated like other lumped dynamic components, such as capacitors. Using backward differentiation formulae for time discretization, the DSV transmission line component is converted to a simple time domain companion model, from which its local truncation error can be derived. As the voltage and current distributions get more complicated with time, a new piecewise exponential with controllable accuracy is invented. A segmentation algorithm is also devised so that the line is dynamically bisected to guarantee that the total piecewise exponential error is a small fraction of the local truncation error. Using this approach, the user can see the line voltage and current at any point and time freely without explicitly segmenting the line before starting the simulation.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.807-810
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• 2002

The suitability of high-order accurate, central and upwind-biased compact difference schemes is evaluated for the large-eddy simulations of flows in complex geometry. Two flow geometries are considered: channel and circular cylinder. The effects of numerical dissipation and aliasing error on the evaluation of subgrid scale stress are investigated by extending the analysis by Ghosal (1) to centered and upwind compact schemes. It is shown that the failure of upwind schemes mainly comes from the aliasing error.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.529-550
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• 2011

In this work, a numerical solution of the incompressible Navier-Stokes equations is proposed. The method suggested is based on an algorithm of discretization by mixed finite elements with a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

• Proceedings of the SAREK Conference
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• 2006.06a
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• pp.116-121
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• 2006

Numerical simulations for dendritic growth of crystals are conducted in this study by the level set method. The effect of order of difference is tested for reinitialization error in simple problems and authors founded in case of 1st order of difference that very fine grids have to be used to minimize the error and higher order of difference is desirable to minimize the reinitialization error The 2nd and 4th order Runge-Kutta scheme in time and 3rd and 5th order of WENO schemes with Godunov scheme are applied for space discretization. Numerical results are compared with the analytical theory, phase-field method and other researcher's level set method.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2004.10a
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• pp.75-78
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• 2004

A mesh generation algorithm adapted to the mesh density map using the Delaunay mesh generation technique is developed. In the finite element analyses of the forging processes, the numerical error increases as the process goes on because of discrete property of the finite elements or severe distortion of elements. Especially, in the region where stresses and strains are concentrated, the numerical discretization error will be highly increased. However, it is too time consuming to use a uniformly fine mesh in the whole domain to reduce the expected numerical error. Therefore, it is necessary to construct locally refined mesh at the region where the error is concentrated such as at the die corner. In this study, the point insertion algorithm is used and the mesh size is controlled by moving nodes to optimized positions according to a mesh density map constructed with a posteriori error estimation. An optimization technique is adopted to obtain a good position of nodes. And optimized smoothing techniques are also adopted to have smooth distribution of the mesh and improve the mesh element quality.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.323-340
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• 1997

In this study we prove the mesh-independence principle via Steffensen's method. This principle asserts that when Steffensen's method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation then the behavior of th discretized process is asymptoti-cally the same as that for the original iteration. Local and semilo-cal convergencve results as well as an error analysis for Steffensen's method are also provided.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.411-421
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• 2016

Large frequency limiting distributions of two errors in realized covariance are investigated under noisy and non-synchronous high frequency sampling situations. The first distribution characterizes increased variance of the realized covariance due to noise for large frequency and the second distribution characterizes decreased variance of the realized covariance due to discretization for large frequency. The distribution of the combined error enables us to determine the sampling frequency which depends on a nuisance parameter. A consistent estimator of the nuisance parameter is proposed.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.293-300
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• 1998

The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernels using the Toeplitz matrices. The solution has a computing time requir-ment of O(N2) where 2N+1 is the number of discretization points used. Also the error estimate is computed. Some numerical Exam-ples are computed using the Mathcad package.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.139-148
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• 2005

In this paper we extend the mixed finite element method and its $L_2$-error estimate for postprocessed solutions by using Crank-Nicolson time-discretization method. Global $O(h^2+({\Delta}t)^2)$-superconvergence for the lowest order Raviart-Thomas element ($Q_0-Q_{1,0}{\times}Q_{0,1}$) are obtained. Numerical examples are presented to confirm superconvergence phenomena.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.65-73
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• 2003

In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of $0(N^2)$, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.