• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.3
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• pp.253-266
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• 2019

In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.46.1-46.1
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• 2019

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.

• Journal of Korean Tunnelling and Underground Space Association
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• v.20 no.6
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• pp.1147-1159
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• 2018

This study focuses on the verification of a rapid protection automation system using an inflatable structure. The inflatable structure is an automatic rapid protection system against human and material damage when the subsea tunnel is flooded. Especially, it is essential for construction and operation of subsea tunnels. In this study, we have experimentally verified the rapid protection automation system using the inflatable structure designed for this problem. In order to verify this, a model tunnel with a 40: 1 reduction ratio was constructed, and air pressure of 0.1 bar and 0.15 bar was injected to divide the tunnel according to the expansion rate at 10 sec and 20 sec. According to the results of the study, the protection efficiency was better at 0.15 bar than 0.1 bar when the expansion structure was expanded, and the protection efficiency and influent control efficiency were different according to the pneumatic injection time of the inflating structure. As a result of this study, it was found that the higher the internal air pressure of the inflated structure and the faster the inflation of rate, the more effectively the inflated structure was inflated. As a result of this study, it is necessary to further study the wedge type structure which is useful for the storage method of expansion structure, shape and expansion derivative, inhibition of expansion structure during protection and control of inflow water.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.113-118
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• 2009

A designer regards the vibration system as a linear system. However, in real world, nonlinearity of a vibration system should exist caused by various factors like manufacturing conditions or uncertain material properties. So, properties of a spring and a damper which are consisting the vibration system have statistical distribution. Therefore, a designer needs to analyze the statistical nonlinearity in a vibration system. In this paper, $1^{st}$ Taylor series expansion method and univariate dimension reduction method apply to a performance measure of nonlinear vibration system, and compare each result. And then, merits and demerits of each method are discussed. For apply more actual problem, a performance measure population is estimated based on design variable samples like properties of spring or damper.

• Coupled systems mechanics
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• v.1 no.2
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1210-1216
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• 2003

Topology optimization is applied to determine the layout of a structural component with a specified frequency by minimizing the difference between the specified structural frequency and a given frequency. The homogenization design method is employed and the topology design problem is solved by the optimality criteria method. The value of a weighting factor in the optimality criteria plays an important role in this topology design problem. The modified optimality criteria method approximated by using the binomial expansion is suggested to determine the suitable value of the weighting factor, which makes convergence stable. If a given frequency is set as an excited frequency, it is possible to avoid resonance by moving away the specified structural frequency from the given frequency. The results of several test problems are compared with previous works and show the validity of the proposed algorithm.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.54 no.3
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• pp.148-154
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• 2005

Various methods for analyze optical components which are necessary before the fabrication of optical circuit component and as its applications, designing method of Wavelength Division Multiplexer(WDM) filter using arrayed-waveguide grating(AWG) is paper. In the case of analyzing uniform optical waveguide, effective index method(EIM), harmonic expansion method are used, and in the case of non-uniform optical waveguide, beam propagation method(BPM) are used. In this paper, to use arrayed-waveguide grating as WDM filter of centered wavelength of $1.55{\mu}m$ and wavelength spacing of 0.8nm, all of the parameter of AWG is calculated by the HEM and the BPM using EIM. As a result of calculation, free spectral range is 12.8nm, focal length $9336.55{\mu}m$, path difference $129.36{\mu}m$ and the number of slab waveguide 91 when the distance of core center to center on row land circle is $20{\mu}m$.

• Journal of computational fluids engineering
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• v.7 no.3
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• pp.53-59
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• 2002

A two-dimensional laminar flow through a channel with a pair of symmetric vertical fins is investigated. At far up- and down-stream from the fins, the plane Poiseuille flow exists in the channel. The Stokes flow for this channel is first investigated analytically and then the other laminar flows by numerical method. For analytic method, the method of eigen function expansion and collocation method are employed. In numerical solution for laminar flows, finite difference method(FDM) is used to obtain vorticity and stream function. From the results, the streamline patterns are shown and the additional pressure drop due to the attached fins and the force exerted on the fin are calculated. It is clear that the force depends on the length of fins and Reynolds number. When the Reynolds number exceeds a critical value, the flow becomes asymmetric. This critical Reynolds number Re/sub c/ depends on the length of the fins.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.20-28
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• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline(NURBS) of an approximation method. Many of NURBS intrinsic properties are introduced and much more easily understood. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper. The object of this study is to develop the surface grid generation and the grid cluster techniques capable of resolving complex flows with shock waves, expansion waves, shear layers. The knot insert method of Non-Uniform Rational B-Spline seems well worked. In addition, NURBS has been widely utilized to generate grids in the computational fluid dynamics community. Computational examples associated with practical configurations have shown the utilization of the algorithm.

• Journal of Korea Multimedia Society
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• v.8 no.1
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• pp.27-33
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• 2005

In this paper, an effective skeleton method is proposed in order to obtain an enhanced digital image of skeleton line. The binary image using the threshold values is applied in the preprocessing stage and then The proposed method is applied to obtain the improved image of skeleton line. We used the existing skeleton methods and SPTA(Shin's Parallel Thinning Algorithm) method for the comparison. The demerits of the existing skeleton methods have a result of noise branch, expansion and contraction. and then we are proposed a SPTA method.