• Publications of The Korean Astronomical Society
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• v.13 no.1 s.14
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• pp.167-180
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• 1998

We have carried out high precision orbit calculation, by using various numerical techniques with accuracy of higher than fourth order, in order for exact prediction on position and velocity of celestial bodies and artificial satellites. General second order ordinary differential equation has been solved numerically to test the performance for each of numerical methods. We have compared computed values with exact solution obtained by using universal variables for two body problem and discussed overall results of numerical methods used in our calculation. As a result, it is found that high order difference table method called as Gauss-Jackson method is best one with easiness and efficiency in the increase of accuracy by number of initial values.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.463-468
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• 1987

In this paper, a high impedance fault detection on 22.9kV multigrounded distribution system that has been very difficult by any existing conventional protective relaying systems is studied. Because the fault current is very low, it cannot be distinguished from neutral current caused by load unvalanced on multigrounded distribution system. We developed the new and best algorithms of high impedance ground fault detection. This algorithms are 'the even order power method, even order ratio method', 'and even order ratio varience method'. Using this algorithms, a detection device for high impedance faults is constructed and tested in the laboratory. And continually, it is installed and has been tested in KEPCO substations.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.131-134
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• 2005

Conventional high order interpolation schemes are limitative in several aspects mainly because they need data of neighboring cells at the reconstruction step. However, discontinuous Galerkin method and spectral volume method, two high order flux schemes which will be analyzed and compared in this paper, have an important benefit that they are not necessary to determine the flow gradients from data of neighboring cells or elements. These two schemes construct polynomial of variables within a cell so that even near wall or discontinuity, the high order does not deteriorate.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.369-372
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• 2002

Under the assumption of potential flow, free-surface flows around a 2-dimensional hydrofoil are calculated by high-order spoctral/boundary-integral method. This method is one of the most efficient numerical methods by which the nonlinear interactions between hydrofoil and free-surface can be simulated in time-domain. Comparisons of the calculated free-surface profiles with other experimental results show relatively good agreements. As another example, free-surface flow generated by the heaving and translating hydrofoil is calculated and discussed.

• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.113-120
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• 1999

In this paper, mathematical formulation of the high-order spectral/boundary-element method is shown. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated in time-domain. Three-dimensional waves generated by a uniformly translating suriace pressure are calculated and discussed. The obtained results are compared with others results, The comparisons show good agreements.

• Journal of Environmental Science International
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• v.20 no.11
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• pp.1465-1481
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• 2011

The accuracy of ozone sensitivity coefficients estimated with HDDM (High-order Decoupled Direct Method) can vary depending on the $NO_x$ (Nitrogen Oxides) and VOC (Volatile Organic Compound) conditions. In order to evaluate the applicability of HDDM over the Seoul Metropolitan Area (SMA) during a high ozone episode in 2007 June, we compare BFM (Brute Force Method) and HDDM in terms of the $1^{st}$-order ozone sensitivity coefficient to explain ozone change in response to changes in NOx and VOC emissions, and the $2^{nd}$-order ozone sensitivity coefficient to represent nonlinear response of ozone to the emission changes. BFM and HDDM estimate comparable ozone sensitivity coefficients, exhibiting similar spatial and temporal variations over the SMAduring the episode. NME (Normalized Mean Error) between BFM and HDDM for the episode average $1^{st}$- and $2^{nd}$-order ozone sensitivity coefficients to NOx and VOC emissions are less than 3% and 9%, respectively. For the daily comparison, NME for the $1^{st}$- and $2^{nd}$-order ozone sensitivity coefficients are less than 4% ($R^2$ > 0.96) and 15% ($R^2$ > 0.90), respectively. Under the emission conditions used in this study, two methods show negative episode average $1^{st}$-order ozone sensitivity coefficient to $NO_x$ emissions over the core SMA. The $2^{nd}$-order ozone sensitivity coefficient to $NO_x$ emissions leads ozone to respond muchnonlinear to the reduction in $NO_x$ emissions over Seoul. Nonlinear ozone response to reduction in VOC emissions is mitigated due to the $2^{nd}$-order ozone sensitivity coefficient which is much smaller than the $1^{st}$-order ozone sensitivity coefficient to the emissions in the magnitude.

• Honam Mathematical Journal
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• v.41 no.2
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.511-527
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• 2014

This paper provides a new application similar to the Local Defect Correction (LDC) technique to solve Poisson problem -u"(x) = f(x) with Dirichlet boundary conditions. The exact solution is supposed to have high activity in some region of the domain. LDC is combined with a fourth order compact scheme which is recently developed in Abbas (Num. Meth. Partial differential equations, 2013). Numerical tests illustrate the interest of this application.

• The Journal of the Korea Contents Association
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• v.11 no.8
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• pp.475-487
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• 2011

In this paper, we present a systematic method to derive spectrum of high-order pulse and a novel design of e-Learning system that deals with deriving the spectrum using concept-based branching method. Spectrum of high-order pulse can be derived using conventional methods including 'Consecutive Differentiations' or 'Convolutions', however, their complexity of calculation should be too high to be used as the order of the pulse increase. We develop a recursive algorithm according to the order of pulse, and then derive the formula of spectrum connected to the order with a newly designed look-up table. Moving along, we design an e-Learning content for studying the procedure of deriving high-order pulse spectrum described above. In this authoring, we use the concept-based object branching method including conventional page or title-type branching in sequential playing. We design all four Content-pages divided into 'Modeling', 'Impulse Response and Transfer Function', 'Parameters' and 'Look-up Table' by these conceptual objects. And modules and sub-modules are constructed hierarchically as conceptual elements from the Content-pages. Students can easily approach to the core concepts of the analysis because of the effects of our new teaching method. We offer step-by-step processes of the e-Learning content through unit-based branching scheme for difficult modules and sub-modules in our system. In addition we can offer repetitive learning processes for necessary block of given learning objects. Moreover, this method of constructing content will be considered as an advanced effectiveness of content itself.

• Journal of computational fluids engineering
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• v.13 no.3
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• pp.69-78
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• 2008

The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.