• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.

• 한국전산유체공학회:학술대회논문집
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• 1999.11a
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• pp.59-64
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• 1999

The Equations of Chemical kinetics ate very stiff, which forces the use of an implicit scheme. The problem of implicit scheme, however, is that the jacobian must be solved at each time step. In this paper, we examined the approximate chemical jacobian methods such as Gauss-Seidel, Jacobi partial jacobian and diagonalized jacobian that can be stable without full jacobian, We show that Gauss-Seidel jacobian method is stable and accurate as well as full jacobian and that this is more efficient in supersonic combustion problem about $20\%$ than the full jacobian method with same accuracy,

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.53 no.4
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• pp.210-215
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• 2004

This paper proposes an implicit method for computing the minimum cost feedback vertex set for a graph. For an arbitrary graph, a Boolean function is derived, whose satisfying assignments directly correspond to feedback vertex sets of the graph. Importantly, cycles in the graph are never explicitly enumerated, but rather, are captured implicitly in this Boolean function. This function is then used to determine the minimum cost feedback vertex set. Even though computing the minimum cost satisfying assignment for a Boolean function remains an NP-hard problem, it is possible to exploit the advances made in the area of Boolean function representation in logic synthesis to tackle this problem efficiently in practice for even reasonably large sized graphs. The algorithm has obvious application in flip-flop selection for partial scan. The algorithm proposed in this paper is the first to obtain the MFVS solutions for many benchmark circuits.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.391-397
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• 2004

The performance characteristics of partial admission supersonic turbines are analyzed by using the commercial CFD program FLUENT6.0. The governing equations were discretized with Euler implicit method in time and 2nd-order upwind scheme of FVM in space. The k-$\varepsilon$ turbulence model was utilized to describe the turbulent flow field. In order to investigate the nozzle--rotor interactions and the effect of partial admission, the flows in supersonic turbine rotor cascades with a nozzle are computed. Extensive computations of partial admission supersonic turbines provide the shock structures and flow patterns in the nozzle and rotor. It is clearly shown that the nozzle flow is highly affected by the shocks or expansion waves propagated from the rotor leading edge. And the rotor flow is also affected by the shocks or wakes originated from the nozzle.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.4
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• pp.30-37
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• 1998

In this paper, we propose a test generation method for large scale sequential circuits based on circuit partitioning to increase the size of circuits that the implicit product machine traversal (IPMT) method can handle. Our method paratitions a circuit under test into subset circuits with only single output, and performs a partial scan design using the state transtition cost that represents a degree of the connectivity of the subset circuit. The IPMT method is applied to the partitioned partial scan circuits in test generation. Experimental results for ISCAS89 benchmark circuits with more thatn 50 flip-flops show that our method has generated test patterns with almost 100% fault coverage at high speed by use of 34%-73% scanned flip-flops.

• Structural Engineering and Mechanics
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• v.56 no.4
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• pp.549-567
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• 2015

A first-order moment method (FORM) reliability analysis is commonly used for structural stability analysis. It requires the values and partial derivatives of the performance to function with respect to the random variables for the design. These calculations can be cumbersome when the performance functions are implicit. A Gaussian process (GP)-based response surface is adopted in this study to approximate the limit state function. By using a trained GP model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis with a FORM, thereby reducing the number of stability analysis calculations. This dynamic renewed knowledge source can provide great assistance in improving the predictive capacity of GP during the iterative process, particularly from the view of machine learning. An iterative algorithm is therefore proposed to improve the precision of GP approximation around the design point by constantly adding new design points to the initial training set. Examples are provided to illustrate the GP-based response surface for both structural and non-structural reliability analyses. The results show that the proposed approach is applicable to structural reliability analyses that involve implicit performance functions and structural response evaluations that entail time-consuming finite element analyses.

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1171-1184
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• 2022

We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.17 no.2
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• pp.71-76
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• 1981

In order to make a numerical modeling for the one dimensional unsteady flow which expressed by Saint Venant partial differential equations, Preissmann's implicit scheme was used, and it's stability and accuracy was mentioned. By introducing recurrence relations make it possible to use double sweep algorithm. Effective parameters to the result were the values of the $\Delta$t/$\Delta$x, $\theta$ and the chezy coefficient. In oder to get numerical solutions with enough accuracy, $\Delta$t/$\Delta$x should not be far from the value of 1, and the criteria of the $\theta$ was 0.6<$\theta$<1.0 for the stability without condition. This model should be calibrated by real field data, and expected to be developed for the simulation of the river system and to the long wave analysis for one dimensional coastal zone problem.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.595-598
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• 2004

In recognizing knowledge as a new resource in gaining organizational competitiveness, knowledge management suggests a method in managing and applying knowledge for improving organizational performance. Much knowledge management research has focused on identifying, storing, and disseminating process related knowledge in an organized manner. Applying knowledge to decision making has a significant impact on organizational performance than solely processing transactions for knowledge management. In this research, we suggest a method of knowledge-based decision-making using system dynamics, with an emphasis to strategic problems. The proposed method transforms individual mental models into explicit knowledge by translating partial and implicit knowledge into an integrated knowledge model. The scenario-based test of the organized knowledge model enables decision-makers to understand the structure of the target problem and identify its basic cause, which facilitates effective decision-making. This method facilitates the linkage between knowledge management initiatives and achieving strategic goals and objectives of an organization.