• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.59-64
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• 2002

In this paper, the preconditioned multistage time stepping methods which are popular multigrid smoothers is implemented for the compressible Navier-Stokes calculation with full-coarsening multigrid method. The convergence characteristic of the point-Jacobi and Alternating direction line Jacobi(DDADI) preconditioners are studied. The performance of 2nd order upwind numerical fluxes such as 2nd order upwind TVD scheme and MUSCL-type linear reconstruction scheme are compared in the inviscid and viscous turbulent flow caculations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.411-418
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• 2004

Using a level set method we develop a shape optimization method applied to energy flow problems in steady state. The boundaries are implicitly represented by the level set function obtainable from the 'Hamilton-Jacobi type' equation with the 'Up-wind scheme.' The developed method defines a Lagrangian function for the constrained optimization. It minimizes a generalized compliance, satisfying the constraint of allowable volume through the variations of implicit boundary. During the optimization, the boundary velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian function. Compared with the established topology optimization method, the developed one has no numerical instability such as checkerboard problems and easy representation of topological shape variations.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.267-281
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• 2022

Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Chebyshev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA^® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical examples are given in support of our theoretical analysis.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.203-224
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• 2014

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.9
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• pp.1998-2016
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• 2012

Reliable spectrum sensing algorithm is a fundamental component in cognitive radio. In this paper, a non-cooperative spectrum sensing algorithm which needs only one cognitive radio node named CORDIC (Coordinate Rotation Digital Computer) Jacobi based method is proposed. The algorithm computes the eigenvalues of the sampled covariance of received signal mainly by shift and additional operations, which is suitable for hardware implementation. Based the latest random matrix theory (RMT) about the distribution of the limiting maximum and minimum eigenvalue ratio, the relationship between the probability of false alarm and the decision threshold is derived. Simulations and discussions show the method is effective. Real captured digital television (DTV) signals and Universal Software Radio Peripheral (USRP) are also employed to evaluate the performance of the algorithm, which prove the proposed algorithm can be applied in practical spectrum sensing applications.

• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.653-654
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• 2008

This paper presents a topological shape optimization for electromagnetic system using a level set method. The optimization is progressed by updating the implicit level set function from the Hamilton-Jacobi equation. The up-wind scheme is used for numerical implementation of the Hamilton-Jacobi equation. In order to validate the proposed optimization, the core part of a C-core actuator is optimized by three cases using different materials; (single steel), (two steels), and (steel and magnet).

• Proceedings of the KIEE Conference
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• 2008.10c
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• pp.23-25
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• 2008

This paper presents a topological shape optimization for electromagnetic system using a Level Set method. The optimization is progressed by updating the implicit Level Set function from the Hamilton-Jacobi equation. The up-wind scheme is used for numerical implementation of the Hamilton-Jacobi equation. In order to validate the proposed optimization, the core part of a C-core actuator is optimized by three cases using different materials; (single steel), (two steels), and (steel and magnet).

• Honam Mathematical Journal
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• v.42 no.1
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• pp.139-150
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• 2020

Let p be a prime number with p > 3, p ≡ 3 (mod 4) and let n be a positive integer. In this paper, we prove that the Diophantine equation (5pn² - 1)^x + (p(p - 5)n² + 1)^y = (pn)^z has only the positive integer solution (x, y, z) = (1, 1, 2) where pn ≡ ±1 (mod 5). As an another result, we show that the Diophantine equation (35n² - 1)^x + (14n² + 1)^y = (7n)^z has only the positive integer solution (x, y, z) = (1, 1, 2) where n ≡ ±3 (mod 5) or 5 | n. On the proofs, we use the properties of Jacobi symbol and Baker's method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.85-97
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• 2000

A quadrature rule for the solution of Cauchy singular integral equation is constructed and investigated. This method to calculate numerically singular integrals uses classical Jacobi quadratures adopting Hunter's method. The proposed method is convergent under a reasonable assumption on the smoothness of the solution.

• Journal of Advanced Navigation Technology
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• v.15 no.4
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• pp.543-548
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• 2011

In this paper, H-polarized electromagnetic scattering problems by a resistive strip grating over a grounded dielectric plane according to the strip width and grating period, the relative permittivity and thickness of a dielectric layer, and incident angles of a TE (transverse electric) plane wave are analyzed by applying the FGMM (Fourier-Galerkin Moment Method). The tapered resistivity of resistive strips in this paper varies from finite resistivity at one edge to zero resistivity at the other edge, then the induced surface current density on the resistive strip is expanded in a series of Jacobi polynomials of the order ${\alpha}=1$, ${\beta}=0$ as a kind of orthogonal polynomials. The numerical results of the normalized reflected power show in good agreement with those of existing papers.