• 대한기계학회논문집B
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• 제23권2호
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• 한국수자원학회논문집
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• 제38권2호
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• pp.155-166
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• 2005

상류이송기법은 불연속 흐름을 해석할 수 있기 때문에 댐붕괴류, 천이류 등의 해석에 많이 이용되고 있다. 그러나 상류이송기법은 생성항 처리과정에서 발생하는 오차로 인해 불균일한 단면을 가진 자연하천에는 거의 적용되지 못하고 단순화된 하도에만 주로 적용되어 왔다. 본 논문에서는 생성항의 차분화를 위해서 정규화된 Jacobian을 사용하는 상류이송형 생성항 처리기법을 개발하였다. 적용 결과 본 연구에서 제안된 생성항 처리기법이 정확하면서 효율적인 것으로 나타났다. 본 연구에서 제안한 방법은 단순한 형태를 지니고 있으며 다른 상류이송기법에도 다양하게 적용될 수 있을 것으로 판단된다.

• Nuclear Engineering and Technology
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• 제54권7호
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• pp.2625-2634
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• 2022

Discretization errors are extremely challenging conundrums of discrete ordinates calculations for radiation transport problems with void regions. In previous work, we have presented a multi-collision source method (MCS) to overcome discretization errors, but the efficiency needs to be improved. This paper proposes a goal-oriented algorithm for the MCS method to adaptively determine the partitioning of the geometry and dynamically change the angular quadrature in remaining iterations. The importance factor based on the adjoint transport calculation obtains the response function to get a problem-dependent, goal-oriented spatial decomposition. The difference in the scalar fluxes from one high-order quadrature set to a lower one provides the error estimation as a driving force behind the dynamic quadrature. The goal-oriented algorithm allows optimizing by using ray-tracing technology or high-order quadrature sets in the first few iterations and arranging the integration order of the remaining iterations from high to low. The algorithm has been implemented in the 3D transport code ARES and was tested on the Kobayashi benchmarks. The numerical results show a reduction in computation time on these problems for the same desired level of accuracy as compared to the standard ARES code, and it has clear advantages over the traditional MCS method in solving radiation transport problems with reflective boundary conditions.

• 대한수학회지
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• 제58권3호
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• 대한수학회논문집
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• 제20권3호
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• pp.563-578
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• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.146-151
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• 1994

An empirical comparison of static fuzzy relational models which are identified with different fuzzy implication operators and inferred by different composition operators is made in case that all the information is represented by the fuzzy discretization. Four performance measures (integral of mean squared error, maximal error, fuzzy equality index and mean lack of sharpness) are adopted to evaluate and compare the quality of the fuzzy relational models both at the numerical level and logical level. As the results, the fuzzy implication operators useful in various fuzzy modeling problems are discussed and it is empirically shown that the selection of data pairs is another important factor for identifying the fuzzy model with high quality.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• 대한수학회보
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• 제57권1호
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• pp.219-244
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• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

• 전기학회논문지
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• 제66권1호
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• pp.159-164
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• 2017

In this paper, we propose a method of designing the sampled-data tracking controller for nonlinear systems expressed by the Takagi-Sugeno (T-S) fuzzy model. A sufficient condition that asymptotically stabilizes the state error between the linear reference model and the T-S fuzzy model is derived in terms of linear matrix inequalities. To this end, error dynamics are constructed, and the exact discretization method and the Lyapunov stability theory are employed in this paper. Finally, we validate the proposed method through the simulation example.