• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.249-256
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• 2002

A new optimization procedure with approximate reanalysis module, using the staged hybrid methods with substructuring, is proposed in is study. In this procedure, displacements are calculated with two step mixed procedures. First step is to introduce the conservative approximation, which is a hybrid form of the linear and reciprocal approximation, as local approximation. In the next step, it is combined with the global approximation by reduced basis approach. The quality of reanalyzed quantities can be greatly improved through these staged hybrid approximations, specially for large changes in the design. Overall procedures are based on substructuring scheme. Several numerical examples illustrate the validity and effectiveness of the proposed methods.

• International Journal of Reliability and Applications
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• 제13권2호
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• pp.71-80
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• 2012

This paper introduces a new approach for evaluating reliability of a complex system in terms of distributional parameters where analytical determination of reliability is intractable. The concept of discrete approximation, reported in the literature so far, fails to meet the latter requirement in terms of distributional parameters. The current work aims at offering a bound based approach where reliability planners not only get a clear idea about the extent of error but also can manipulate in terms of distributional parameters. This reliability approximation has been under taken under the Weibull frame work which is the most widely used model for reliability analysis. Numerical study has been carried out to examine the strength of our proposed reliability approximation via closeness between the two reliability bounds. This approach will be very useful during the early stages of product design as the distributional parameters can be adjusted.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.277-302
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• 2017

In this paper, we have proposed a numerical method for Singularly Perturbed Boundary Value Problems (SPBVPs) of reaction-diffusion type of third order Ordinary Differential Equations (ODEs). The SPBVP is reduced into a weakly coupled system of one first order and one second order ODEs, one without the parameter and the other with the parameter ${\varepsilon}$ multiplying the highest derivative subject to suitable initial and boundary conditions, respectively. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference scheme. The weakly coupled system is decoupled by replacing one of the unknowns by its zero-order asymptotic expansion. Finally the present numerical method is applied to the decoupled system. In order to get a numerical solution for the derivative of the solution, the domain is divided into three regions namely two inner regions and one outer region. The Shooting method is applied to two inner regions whereas for the outer region, standard finite difference (FD) scheme is applied. Necessary error estimates are derived for the method. Computational efficiency and accuracy are verified through numerical examples. The method is easy to implement and suitable for parallel computing. The main advantage of this method is that due to decoupling the system, the computation time is very much reduced.

• 한국해양공학회지
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• 제36권1호
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• pp.11-20
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• 2022

Generally, tsunamis are generated by the rapid crustal movements of the ocean floor. Other factors of tsunami generation include landslides on coastal and ocean floor slopes, glacier collapses, and meteorite collisions. In this study, two numerical analyses were conducted to examine the formation, propagation, and deformation properties of landslide tsunamis. First, LS-DYNA was adopted to simulate the formation and propagation processes of tsunamis generated by dropping rigid bodies. The generated tsunamis had smaller wave heights and wider waveforms during their propagation, and their waveforms and flow velocities resembled those of theoretical solitary waves after a certain distance. Second, after the formation of the landslide tsunami, a tsunami based on the solitary wave approximation theory was generated in a numerical wave tank (NWT) with a computational domain that considered the stability/steady phase. The comparison of two numerical analysis results over a certain distance indicated that the waveform and flow velocity were approximately equal, and the maximum wave pressures acting on the upright wall also exhibited similar distributions. Therefore, an effective numerical model such as LS-DYNA was necessary to analyze the formation and initial deformations of the landslide tsunami, while an NWT with the wave generation method based on the solitary wave approximation theory was sufficient above a certain distance.

• 한국전산구조공학회논문집
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• 제32권4호
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• pp.215-222
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• 2019

복합재료의 열전달 문제는 일반적으로 만족시켜야 하는 보존방정식과 경계조건 외에 추가적으로 만족시켜야 하는 계면경계조건의 존재로 인해 새로운 수치기법의 개발에 어려움이 있다. 계면경계조건이 미분방정식의 해에 불연속성을 유발시키기 때문에 이것을 적절하게 처리할 수 있는 특수한 함수의 도입이 필요하며, 이산화를 통한 계 방정식의 구성도 쉽지 않다. 본 논문에서는 계면경계의 불연속성을 모사하는 특수함수를 포함하면서 계면경계조건을 항상 만족시킬 수 있도록 계면경계식 자체를 매입한 미분근사식을 제안하고, 불연속 재료상수를 갖는 열전달 문제를 무요소 강형식으로 이산화한 이동최소제곱 차분법을 제시한다. 개발된 수치기법은 기존의 수치기법들과 달리 수치적분과 계면경계조건을 만족시키기 위한 별도의 구속 방정식이 필요없으며, 빠르고 정확하게 이종재료 열전달 문제의 수치해를 구해준다. 개발된 수치기법으로 다양한 복합재료 열전달 문제를 해석하고 오차의 수렴률을 조사한 결과, 높은 정확성과 계산 효율성을 갖는다는 것을 확인할 수 있었으며, 특히, 계면경계가 기하학적 특이성을 나타내는 문제에서도 우수한 성능을 발휘하는 것을 보였다.

• 한국해양공학회지
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• 제28권4호
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• pp.324-330
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• 2014

In this study, the numerical model developed by Hong et al.(2008) was improved to be applied to rapidly varying flows such as the inundation of dry land or flow transitions due to large gradients of the bathymetry. A numerical approximation was applied that was consistent with the conservation of momentum in flow expansions and with the Bernoulli equation in flow contractions. The approximation was second order, but the accuracy reduced to first order near extreme values by the use of a minmod limiter. The modified model was verified by acomparison with the theoretical critical depth of weir, and for sufficiently smooth conditions and a fine grid size, both approximations converged to the same solution. In terms of the grid size, it was more effective at obtaining solutions than the previous model and reproduced the inundation of dry land.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.1-14
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• 2008

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and $Gr\ddot{u}nwald$-Letnikov(G-L) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.609-621
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• 2013

At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.324-329
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• 2001

A novel method for non-matching interfaces on the boundaries of the finite elements in partitioned domains is presented by introducing interface elements in this paper. The interface element method (IEM) satisfies the continuity conditions exactly through interfaces without recourse to the Lagrange multiplier technique. The moving least square (MLS) approximation in the present study is implemented to construct the shape functions of the interface elements. Alignment of the boundaries of sub-domains in the MLS approximation and integration domains provides a consistent numerical integration due to one form of rational functions in an integration domain. The compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method, and the completeness of the shape functions of the interface elements guarantees the convergence of numerical solutions. The numerical examples show that the interface element method is a useful tool for the analysis of a partitioned system and for a global-local analysis.

• 대한기계학회논문집A
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• 제30권12호
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• pp.1626-1633
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• 2006

In the present paper, in the context of the meshless interpolation of a moving least squares (MLS) type, a novel method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The support domains for the shape functions in the MLS approximation are defined from the primary nodes, and the secondary nodes use the same support domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and moved without an additional mesh. Several numerical examples are presented to illustrate the effectiveness of the present method.