• Structural Engineering and Mechanics
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• 제64권4호
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• pp.495-504
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• 2017

This paper proposes a new direct numerical integration algorithm for solving equation of motion in structural dynamics problems with nonlinear stiffness. The new implicit method's degree of accuracy is higher than that of existing methods due to the higher order of the acceleration. Two parameters are defined, leading to a new family of unconditionally stable methods, which helps to take greater time steps in integration and eliminate concerns about the duration of solving. The method developed can be utilized for a number of solid plane finite elements, examples of which are given to compare the proposed method with existing ones. The results indicate the superiority of the proposed method.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2000년도 제18회 학술발표회 논문개요집
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• pp.194-194
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• 2000

There are difficulties on transport modelling on high density plasma discharge, because of severe restrictions on space grid size and time step size. We present a new unconditionally stable algorithm for fluid simulation of high density process plasma. The origin of the restriction is investigated and a new method to solve the problem is suggested, The simulation result is compared with the other methods previously developed.

• Structural Engineering and Mechanics
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• 제18권4호
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• pp.411-428
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• 2004

In this study, a newly developed unconditionally stable explicit method is employed to solve momentum equations of motion in performing pseudodynamic tests. Due to the explicitness of each time step this pseudodynamic algorithm can be explicitly implemented, and thus its implementation is simple when compared to an implicit pseudodynamic algorithm. In addition, the unconditional stability might be the most promising property of this algorithm in performing pseudodynamic tests. Furthermore, it can have the improved properties if using momentum equations of motion instead of force equations of motion for the step-by-step integration. These characteristics are thoroughly verified analytically and/or numerically. In addition, actual pseudodynamic tests are performed to confirm the superiority of this pseudodynamic algorithm.

• 한국공간구조학회논문집
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• 제14권1호
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• pp.101-108
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• 2014

In order to overcome the key shortcoming of Hamilton's principle, recently, the extended framework of Hamilton's principle was developed. To investigate its potential in further applications especially for material non-linearity problems, the focus is initially on a classical single-degree-of-freedom elasto-viscoplastic model. More specifically, the extended framework is applied to the single-degree-of-freedom elasto-viscoplastic model, and a corresponding weak form is numerically implemented through a temporal finite element approach. The method provides a non-iterative algorithm along with unconditional stability with respect to the time step, while yielding whole information to investigate the further dynamics of the considered system.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권4호
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• pp.281-294
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• 2006

Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권3호
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• pp.233-251
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• 2011

The Gauge-Uzawa method [GUM] in [9] which is a projection type algorithm to solve evolution Navier-Stokes equations has many advantages and superior performance. But this method has been studied for backward Euler time discrete scheme which is the first order technique, because the classical second order GUM requests rather strong stability condition. Recently, the second order time discrete GUM was modified to be unconditionally stable and estimated errors in [12]. In this paper, we contemplate several GUMs which can be derived by the same manner within [12], and we dig out properties of them for both stability and accuracy. In addition, we evaluate an stability condition for the classical GUM to construct an adaptive GUM for time to make free from strong stability condition of the classical GUM.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권4호
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• pp.333-342
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• 2022

In this paper, we perform a direct comparison study of real experimental data for domain rearrangement and the Cahn-Hilliard (CH) equation on the dynamics of morphological evolution. To validate a mathematical model for physical phenomena, we take initial conditions from experimental images by using an image segmentation technique. The image segmentation algorithm is based on the Mumford-Shah functional and the Allen-Cahn (AC) equation. The segmented phase-field profile is similar to the solution of the CH equation, that is, it has hyperbolic tangent profile across interfacial transition region. We use unconditionally stable schemes to solve the governing equations. As a test problem, we take domain rearrangement of lipid bilayers. Numerical results demonstrate that comparison of the evolutions with experimental data is a good benchmark test for validating a mathematical model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• 전산구조공학
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• 제8권3호
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• pp.59-66
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• 1995

점소성이론을 이용하여 충격하중을 받는 구조물의 거동을 하중시간에 따라 조사하였다. 점소성이론은 재료의 소성특성과 시간변화특성을 나타내는 Rheology 이론을 동시에 고려한 이론이다. 점소성 구성방정식을 구한 후, 이를 이차원 유한요소해석프로그램에서 심어서 평면응력, 평면 변형률, 축대칭 구조물의 동적 거동을 해석할 수 있도록 기존프로그램을 수정.개발하였다. Perzyna에 의한 점소성 구성방정식은 유한요소해석에서 Explicit 적분법을 사용해야 하는데 반하여, 본 연구에서 구한 구성방정식은 Implicit 적분법을 적용할 수 있도록 Algorithm을 개발하였다. 다양한 하중시간을 갖는 충격하중을 선택한 구조물에 가해 해석한 결과, 하중시간이 길수록 변형이 증가하여 점소성 거동을 하며, 높은 고유진동수 성분이 점소성거동으로 거의 소멸된다는 결론을 얻었다.

• 대한전기학회논문지:전력기술부문A
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• 제49권3호
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• pp.95-106
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• 2000

The load frequency control of power system is one of important subjects in view of system operation and control. That is even though the rapid load disturbances were applied to the given power system, the stable and reliable power should be supplied to the users, converging unconditionally and rapidly the frequency deviations and the tie-line power flow one on each area into allowable boundary limits. Nonetheless of such needs, if the internal parameter perturbation and the sudden load variation were given, the unstable phenomenal of power system can be often brought out because of the large frequency deviation and the unsuppressible power line one. Therefore, it is desirable to design the robust neuro-fuzzy controller which can stabilize effectively the given power system as soon as possible. In this paper the robust neuro-fuzzy controller was proposed and applied to control of load frequency over multi-area power system. The architecture and algorithm of a designed NFC(Neuro-Fuzzy Controller) were consist of fuzzy controller and neural network for auto tuning of fuzzy controller. The adaptively learned antecedent and consequent parameters of membership functions in fuzzy controller were acquired from the steepest gradient method for error-back propagation algorithm. The performances of the resultant NFC, that is, the steady-state deviations of frequency and tie-line power flow and the related dynamics, were investigated and analyzed in detail by being applied to the load frequency control of multi-area power system, when the perturbations of predetermined internal parameters. Through the simulation results tried variously in this paper for disturbances of internal parameters and external stepwise load stepwise load changes, the superiorities of the proposed NFC in robustness and adaptive rapidity to the conventional controllers were proved.