• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 추계 학술대회 학술발표 논문집
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• pp.129-132
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• 2003

This paper proposes a novel and efficient intelligent digital redesign technique for a Takagi-Sugeno (TS) fuzzy system. The term of intelligent digital redesign involves converting an existing analog fuzzy-model-based controller into an equivalent digital counterpart in the sense of state matching. In this paper, we suggest the discretization method based on the dual-rate sampling approximation is first proposed, and then attempt to globally match the states of the overall closed-loop TS fuzzy system with the pre-designed analog fuzzy-model-based controller and those with the digitally redesigned fuzzy-model-based controller. To show the feasibility and the effectiveness of the proposed method, a computer simulation is provided.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권10호
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• pp.464-472
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• 2001

This study uses distributed parameter systems as the spatial discretization technique, modelling in lumped parameter systems, and applies fast WALSH transform and the Picard's iteration method to high order partial differential equations and matrix partial differential equations. This thesis presents a new algorithm which usefully exercises the optimal control in the distributed parameter systems. In exercising optimal control of distributed parameter systems, excellent consequences are found without using the existing decentralized control or hierarchical control method. This study will help apply to linear time-varying systems and non-linear systems. Further research on algorithm will be required to solve the problems of convergence in case of numerous applicable intervals.

• 대한수학회보
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• 제53권3호
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• pp.853-874
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• 2016

Based on a particular overlapping domain decomposition technique, a parallel finite element discretization algorithm for the generalized Stokes equations is proposed and investigated. In this algorithm, each processor computes a local approximate solution in its own subdomain by solving a global problem on a mesh that is fine around its own subdomain and coarse elsewhere, and hence avoids communication with other processors in the process of computations. This algorithm has low communication complexity. It only requires the application of an existing sequential solver on the global meshes associated with each subdomain, and hence can reuse existing sequential software. Numerical results are given to demonstrate the effectiveness of the parallel algorithm.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2002년도 추계학술대회 논문집
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• pp.3-10
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• 2002

This study proposed a technique for inverse problem, linear approximation of contact position and loading in single and double meshing of spur gear, using 2-dimension model considered near the tooth by root stress. Determine root stress is carried out for the gear tooth by finite element method and boundary element method. Boundary element discretization near contact point is carefully performed to keep high computational accuracy. And from those estimated results, the comparing estimate value with boundary element method value was discussed.

• 한국공작기계학회논문집
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• 제10권5호
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• pp.85-95
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• 2001

This study proposed a technique for inverse problem, linear approximation of contact position and loading in single and double meshing of spiral bevel gear , using 2-dimension model considered near the tooth by root stress. Determine root stress is carried out far the gear tooth by finite element method and boundary element method. Boundary element discretization near contact point is carefully performed to keep high computational accuracy. And from those estimated results, the comparing estimate value with boundary element method value was discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권1호
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• pp.17-27
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• 2010

In this paper, we apply homotopy perturbation method (HPM) for solving ninth and tenth-order boundary value problems. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed homotopy perturbation method solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method.

• 한국정밀공학회지
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• 제18권8호
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• pp.79-86
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• 2001

A method for actively minimizing dynamic reaction forces in a flexible structure subject to persistent excitations is presented. One difficulty with the method, however, is that forces and moments do not converge as quickly as displacements in mathematical discretization of continuous systems, so a controller based on a truncated model of a continuous system can produce poor results. A technique using residual flexibility matrix is presented for correcting the truncated force representation. A controller designed for reaction force minimization, using the residual flexibility matrix, is applied to a model of a flexible structure, and the results are presented. Implications of various reaction force penalty combinations on the resulting control performance are also discussed.

• Computers and Concrete
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• 제16권5호
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• pp.683-701
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• 2015

When approached using nonlinear finite element (FE) techniques, structural analyses generate, for real RC structures, large complex numerical problems. Damage is a major part of concrete behavior, and the discretization technique is critical to limiting the size of the problem. Based on previous work, the ${\mu}$ damage model has been designed to activate the various damage effects correlated with monotonic and cyclic loading, including unilateral effects. Assumptions are formulated to simplify constitutive relationships while still allowing for a correct description of the main nonlinear effects. After presenting classical 2D finite element applications on structural elements, an enhanced simplified FE description including a damage description and based on the use of multi-fiber beam elements is provided. Improvements to this description are introduced both to prevent dependency on mesh size as damage evolves and to take into account specific phenomena (permanent strains and damping, steel-concrete debonding). Applications on RC structures subjected to cyclic loads are discussed, and results lead to justifying the various concepts and assumptions explained.

• 전산구조공학
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• 제3권3호
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• pp.125-131
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• 1990

본 논문에서는 시간 종속 하중을 받는 대형 전산구조응력 해석 문제를 위한 유한요소 모델링 기법이 소개된다. 유한요소모델링의 분할기준은 문제에 대한 해석 결과에 대한 오차선정에 근거를 둔다. 이 오차산정은 해석결과치에 의한 잔유 에너지의 크기를 유한요소별로 산정한다. 이의 시간존장 구조물에 대한 응용은, 구조연속체의 Ritz 고유진동 모드를 계산하고 이들 진동 모드 중에서 저주파에 상응하는 진동모드에 대해 잔유 에너지의 크기가 구조체 전체영역에서 평형을 유지하도록 유한요소 모델링을 수행한다. 마지막으로, 여기서 제안된 알고리즘이 몇 예제들을 통해서 검증된다.