• 한국안전학회지
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• 제21권2호
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• pp.143-149
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• 2006

본 논문은 2차원 동적 진동문제를 공간-시간 유한요소법으로 해석하고 있다. 공간-시간 유한요소법은 공간만 분할하는 재래식 유한요소해석에 비해 보다 해를 빠르고 쉽게 얻을 수 있다. 상대적으로 큰 시간간격에 대해서 공간과 시간을 동시에 분할하는 공간-시간 유한요소 근사법을 제시한다. 가중잔차법으로 공간-시간 영역에 대해 유한요소법을 정식화하였으며 선형 사변형 공간-시간 유한요소를 선택하여 해의 안정성에 관하여 언급하였다. 일반적 동적문제에서는 상대적인 큰 시간간격으로 인하여 해의 불안정을 야기 시키고 있으나 본 연구에서는 수치의 안정성을 보여주고 있다. 비구조 공간-시간 유한요소법은 재래식 수치해석에서 흔히 발생하는 해의 불안정성에 대한 결점을 보완함은 물론 효과적인 계산방법을 지니고 있다. 이 방법의 효율성을 위해 수치예제들을 제시하였다.

• 한국전산구조공학회논문집
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• 제19권1호
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• pp.39-46
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• 2006

본 연구는 파 해석에 있어서 공간-시간 분할 개념을 도입하여 켈러킨 방법으로 해석하였다. 공간-시간 유한요소법은 오직 공간에 대해서만 분할하는 일반적인 유한요소법보다 간편하다. 비교적 큰 시간간격에 대해서 공간과 시간을 동시에 분할하는 방법을 제시하며 가중잔차법이 공간-시간 영역에서 유한요소 정식화에 이용되었다. 큰 시간 간격으로 인하여 문제의 해가 발산하는 경우가 동적인 문제에서 흔히 발생한다. 이러한 결점을 보완한 사각형 공간-시간 요소를 취하여 문제를 해석하고 해의 안정에 대해 기술하였다. 다수의 수치해석을 통하여 이 방법이 효과적 임을 알 수 있었다.

• 한국안전학회지
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• 제8권4호
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• pp.201-206
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• 1993

동적 문제에 대한 공간-시간 유한요소법을 제시하였다. 이 방법은 공간과 시간을 동일한 변수로 취급하였으며 공간-시간 영역에서의 유한요소 전개에 있어서는 연속적 갤러킨 방법에 근거하여 가중여분법을 이용하였다. 이 방법은 조건부 안정을 주는 고차원적 정확성을 주는 해법인 것이다.

• Earthquakes and Structures
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• 제9권1호
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• pp.173-194
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• 2015

Site response analysis is an important topic in earthquake engineering. A time-domain numerical method called as one-dimensional (1D) finite element artificial boundary method is proposed to simulate the homogeneous plane elastic wave propagation in a layered half space subjected to the obliquely incident plane body wave. In this method, an exact artificial boundary condition combining the absorbing boundary condition with the inputting boundary condition is developed to model the wave absorption and input effects of the truncated half space under layer system. The spatially two-dimensional (2D) problem consisting of the layer system with the artificial boundary condition is transformed equivalently into a 1D one along the vertical direction according to Snell's law. The resulting 1D problem is solved by the finite element method with a new explicit time integration algorithm. The 1D finite element artificial boundary method is verified by analyzing two engineering sites in time domain and by comparing with the frequency-domain transfer matrix method with fast Fourier transform.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1129-1141
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• 2011

In this paper, a class of large time-stepping method based on the finite element discretization for the Cahn-Hilliard equation with the Neumann boundary conditions is developed. The equation is discretized by finite element method in space and semi-implicit schemes in time. For the first order fully discrete scheme, convergence property is investigated by using finite element analysis. Numerical experiment is presented, which demonstrates the effectiveness of the large time-stepping approaches.

• 대한수학회보
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• 제35권2호
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.29-51
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• 2004

In this paper, we propose a new mixed finite element method, called the characteristics-mixed method, for approximating the solution to Burgers' equation. This method is based upon a space-time variational form of Burgers' equation. The hyperbolic part of the equation is approximated along the characteristics in time and the diffusion part is approximated by a mixed finite element method of lowest order. The scheme is locally conservative since fluid is transported along the approximate characteristics on the discrete level and the test function can be piecewise constant. Our analysis show the new method approximate the scalar unknown and the vector flux optimally and simultaneously. We also show this scheme has much smaller time-truncation errors than those of standard methods. Numerical example is presented to show that the new scheme is easily implemented, shocks and boundary layers are handled with almost no oscillations. One of the contributions of the paper is to show how the optimal error estimates in $L^2(\Omega)$ are obtained which are much more difficult than in the standard finite element methods. These results seem to be new in the literature of finite element methods.

• 한국산업융합학회 논문집
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• 제12권3호
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• pp.149-155
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• 2009

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

• Journal of applied mathematics & informatics
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• 제5권1호
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1994년도 봄 학술발표회 논문집
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• pp.1-8
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• 1994

An automated procedure which allows adaptation of spatial and time discretization simultaneously in finite element analysis of linear elastodynamic problems is presented. For dynamic problems having responses dominated by high frequency modes, such as those with impact, explosive, traveling and earthquake loads high gradient stress regions change their locations from time to time. And the time step size may need to vary in order to deal with whole process ranging from transient phase to steady state phase. As the sizes of elements in space vary in different regions, the procedure also permits different time stepping. In such a way, the best performance attainable by the finite element method can be achieved. In this study, we estimate both of the kinetic energy error and stran energy error induced by spatial and time discretization in a consistent manner. Numerical examples are used to demonstrate the performance of the procedure.