• Journal of the KSME
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• v.23 no.3
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• pp.200-206
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• 1983

FAM의 기본적인 구상은 해석 하고자하는 선형 또는 비선형 편미분 방정식을 국부적으로 해석 적인 해를 구하여 이용하자는 것이다. 그러기 위하여 유한차분법(FDM)과 유한변분법(FEM)에 서와 같이 전체유동장을 작은 요소로 나누고 그 요소 내에서 국부해를 구한 다음 이들 요소를 중첩시킴으로써 각 요소의 미지수에 대한 대수식을 얻어서 수치해를 구하자는 것이다. 그러나 FDM에서와 같이 국부요소에서 미분항을 구하지 않고, FEM 에서와 같이 요소에서 형상함수를 도입하지 않는 상태에서 해석적인 해를 구하고 있기 때문에 수치해석에서 얻어지는 미분양들은 비교적 정확하게 구해진다. 따라서 Navier-Stokes 방정식이나 에너지 방정식에서 최고차항이 작은 파라메타, 즉 레이놀즈수나 피크리수의 역수로 곱하여서 있는 경우에도 안정된 해를 구할 수 있다고 알려져 있다. 요소자체의 계수를 구하는 데는 계산시간이 많이 소요되지만 수치해석 상의 안정성이나 수렴성이 좋기 때문에 전체계산시간은 오히려 적게 걸리는 경우도 있다고 한다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.6
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• pp.1408-1416
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• 1990

A powerful and efficient method for finding approximate solutions to initial-boundary-value problems in the transient coupled thermoelasticity is formulated in time domain using the finite element technique with time-marching strategy. The final system equations can be derived by the Guritin's variational principle using the definition of convolution integral. But, the finite element formulation for the equations of motion is modified by differentiating in time. Numerical results to some test problems are compared with analytical and other sophisticated approximate solutions. Stable responces are observed in all the given examples irrespective of incremental time steps and mesh shapes. In addition, it is shown that good numerical results are obtained even in coarser mesh or larger time step comparing to other numerical methods.

• Proceedings of the Korean Society of Computer Information Conference
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• 2013.01a
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• pp.3-6
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• 2013

반도체 공정에서 소자의 제조 비용 감소를 위해 제조 공정 검증을 위한 시뮬레이션을 수행하게 된다. 이 시뮬레이션은 반도체 소자 내부의 물리량 계산을 통해 반도체 소자 내부의 불순물의 거동을 해석하게 된다. 이를 위해 사용되는 알고리즘으로 3차원적 형상을 표현하는 물리적 미분 미분방정식을 계산하게 되는데, 정확한 계산을 위해 유한 차분 시간 영역법(이하 FDTD)과 같은 수치해석 기법을 이용한다. 실제적으로 반도체 공정의 시뮬레이션에서 FDTD연산의 실행 시간은 90% 이상을 소요하게 된다. 이러한 연산에서 더욱 빠른 성능을 확보하기 위해 본 논문에서는 기존의 CUDA(Compute Unified Device Architecture)로 구현된 FDTD알고리즘을 OpenMP를 통한 다중 GPU제어를 이용하여 연산 수행시간을 감소하고, 그 결과물을 통하여 성능 향상도를 측정한다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5A
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• pp.457-465
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• 2009

This study presents a moving least squares (MLS) finite difference method for solving elastic crack problems with stress singularity at the crack tip. Near-tip functions are intrinsically employed in the MLS approximation to model near-tip field inducing singularity in stress field. employment of the functions does not lose the merit of the MLS Taylor polynomial approximation which approximates the derivatives of a function without actual differentiating process. In the formulation of crack problem, computational efficiency is considerably improved by taking the strong formulation instead of weak formulation involving time consuming numerical quadrature Difference equations are constructed on the nodes distributed in computational domain. Numerical experiments for crack problems show that the intrinsically enriched MLS finite difference method can sharply capture the singular behavior of near-tip stress and accurately evaluate stress intensity factors.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.87-95
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• 2018

This paper introduces a new explicit spectral element method for the simulation of SH-waves in semi-infinite domains. To simulate the wave motion in unbounded domains, it is necessary to reduce the infinite extent to a finite computational domain of interest. To prevent the wave reflection from the trunctated boundaries, perfectly matched layer(PML) wave-absorbing boundary is introduced. The forward problem for simulating SH-waves in PML-truncated domains can be formulated as second-order PDEs. The second-order semi-discrete form of the governing PDEs is constructed by using a mixed spectral elements with Legendre-gauss-Lobatto quadrature method, which results in a diagonalized mass matrix. Then the second-order semi-discrete form is transformed to a first-order, whose solutions are calculated by the fourth-order Runge-Kutta method. Numerical examples showed that solutions of SH-wave in the two-dimensional analysis domain resulted in stable and accurate, and reflections from truncated boundaries could be reduced by using PML boundaries. Elastic wave propagation analysis using explicit time integration method may be apt for solving larger domain problems such as three-dimensional elastic wave problem more efficiently.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.6
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• pp.36-44
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• 2003

In this paper, an analytic solution method is proposed to overcome the numerical problems when the slewing dynamics of hybrid coordinate systems is investigated via time finite element analysis. It is shown that the dynamics of the hybrid coordinate systems is governed by the coupled dual differential equations for both slewing and structural modes. Structural modes are transformed into the time-based modal coordinates and analytic spatial propagation equations are derived for each space-dependent time mode. Slew angle history is obtained analytically by appropriate applications of the boundary conditions and structural propagation is re-calculated using the slew angle. Numerical examples are demonstrated to validate the proposed analytic method in comparison to the existing state transition matrix method.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.9
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• pp.56-65
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• 2005

A dynamic analysis method that freezes a time domain by discretization and solves the spatial propagation equation has a unique feature that provides a degree of freedom on spatial domain compared with the space discretization or space-time discretization finite element method. Using this feature, the time finite element analysis can be effectively applied to optimize the spatial characteristics of distributed type actuators. In this research, the time domain finite element method was used to discretize the model. A state variable vector was used in the discretization to include arbitrary initial conditions. A performance index was proposed on spatial domain to consider both potential and vibrational energy, so that the resulting shape of the distributed actuator was optimized for dynamic control of the structure. It is assumed that the structure satisfies the final rest condition using the realizable control scheme although the initial disturbance can affect the system response. Both equations on states and costates were derived based on the selected performance index and structural model. Ricatti matrix differential equations on state and costate variables were derived by the reconfiguration of the sub-matrices and application of time/space boundary conditions, and finally optimal actuator distribution was obtained. Numerical simulation results validated the proposed actuator shape optimization scheme.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.139-148
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• 2012

The MLS(Moving Least Squares) Difference Method is a numerical scheme that combines the MLS method of Meshfree method and Taylor expansion involving not numerical quadrature or mesh structure but only nodes. This paper presents an dynamic algorithm of MLS difference method for solving transient solid mechanics problems. The developed algorithm performs time integration by using Newmark method and directly discretizes strong forms. It is very convenient to increase the order of Taylor polynomial because derivative approximations are obtained by the Taylor series expanded by MLS method without real differentiation. The accuracy and efficiency of the dynamic algorithm are verified through numerical experiments. Numerical results converge very well to the closed-form solutions and show less oscillation and periodic error than FEM(Finite Element Method).

• Journal of the Korean Society for Precision Engineering
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• v.23 no.6 s.183
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• pp.160-165
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• 2006

We have designed a high-transmission nano aperture in a perfect electric conductor film with the incident beam of 532 nm wavelength. The aperture basically has a C-shape and is known to produce a bright spot nearby the aperture in small size less than diffraction limit. The bright spot is strongly coupled with the local plasmon excited through the aperture hole. The characteristics of transmission and peak power of the aperture output were calculated using finite differential time domain (FDTD) technique, and the geometry of the aperture was determined to get a maximum transmission and peak power. To find the effect of the surface plasmon induced near by the aperture, we calculated the variations of the transmittance and the beam sizes by changing the size of the input beam irradiated on the aperture.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.108-115
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• 2007

We have designed a high transmission C-shaped aperture using finite differential time domain (FDTD) technique. The C-shaped aperture was fabricated in the aluminum thin film on a glass substrate using a focused ion beam (FIB) milling. Nano-size patterning was demonstrated with a vacuum contact device to keep tight contact between the Al mask and the photoresist. Using 405 nm laser, we recorded a 50 nm-size dot pattern on the photoresist with the aperture and analyzed the spot size dependent on the dose illuminated on the aperture.