• 한국컴퓨터정보학회논문지
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• 제26권1호
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• pp.69-76
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• 2021

최근 특이성 교란 미적분 경계값 문제를 해결하기 위해 신경회로망 접근이 연구되고 있다. 특히 다양한 학습 알고리즘을 가진 백프로파게이션 알고리즘에 의해 훈련하는 피드-포워드 신경회로망의 이론적 모델이 제시되고 있으며, 딥러닝, 전이학습, 연합학습 등의 신경회로망 모델이 매우 빠르게 개발되고 있다. 본 논문의 목적은 특이성 교란 문제를 점근법적 방법과 함께 해결하기 위해 고도의 정확성과 속도를 가진 신경회로망 접근법에 관해 연구하는 것이다. 이를 위해 본 논문에서는 특이성 교란문제의 결과치와 교란되지 않은 문제의 결과치의 차이에 대해 신경회로망 접근 식을 사용하여 시뮬레이션 하였고 신경회로망 접근식의 효율성도 제시하였다. 결론적으로 특이성 교란 문제를 수식이 아닌 단순한 신경회로망 접근으로 효율적으로 해결할 수 있음을 제시한 것이 본 논문의 주요 기여사항이다.

• 한국항공우주학회지
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• 제31권3호
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• pp.39-49
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• 2003

본 논문에서는 먼저 델타연산자 접근법과 섭동기법을 소개하였다. 전자는 수치연산에 있어서 round-off error를 줄여주고 후자는 시스템을 빠른 종속시스템과 느린 종속시스템으로 분리하여 연산시간을 줄여준다. 항공기의 동력학은 종방향 혹은 횡방향 모두 장주기(Phugoid)와 단주기 운동을 동시에 보여준다. 여기서는 경비행기 Beaver의 횡방향 모델에 섬동기법과 델타접슨법을 적용하여 얻는 근사치 해를 정확한 해와 비교하였다. 그 겨로가 개루프 시스템의 경우는 단 한번의 iteration을 시행하여 얻은 근사치 해가 정확한 해와 일치했고, 페루프 시스템의 경우는 iteration없이도 근사치 값이 정확한 해와 일치하였다. 이로써 제안된 방법들의 적용이 항공기 동력학 및 제어에 있어서 매우 유효함이 검증되었다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1297-1301
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• 1997

Generally, singularity analysis of 6-DOF parallerl manipulators is very difficult and, as result, velocity relation has many uncertainties. In this paper, an alternative method using the local structurizatioin method(LSM) for the analysis of singular configuraions is presented. With LSM, the velocity relation can be represented in a simple form, and the result is totally equivalent to the conventional velocity relation. The velocity relation suggested in this paper gives a closed-form solution of singularities.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• 대한기계학회논문집
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• 제16권5호
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• pp.883-890
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• 1992

본 연구에서는 Laplace 변환법에 의한 2차원 동적 문제의 경계요소 프로그램 을 작성하고, 간단한 모델을 해석하여 프로르램의 정도 및 그 유용성을 검토하고, 응 용문제로 동적하중을 받는 균열문제의 몇 가지 모델에 대하여 변위 외삽법으로 균열의 파괴 역학적 파라미터인 동적응력확대계수(dynamic stress intensity factor)를 구하 여 결과를 검토하여 보고자 한다.

• Structural Engineering and Mechanics
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• 제76권4호
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• pp.505-512
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• 2020

This paper presents an error estimation technique for 2-D crack analysis by an enriched natural element (more exactly, enriched Petrov-Galerkin NEM). A bare solution was approximated by PG-NEM using Laplace interpolation functions. Meanwhile, an accurate quasi-exact solution was obtained by a combined use of enriched PG-NEM and the global patch recovery. The Laplace interpolation functions are enriched with the near-tip singular fields, and the approximate solution obtained by enriched PG-NEM was enhanced by the global patch recovery. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated using the errors which obtained by FEM using a very fine mesh. The error distribution was investigated by calculating the local element-wise errors, from which it has been found that the relative high errors occurs in the vicinity of crack tip. The differences between the enriched and non-enriched PG-NEMs have been investigated from the effective index, the error distribution, and the convergence rate. From the comparison, it has been justified that the enriched PG-NEM provides much more accurate error information than the non-enriched PG-NEM.

• Kyungpook Mathematical Journal
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• 제61권3호
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• pp.591-612
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• 2021

In this paper, a uniformly convergent numerical scheme is designed for solving singularly perturbed reaction-diffusion problems. The problem is converted to an equivalent weak form and then a Galerkin finite element method is used on a piecewise uniform Shishkin mesh with linear basis functions. The convergence of the developed scheme is proved and it is shown to be almost fourth order uniformly convergent in the maximum norm. To exhibit the applicability of the scheme, model examples are considered and solved for different values of a singular perturbation parameter ε and mesh elements. The proposed scheme approximates the exact solution very well.

• 대한전자공학회논문지
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• 제23권6호
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• pp.820-832
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• 1986

In contrast to conventional liquid phase epitaxy of GaAs, surface kinetics limited growth is predominant in selective liquid phase epitaxy. For the stripe openings in the high-index crystal-lographic directions, the well-known facet formations and the decompositions into the low index planes or smooth circular surfaces are observed depending on the growth kinetics. For the low index direction stripe, surface kinetics limited growth is evident. By a numerical calcualtion we show that these phenomena are due to the enhanced masstransport by two dimensional diffusion and growth rate anisotropy which is found to be very stdrong with cusped minima for some singular planes in the solution growth as well as in vapor phase epitaxy. Morphological stability is briefly treated in terms of diffusion and its implications on device application are stated. Tese phenomena may be common to III-V compound semiconductors as well as GaAs.