• 대한수학회보
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• 제51권3호
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• pp.739-763
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• 2014

In this paper, the nonlinear matrix equation $$X+\sum_{i=1}^{m}A_i^*X^{-q}A_i=Q(0<q{\leq}1)$$ is investigated. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Two iterative methods for the maximal positive definite solution are proposed. A perturbation estimate and an explicit expression for the condition number of the maximal positive definite solution are obtained. The theoretical results are illustrated by numerical examples.

• 대한기계학회논문집
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• 제19권3호
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• pp.697-704
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents the stochastic model of a nonlinear dynamic system with uncertain parameters under nonstationary stochastic inputs. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method and the second moment equation is numerically evaluated by stochastic process closure method, 4th cumulant neglect closure method and Runge-Kutta method. But the first and the second moment equations are coupled each other, so this equations are approximately evaluated by a iterative method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.381-394
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• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 제36회 하계학술대회 논문집 C
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• pp.2315-2317
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• 2005

In this paper, an iterative method to model the electromagnetic heating of electrically large lossy dielectrics is presented. Frequency domain finite element (FEM) solutions of the wave equation are determined for the lossy inhomogeneous dielectric as the material properties are change with temperature and time. The power absorbed from microwave losses is applied to a finite element time domain (FETD) calculation of the heat diffusion equation. Time steps appropriate for updating the piecewise material properties in the wave equation and the time stepping of the heat equation are presented. The effects of preheating and source frequency are investigated.

• 소성∙가공
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• 제30권4호
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• pp.186-194
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• 2021

Finite element simulation is a widely applied method for practical purpose in various metal forming process. However, in the simulation of elasto-plastic behavior of porous material or in crystal plasticity coupled multi-scale simulation, it requires much calculation time, which is a limitation in its application in practical situations. A machine learning model that directly outputs the constitutive equation without iterative calculations would greatly reduce the calculation time of the simulation. In this study, we examined the possibility of artificial intelligence based constitutive equation with the input of existing state variables and current velocity filed. To introduce the methodology, we described the process of obtaining the training data, machine learning process and the coupling of machine learning model with commercial software DEFROM^TM, as a preliminary study, via rigid plastic finite element simulation.

• 대한전기학회논문지
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• 제45권1호
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• pp.1-8
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• 1996

Recently, much attention has been paid to problems which is concerned with voltage instability phenomena and much works on these phenomena have been made. In this paper, by substituting d $P_{k}$ d $e_{k}$ ( $v^{\rarw}$= e +j f) for $P_{k}$ in conventional load flow, direct method for finging the limit of voltage stability is proposed. Here, by using the fact that taylor se- ries expansion in .DELTA. $P_{k}$ and .DELTA. $Q_{k}$ is terminated at the second-order terms, constraint equation (d $P_{k}$ d $e_{k}$ =0) and power flow equations are formulated with new variables .DSLTA. e and .DELTA.f, so partial differentiations for constraint equation are precisely calculated. The fact that iteratively calculated equations are reformulated with new variables .DELTA.e and .DELTA.f means that limit of voltage stability can be traced precisely through recalculation of jacobian matrix at e+.DELTA.e and f+.DELTA.f state. Then, during iterative process divergence may be avoid. Also, as elements of Hessian mat rix are constant, its computations are required only once during iterative process. Results of application of the proposed method to sample systems are presented. (author). 13 refs., 11 figs., 4 tab.

• 한국전자파학회논문지
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• 제26권5호
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• pp.445-454
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• 2015

본 논문에서는 고이득 이중 반사경 안테나(DTA: Dual Reflector Antenna)의 성능 향상을 위한 최적설계 기법으로 유전 알고리즘(GA: Genetic Algorithm)을 적용하였다. 또한, 최적설계과정에서 반복해석에 요구되는 계산 시간을 줄이고자 ADE 안테나의 각 반사경의 표면전류분포 계산에 반복적 물리광학법(IPO: Iterative Physical Optics)을 이용하였다. 물리광학법 적용시 음영지역에 대한 고려 및 다중반사에 의한 영향을 MFIE(Magnetic Field Integral Equation) 기반의 반복적인 계산을 통해서 해의 정확도를 향상시켰다. 또한, 설계변수의 축소 및 제작 가능한 부드러운 곡면 형성을 위하여 베지어 곡선을 적용하였다. 이럴 경우, 베지어 곡선의 제어점이 설계변수로 설정이 된다. 최적설계를 위한 목적함수로 HPBW(Half Power Beam Width), FNBW(First Null Beam Width), SLL(Side Lobe Level) 등을 고려하였으며, 설계 및 해석의 결과를 기존의 상용 해석프로그램과 비교하였다.

• 한국지능시스템학회논문지
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• 제13권2호
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• pp.175-179
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• 2003

반복 학습 제어에서 수렴 조건은 수렴 속도와 잔존 오차와 같은 성능을 결정한다. 따라서, 덜 신중한 수렴 조건을 구할 수 있다면, 그 성능은 향상될 것이고 사용 적합한 학습 제어기의 수는 증가된다. 주파수 영역에서, 연속적인 오차들간의 전달 함수의 $H_{\infty}$ 놈(norm)을 학습 시스템의 수렴성을 조사하기 위해 사용해왔다. 그러나, $H_{\infty}$ 놈을 바탕으로 한 수렴 조건이 단조 수렴성에 대하여 명확한 특성을 가진다하더라도, 특히, 다중 입출력 시스템에서 몇 가지 단점을 가진다. 본 논문에서 는 수렴 조건과 수렴의 단조성간의 관계를 밝힌다. 또한 주파수 영역에서 기존의 수렴 조건을 대신할 수 있는 수정된 수렴 조건을 주파수 영역 리아프노프(Lyapunov) 방정식을 이용하여 구한다.

• 한국통신학회논문지
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• 제27권6A호
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• pp.524-532
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• 2002

이 논문은, 램버트 W 함수가 라플라스 신호원에 대한 최적 (최소평균제곱오차) 양자기의 비반복적 설계에 이용될 수 있다는 사실을 보고한다. 구체적으로, 라플라스 신호원에 최적인 양자기의 비반복적 설계법을 고찰하며, 설계에 필수적인 비선형 방정식의 점화식의 풀이가 램버트 W 함수를 사용한 닫힌 식으로 표현된다는 것을 발견하였고, 또 이 논문에서는 이 설계법이 지수함수 형태나 라플라스 확률밀도함수 형태를 갖는 신호원에만 적용된다는 것을 증명하였다. 이 논문의 기여점은, 양자기의 설계가 비반복적이며, 원하는 만큼의 정확도로 설계되기 때문에 설계에 필요한 계산 회수가 감소되고, 양자점과 경계값을 구하는데 있어 높은 정확도를 갖는다는 점이다. 또한, 수치결과를 통하여 최적 양자 왜곡이 팬터-다잇 상수에 단조 증기적으로 수렴하는 과정을 관찰하였으며, 최적 양자기의 최외곽 경계값인 중요변수의 근사식을 유도하였다.

• Nuclear Engineering and Technology
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• 제52권3호
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• pp.485-498
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• 2020

A diffusion synthetic acceleration (DSA) technique for the S_N transport equation discretized with the linear discontinuous expansion method with subcell balance (LDEM-SCB) on unstructured tetrahedral meshes is presented. The LDEM-SCB scheme solves the transport equation with the discrete ordinates method by using the subcell balances and linear discontinuous expansion of the flux. Discretized DSA equations are derived by consistently discretizing the continuous diffusion equation with the LDEM-SCB method, however, the discretized diffusion equations are not fully consistent with the discretized transport equations. In addition, a fine mesh rebalance (FMR) method is devised to accelerate the discretized diffusion equation coupled with the preconditioned conjugate gradient (CG) method. The DSA method is applied to various test problems to show its effectiveness in speeding up the iterative convergence of the transport equation. The results show that the DSA method gives small spectral radii for the tetrahedral meshes having various minimum aspect ratios even in highly scattering dominant mediums for the homogeneous test problems. The numerical tests for the homogeneous and heterogeneous problems show that DSA with FMR (with preconditioned CG) gives significantly higher speedups and robustness than the one with the Gauss-Seidel-like iteration.