• Nuclear Engineering and Technology
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• 제52권2호
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• pp.223-229
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• 2020

The present work proposes a solution to the static Boltzmann transport equation approximated by the simplified P₃ (SP₃) on angular, and the analytic coarse mesh finite difference (ACMFD) for spatial variables. Multi-group SP₃-ACMFD equations in 3D rectangular geometry are solved using the GMRES solution technique. As the core time dependent analysis necessitates the solution of an eigenvalue problem for an initial condition, this work is hence devoted to development and verification of the proposed static SP₃-ACMFD solver. A 3D multi-group static diffusion solver is also developed as a byproduct of this work to assess the improvement achieved using the SP₃ technique. Static results are then compared against transport benchmarks to assess the proximity of SP₃-ACMFD solutions to their full transport peers. Results prove that the approach can be considered as an acceptable interim approximation with outputs superior to the diffusion method, close to the transport results, and with the computational costs less than the full transport approach. The work would be further generalized to time dependent solutions in Part II.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권11호
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• pp.4604-4622
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• 2015

It is not easy to reconstruct the geometrical characteristics of the distorted images captured by the devices. One of the most popular optimization methods is fast iterative shrinkage/ thresholding algorithm. In this paper, to deal with its approximation error and the turbulence of the decrease process, an adaptive proximal conjugate gradient (APCG) framework is proposed. It contains three stages. At first stage, a series of adaptive penalty matrices are generated iterate-to-iterate. Second, to trade off the reconstruction accuracy and the computational complexity of the resulting sub-problem, a practical solution is presented, which is characterized by solving the variable ellipsoidal-norm based sub-problem through exploiting the structure of the problem. Third, a correction step is introduced to improve the estimated accuracy. The numerical experiments of the proposed algorithm, in comparison to the favorable state-of-the-art methods, demonstrate the advantages of the proposed method and its potential.

• 대한조선학회논문집
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• 제52권4호
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• pp.338-348
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• 2015

In this study, the added resistance of ships in short waves is systematically studied by using two different numerical methods - Rankine panel method and Cartesian grid method – and existing asymptotic and empirical formulae. Analysis of added resistance in short waves has been preconceived as a shortcoming of numerical computation. This study aims to observe such preconception by comparing the computational results, particularly based on two representative three-dimensional methods, and with the existing formulae and experimental data. In the Rankine panel method, a near-field method based on direct pressure integration is adopted. In the Cartesian grid method, the wave-body interaction problem is considered as a multiphase problem, and volume fraction functions are defined in order to identify each phase in a Cartesian grid. The computational results of added resistance in short waves using the two methods are systematically compared with experimental data for several ship models, including S175 containership, KVLCC2 and Series 60 hulls (C_B = 0.7, 0.8). The present study includes the comparison with the established asymptotic and empirical formulae in short waves.

• Nuclear Engineering and Technology
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• 제55권4호
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• pp.1428-1438
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• 2023

A novel Fission Diffusion Synthetic Acceleration (FDSA) method is developed and implemented as a part of a hybrid neutronics method for source convergence acceleration and variance reduction in Monte Carlo (MC) criticality calculations. The acceleration of the MC calculation stems from constructing a synthetic operator and solving a low-order problem using information obtained from previous MC calculations. By applying the P₁ approximation, two correction terms, one for the scalar flux and the other for the current, can be solved in the low-order problem and applied to the transport solution. A variety of one-dimensional (1-D) and two-dimensional (2-D) numerical tests are constructed to demonstrate the performance of FDSA in comparison with the standalone MC method and the coupled MC and Coarse Mesh Finite Difference (MC-CMFD) method on both intended purposes. The comparison results show that the acceleration by a factor of 3-10 can be expected for source convergence and the reduction in MC variance is comparable to CMFD in both slab and full core geometries, although the effectiveness of such hybrid methods is limited to systems with small dominance ratios.

• 대한산업공학회지
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• 제16권2호
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• pp.135-147
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• 1990

A nuclear power plant can be viewed as a large complex man-machine system where high system reliability is obtained by ensuring that sub-systems are designed to operate at a very high level of performance. The chance of severe accident involving at least partial core-melt is very low but once it happens the consequence is very catastrophic. The prediction of risk in low probability, high-risk incidents must be examined in the contest of general engineering knowledge and operational experience. Engineering knowledge forms part of the prior information that must be quantified and then updated by statistical evidence gathered from operational experience. Recently, Bayesian procedures have been used to estimate rate of accident and to predict future risks. The Bayesian procedure has advantages in that it efficiently incorporates experts opinions and, if properly applied, it adaptively updates the model parameters such as the rate or probability of accidents. But at the same time it has the disadvantages of computational complexity. The predictive distribution for the time to next incident can not always be expected to end up with a nice closed form even with conjugate priors. Thus we often encounter a numerical integration problem with high dimensions to obtain a predictive distribution, which is practically unsolvable for a model that involves many parameters. In order to circumvent this difficulty, we propose a method of approximation that essentially breaks down a problem involving many integrations into several repetitive steps so that each step involves only a small number of integrations.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.768-772
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• 2005

외판원문제(TSP)는 아직까지도 쉽게 풀리지 않는 NP-complete군에 속하는 어려운 문제이다. TSP의 결정적인 난점은 {0,1}의 정수해를 보장하면서 동시에 부분순환(sub-tour)을 피해야 한다는 점이다. 우리는 TSP를 두 단계로 나누어 탐색한다. 첫째, 초기해는 2개의 마디로 이루어진 최소단위의 부분순환에 가장 적은 비용의 마디를 하나씩 추가적으로 더하여 모든 마디가 포함될 때까지 반복하여 만든다. 둘째, 선택된 초기해의 마디를 임의의 단위로 잘라내어 그 개선비용이 음수인 경우 다른 마디 자리에 삽입함으로서 새로운 전체순환(grand tour)을 만들어 해를 개선한다. 우리는 최적해가 알려진 TSPLIB에 적용하여 그 결과를 비교하고 또한 랜덤하게 생성된 마디 200개까지의 TSP문제에 대하여 실험을 하였다. 대부분의 해는 최적해로부터 1% 이내의 결과로서 30분 이내에 얻을 수 있었다. 우리의 방법은 실용적인 문제에 적용할 수 있을 것으로 판단된다.

• 대한기계학회논문집A
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• 제37권1호
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• pp.31-37
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• 2013

본 연구의 목적은 최적화 해석 기법을 이용하여 복합재 압력용기의 스커트 치수를 도출하는 것이다. 복합재 압력용기 스커트 최적화 해석은 부분문제 근사법을 사용하였으며, APDL(ANSYS Parametric Design Language)을 이용하여 해석의 모든 과정을 일괄처리하였다. 설계변수로는 압력용기 스커트 부위의 두께와 길이를 선정하였으며, 내압에 의해 발생하는 변위와 무게를 각각 목적함수로 하여 최적화 해석을 통해 최적의 스커트 치수를 도출하였다. 그 결과 복합재 압력용기의 스커트 무게를 최대 4.38% 절감할 수 있었다.

• Steel and Composite Structures
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• 제37권6호
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.773-793
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• 2001

The explicit expressions for the 2n+1 primitive idempotents in R/sub pⁿ/ = F[x]/< x/sup pⁿ/ -1>, where F is the field of prime power order q and the multiplicative order of q modulo pⁿ is ø(pⁿ)/2(n≥1 and p is an odd prime), are obtained. An algorithm for computing the generating polynomials of the minimal QR cyclic codes of length pⁿ, generated by these primitive idempotents, is given and hence some bounds on the minimum distance of some QR codes of prime length over GF(q)(q=2, 3, ...) are obtained.

• 한국지능시스템학회논문지
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• 제26권4호
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• pp.286-294
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• 2016

초기설계 단계에서 시스템의 성능을 고려한 형상의 최적화가 필요하다. 하지만, 일반적으로 공학시스템의 성능예측은 많은 계산 시간이 요구되는 작업이다. 시스템 형상의 최적화를 위해서는 다양한 설계대안에 대한 성능의 평가가 요구되므로 초기 설계과정에서 많은 어려움이 있다. 이러한 문제를 해결하기 위해, 많은 연구자들은 응답표면방법을 이용한 성능예측에 관한 다양한 연구를 시도하고 있다. 하지만, 이 방법은 비선형성이 강한 문제에서 예측오차가 비교적 크게 발생하는 단점이 있다. 따라서 본 연구의 최종목표는 초기설계과정에서 성능예측을 위한 적절한 근사모델을 제시하고, 해양시스템 성능예측문제(부유식 해상발전기 하부구조물 최적화 문제, 유조선의 선저외판 최적화 문제)에 적용하여 제시된 근사모델을 검증하는 것이다.