• Nuclear Engineering and Technology
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• v.43 no.6
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• pp.531-546
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• 2011

The backward differentiation formula (BDF) method is applied to a three-dimensional reactor kinetics calculation for efficient yet accurate transient analysis with adaptive time step control. The coarse mesh finite difference (CMFD) formulation is used for an efficient implementation of the BDF method that does not require excessive memory to store old information from previous time steps. An iterative scheme to update the nodal coupling coefficients through higher order local nodal solutions is established in order to make it possible to store only node average fluxes of the previous five time points. An adaptive time step control method is derived using two order solutions, the fifth and the fourth order BDF solutions, which provide an estimate of the solution error at the current time point. The performance of the BDF- and CMFD-based spatial kinetics calculation and the adaptive time step control scheme is examined with the NEACRP control rod ejection and rod withdrawal benchmark problems. The accuracy is first assessed by comparing the BDF-based results with those of the Crank-Nicholson method with an exponential transform. The effectiveness of the adaptive time step control is then assessed in terms of the possible computing time reduction in producing sufficiently accurate solutions that meet the desired solution fidelity.

• Transactions of Materials Processing
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• v.21 no.7
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• pp.432-440
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• 2012

In this article, the design of the flexible forming process considering die shape compensation using an iterative over-bending method based on numerical simulation was conducted. In this method, the springback shape obtained from the final step of the first forming simulation is compared with the desired objective shape, and a shape error is calculated as a vector norm with three-dimensional coordinates. The error vector is inversely added to the objective surface to compensate both the upper and lower flexible die configurations. The flexible die shapes are recalculated and the punch arrays are adjusted according to the over-bent forming surface. These iterative procedures are repeated until the shape error variation converges to a small value. In addition, experimental verification was conducted using a 2000-kN flexible forming apparatus for thick plates. Finally, the configuration of the prototype obtained from the experiment was compared with the numerical simulation results, which had springback compensation. It is confirmed that the proposed method for compensating for the forming error could be used in the design of flexible forming of thick-curved plates.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.6
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• pp.753-765
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• 2003

A finite element code for the numerical solution of the Navier-Stokes equation is parallelized by vertex-oriented domain decomposition. To accelerate the convergence of iterative solvers like conjugate gradient method, parallel block ILU, iterative block ILU, and distributed ILU methods are tested as parallel preconditioners. The effectiveness of the algorithms has been investigated when P1P1 finite element discretization is used for the parallel solution of the Navier-Stokes equation. Two-dimensional and three-dimensional Laplace equations are calculated to estimate the speedup of the preconditioners. Calculation domain is partitioned by one- and multi-dimensional partitioning methods in structured grid and by METIS library in unstructured grid. For the domain-decomposed parallel computation of the Navier-Stokes equation, we have solved three-dimensional lid-driven cavity and natural convection problems in a cube as benchmark problems using a parallelized fractional 4-step finite element method. The speedup for each parallel preconditioning method is to be compared using upto 64 processors.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.607-623
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• 2024

This article studies the effects of heat generation/absorption and thermal radiation on the unsteady magnetohydrodynamic (MHD) Casson fluid flow past a vertical plate through rotating porous medium with constant temperature and mass diffusion. It is assumed that the plate temperature and concentration level are raised uniformly. For finding the exact solution, a set of non-dimensional partial differential equations is solved analytically using the Laplace transform technique. The influence of various non-dimensional parameters on the velocity are discussed, including the effects of the magnetic parameter M, heat generation/absorption Q, thermal radiation parameter R, Prandtl number Pr, Schmidt number Sc, permeability of porous medium parameter, Casson fluid parameter γ, on velocity, temperature, and concentration profiles, which are discussed through several figures. It is found that velocity, temperature, and concentration profiles in the case of heat generation parameter Q, Casson fluid parameter γ, thermal Grashof number Gr, mass Grashof number Gc, Permeability Porous medium parameter K, and time t have retarding effects. It is also seen that the magnetic field M, Thermal Radiation parameter R, Prandtl field Pr, Schmidt number Sc have reverse effects on it.

• Nuclear Engineering and Technology
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• v.30 no.5
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• pp.452-461
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• 1998

The pin power distribution is determined by analyzing the rotational gamma scanning data for 36 element fuel bundle of HANARO. A fission monitor of Nb$^{95}$ is chosen by considering the criteria of the half-life, fission yield, emitting ${\gamma}$-ray energy and probability. The ${\gamma}$-ray spectra were measured in Korea Atomic Energy Research Institute(KAERI) by using a HPGe detector and by rotating the fuel bundle at steps of 10$^{\circ}$. The counting rates of Nb$^{95}$ 766 keV ${\gamma}$-rays are determined by analyzing the full absorption peak in the spectra. A 36$\times$36 response matrix is obtained from calculating the contribution of each rod at every scanning angle by assuming 2-dimensional and parallel beam approximations for the measuring geometry. In terms of the measured counting rates and the calculated response matrix, an inverse problem is set up for the unknown distribution of activity concentrations of pins. To select a suitable solving method, the performances of three direct methods and the iterative least-square method are tested by solving simulation examples. The final solution is obtained by using the iterative least-square method that shows a good stability. The influences of detection error, step size of rotation and the collimator width are discussed on the accuracy of the numerical solution. Hence an improvement in the accuracy of the solution is proposed by reducing the collimator width of the scanning arrangement.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.63-74
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• 2004

Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K\;\rightarrow\;K$ is a uniformly continuous ${\phi}$-hemicontractive operator or a Lipschitz ${\phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].

• Proceedings of the KIPE Conference
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• 2016.11a
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• pp.11-12
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• 2016

기존 LCL 필터 설계 방법의 경우, 시뮬레이션에 기반한 반복 과정을 통해 필터 파라미터를 최적화므로 많은 시간이 소요된다. 하지만 본 논문에서는 3상 PWM 인버터와 LCL 필터 분석을 통해 설계 시 고려 사항을 단순화할 수 있다. 또한 LCL 필터의 다양한 제약 조건을 파악하고, 이러한 조건 하에서 제작 비용을 최소화할 수 있는 해석 해(analytical solution)를 도출한다. 결과적으로 제안된 단계적(step-by-step) 설계 방법을 통해 빠른 시간내에 최적화된 LCL 필터를 선정할 수 있다. 제안된 방법의 유효성은 시뮬레이션을 통해 최종 검증하였다.

• Smart Structures and Systems
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• v.18 no.5
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• pp.839-864
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• 2016

This paper presents an efficient method for updating the structural finite element model. Model updating is performed through minimizing the difference between the recorded acceleration of a real damaged structure and a hypothetical damaged one. This is performed by updating physical parameters (module of elasticity in this study) in each step using iterative process of modified nonlinear conjugate gradient (M-NCG) and modified Broyden-Fletcher-Goldfarb-Shanno algorithm (M-BFGS) separately. These algorithms are based on sensitivity analysis and provide a solution for nonlinear damage detection problem. Three illustrative test examples are considered to assess the performance of the proposed method. Finally, it is demonstrated that the proposed method is satisfactory for detecting the location and ratio of structural damage in presence of noise.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.673-676
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• 2003

This paper deals with the problem of moving object detection and location in computer vision. We describe a new object-dependent motion analysis method for tracking target in an image sequence taken from a moving platform. We tackle these tasks with three steps. First, we make an active contour model of a target in order to build some of low-energy points, which are called kernels. Then we detect interest points in two windows called tracking windows around a kernel respectively. At the third step, we decide the correspondence of those detected interest points between tracking windows by the probabilistic relaxation method In this algorithm, the detecting process is iterative and begins with the detection of all potential correspondence pair in consecutive image. Each pair of corresponding points is then iteratively recomputed to get a globally optimum set of pairwise correspondences.