• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.553-568
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• 2022

In this paper, we introduce and study two different iterative hybrid projection algorithms for solving a fixed point problem of nonexpansive mappings. The first algorithm is generated by the combination of the inertial method and the hybrid projection method. On the other hand, the second algorithm is constructed by the convex combination of three updated vectors and the hybrid projection method. The strong convergence of the two proposed algorithms are proved under very mild assumptions on the scalar control. For illustrating the advantages of these two newly invented algorithms, we created some numerical results to compare various numerical performances of our algorithms with the algorithm proposed by Dong and Lu [11].

• Communications for Statistical Applications and Methods
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• 제7권1호
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• pp.47-54
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• 2000

This article is concerned with the algorithm for the Chebyshev estimation with/without linear equality and/or inequality constraints. The algorithm employs a linear scaling transformation scheme to reduce the computational burden which is induced when the data set is quite large. The convergence of the proposed algorithm is proved. And the updating and orthogonal decomposition techniques are considered to improve the computational efficiency and numerical stability.

• 대기
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• 제33권4호
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• pp.331-341
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• 2023

A numerical forecasting models usually predict future states by performing time integration considering fixed static time-steps. A time-step that is too long can cause model instability and failure of forecast simulation, and a time-step that is too short can cause unnecessary time integration calculations. Thus, in numerical models, the time-step size can be determined by the CFL (Courant-Friedrichs-Lewy)-condition, and this condition acts as a necessary condition for finding a numerical solution. A static time-step is defined as using the same fixed time-step for time integration. On the other hand, applying a different time-step for each integration while guaranteeing the stability of the solution in time advancement is called an adaptive time-step. The adaptive time-step algorithm is a method of presenting the maximum usable time-step suitable for each integration based on the CFL-condition for the adaptive time-step. In this paper, the adaptive time-step algorithm is applied for the Korean Integrated Model (KIM) to determine suitable parameters used for the adaptive time-step algorithm through the monthly verifications of 10-day simulations (during January and July 2017) at about 12 km resolution. By comparing the numerical results obtained by applying the 25 second static time-step to KIM in Supercomputer 5 (Nurion), it shows similar results in terms of forecast quality, presents the maximum available time-step for each integration, and improves the calculation efficiency by reducing the number of total time integrations by 19%.

• Journal of Advanced Marine Engineering and Technology
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• 제40권1호
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• pp.75-80
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• 2016

유한차분법에 바탕을 둔 수치모델링은 컴퓨터기술의 발전과 함께 다양하게 이용되고 있다. 하지만 대용량의 컴퓨팅 리소스를 필요로 하는 문제를 지니고 있다. 이러한 한계를 극복하기 위해 본 연구에서는 로그격자와 영역확장법을 함께 적용하여 수치모델링 알고리즘을 제안하였다. 기존의 일반적인 등격자 유한차분법과 비교를 통해 알고리즘의 타당성 및 정확성을 검증하였으며, 수치예제를 통해 새롭게 제시된 알고리즘의 계산 효율성을 확인하였다.

• 한국압력기기공학회 논문집
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• 제11권2호
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• pp.31-39
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• 2015

Pipe wall-thinning by flow-accelerated corrosion (FAC) and various types of erosion is a significant and costly damage phenomenon in secondary piping systems of nuclear power plants (NPPs). Most NPPs have management programs to ensure pipe integrity due to wall-thinning that includes periodic measurements for pipe wall thicknesses using ultrasonic tests (UTs). Nevertheless, thinning evaluations are not easy because the amount of thickness reduction being measured is often quite small compared to the accuracy of the inspection technique. U.S. Electric Power Research Institute (EPRI) had proposed Total Point Method (TPM) as a thinning occurrence evaluation method, which is a very useful method for detecting locally thinned pipes or fittings. However, evaluation engineers have to discern manually the measurement data because there are no numerical algorithm for TPM. In this study, numerical algorithms were developed based on non-parametric and parametric statistical method.

• Coupled systems mechanics
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• 제3권2호
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• pp.171-193
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• 2014

The dynamic characterization is important in making accurate predictions of the seismic response of the hybrid structures dominated by different damping mechanisms. Different damping characteristics arise from the construction of hybrid structure with different materials: steel for the upper part; reinforced concrete for the lower main part and interaction with supporting soil. The process of modeling damping matrices and experimental verification is challenging because damping cannot be determined via static tests as can mass and stiffness. The assumption of classical damping is not appropriate if the system to be analyzed consists of two or more parts with significantly different levels of damping. The dynamic response of structures is critically determined by the damping mechanisms, and its value is very important for the design and analysis of vibrating structures. A numerical algorithm capable of evaluating the equivalent modal damping ratio from structural components is desirable for improving seismic design. Two approaches are considered to explore the dynamic response of hybrid tower of cable-stayed bridges: The first approach makes use of a simplified model of 2 coupled lumped masses to investigate the effects of subsystems different damping, mass ratio, frequency ratio on dynamic characteristics and equivalent modal damping; the second approach employs a detailed numerical step-by step integration procedure.

• 한국전산구조공학회논문집
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• 제25권2호
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• pp.139-148
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• 2012

MLS(Moving Least Squares) 차분법은 무요소법의 이동최소제곱법과 Taylor 전개를 이용하여 요소망의 제약 및 수치 적분이 없이 절점만을 이용하여 미분방정식을 수치해석할 수 있는 방법이다. 본 연구에서는 고체역학 문제의 동적해석을 위하여 MLS 차분법의 시간이력해석 알고리즘을 제시한다. 개발된 알고리즘은 Newmark 방법으로 시간적분을 하였으며, 강형식을 그대로 이산화하여 해석을 수행했다. 이동최소제곱법을 이용해 Taylor 전개식을 근사하여 실제 미분계산없이 미분근사식을 얻기 때문에 고차까지 Taylor 다항식의 차수를 증가하는 것이 용이하다. 1차원과 2차원 수치예제들을 통하여 동적해석을 위한 MLS 차분법의 정확성과 효율성을 검증하였다. 수치결과들이 정확해에 잘 수렴하였으며, 유한요소법(FEM)의 해석결과와 비교하여 떨림현상(oscillation) 및 주기성(periodicity) 오차에 대해 보다 안정적인 모습을 보였다.

• Structural Engineering and Mechanics
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• 제45권1호
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• pp.111-127
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• 2013

In this paper, a new version of gravitational search algorithm based on opposition-based learning (OBGSA) is introduced and applied for optimum design of reinforced concrete retaining walls. The new algorithm employs the opposition-based learning concept to generate initial population and updating agents' position during the optimization process. This algorithm is applied to minimize three objective functions include weight, cost and $CO_2$ emissions of retaining structure subjected to geotechnical and structural requirements. The optimization problem involves five geometric variables and three variables for reinforcement setups. The performance comparison of the new OBGSA and classical GSA algorithms on a suite of five well-known benchmark functions illustrate a faster convergence speed and better search ability of OBGSA for numerical optimization. In addition, the reliability and efficiency of the proposed algorithm for optimization of retaining structures are investigated by considering two design examples of retaining walls. The numerical experiments demonstrate that the new algorithm has high viability, accuracy and stability and significantly outperforms the original algorithm and some other methods in the literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권1호
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• pp.75-89
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• 2018

This paper presents the numerical valuation of the arithmetic Asian option by using the operator-splitting method (OSM). Since there is no closed-form solution for the arithmetic Asian option, finding a good numerical algorithm to value the arithmetic Asian option is important. In this paper, we focus on a two-dimensional PDE. The OSM is famous for dealing with plural-dimensional PDE using finite difference discretization. We provide a detailed numerical algorithm and compare results with MCS method to show the performance of the method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권4호
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• pp.201-210
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• 2010

We propose a new robust and accurate method for the numerical solution of medical image segmentation. The modified Allen-Cahn equation is used to model the boundaries of the image regions. Its numerical algorithm is based on operator splitting techniques. In the first step of the splitting scheme, we implicitly solve the heat equation with the variable diffusive coefficient and a source term. Then, in the second step, using a closed-form solution for the nonlinear equation, we get an analytic solution. We overcome the time step constraint associated with most numerical implementations of geometric active contours. We demonstrate performance of the proposed image segmentation algorithm on several artificial as well as real image examples.