• Journal of the Korean Society for Aviation and Aeronautics
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• v.16 no.2
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• pp.21-27
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• 2008

An inverse method is introduced to construct the problem for the error analysis of the numerical solution of initial value problem. These problems constructed through this method have a known exact solution, even though analytical solutions are generally not obtainable. The process leading to the exact solution makes use of an initially available approximate numerical solution. A smooth interpolation of the approximate solution is forced to exactly satisfy the differential equation by analytically deriving a small forcing function to absorb all of the errors in the interpolated approximate solution. Using this special case exact solution, it is possible to investigate the relationship between global errors of a candidate numerical solution process and the associated tuning parameters for a given problem. Under the assumption that the original differential equation is well-posed with respect to the small perturbations, we thereby obtain valuable information about the optimal choice of the tuning parameters and the achievable accuracy of the numerical solution.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.1
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• pp.1-10
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• 1995

The purpose of this paper is to develop a method of the sensitivity analysis that can be applied to a non-tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1a is the well known method applicable to a tree solution. However this method can not be applied to a non-tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient we present a method that the sensitivity analysis of Type 2 is solved by finding the shortest path. Besides we also show that the results of Type 2 and Type 1 are the same in a spanning tree solution. For the right-hand side constant or the capacity, the sensitivity analysis of Type 2 is solved by a simple calculation using arcs with intermediate values.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.4
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• pp.1-14
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• 2000

The methods of sensitivity analysis for linear programming can be classified in two types: sensitivity analysis using an optimal solution, and sensitivity analysis using an approximate optimal solution. As the methods of sensitivity analysis using an optimal solution, there are three sensitivity analysis methods: sensitivity analysis using an optimal basis, positive sensitivity analysis, and optimal partition sensitivity analysis. Since they may provide different characteristic regions under degeneracy, it is not easy to understand and apply the results of the three methods. In this paper, we propose a generalized sensitivity analysis that can integrate the three existing methods of sensitivity analysis. When a right-hand side or a cost coefficient is perturbed, the generalized sensitivity analysis gives different characteristic regions according to the controlling index set that denotes the set of variables allowed to have positive values in optimal solutions to the perturbed problem. We show that the three existing sensitivity analysis methods are special cases of the generalized sensitivity analysis, and present some properties of the generalized sensitivity analysis.

• Proceedings of the KSME Conference
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• 2000.11a
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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 the Korean Society of Tobacco Science
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• v.23 no.1
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• pp.45-52
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• 2001

This study was carried out to evaluate the uncertainty in the analysis of total alkaloids and reducing sugar content in flue-cured tobacco. The sources of uncertainty associated with the analysis of total alkaloids and reducing sugar were the weighing of sample, the preparation of extracting solution, the addition of extracting solution into the sample, the preparation of standard solution, the precision of calibration curve for standard solution, the reproducibility of analysis, and the determination of water content in tobacco, etc. For the calculating uncertainties, Type A of uncertainty was evaluated by the statistical analysis of a series of observation, and Type B by the information based on supplier’s catalogue and/or certificated of calibration. It was shown that the main source of uncertainty was caused by the calibration curve of standard solution, the reproducibility of analysis, the volume measurement of 1$m\ell$, and the purity of nicotine reference material in the preparation of standard solution. The uncertainty in the addition of extracting solution, the sample weighing, the volume measurement of 100$m\ell$, and the determination of water content of tobacco contributed relatively little to the overall uncertainty. The expanded uncertainty of total alkaloids and reducing sugar in flue-cured tobacco at 95% level of confidence was $\pm$0.12% and $\pm$0.54%, respectively.

• IE interfaces
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• v.7 no.3
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• pp.193-199
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• 1994

The purpose of this paper is to develop a method of the sensitivity analysis that can be applicable to a degenerate tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1 is the well known method applicable to a spanning tree solution. However, this method have some difficulties in case of being applied to a degenerate tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds remaining at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient, we present a method that the sensitivity analysis of Type 2 is solved by using the method of a sensitivity analysis of Type 1. Besides we also show that the results of sensitivity analysis of Type 2 are union set of those of Type 1 sensitivity analysis. For the right-hand side constant or the capacity, we present a simple method for the sensitivity analysis of Type 2 which uses arcs with intermediate values.

• International Journal of Aeronautical and Space Sciences
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• v.9 no.2
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• pp.79-86
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• 2008

High performance direct-iterative hybrid linear solver for large scale finite element problem is developed. Direct solution method is robust but difficult to parallelize, whereas iterative solution method is opposite for direct method. Therefore, combining two solution methods is desired to get both high performance parallel efficiency and numerical robustness for large scale structural analysis problems. Hybrid method mentioned in this paper is based on FETI-DP (Finite Element Tearing and Interconnecting-Dual Primal method) which has good parallel scalability and efficiency. It is suitable for fourth and second order finite element elliptic problems including structural analysis problems. We are using the hybrid concept of theses two solution method categories, combining the multifrontal solver into FETI-DP based iterative solver. Hybrid solver is implemented for our general structural analysis code, IPSAP.

• Journal of the Korean institute of surface engineering
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• v.55 no.2
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• pp.120-132
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• 2022

In the non-cyanide-based electroless Au plating solution using thiomalic acid as a complexing agent and aminoethanethiol as a reducing agent, analysis of each component constituting the plating solution is essential for the analysis of the reaction mechanism. And component analysis in the plating solution is important for monitoring component changes in the plating process and optimizing the management method. Capillary Electrophoresis (CE) method is rapid, sensitive and quantitative and could be readily applied to analysis of Auⁿ⁺ ion, complexing agent and reducing agent in electroless Au plating solution. In this study, the capillary electrophoresis method was used to analyze each component in the electroless Au plating solution in order to elucidate the complex bonding form and the plating mechanism of the non-cyanide-based electroless Au plating bath. The purpose of this study was to establish data for optimizing the monitoring and management method of plating solution components to improve the uniformity of precipitation and stability. As a result, it was confirmed that the analysis of thiomalic acid as a complexing agent and Auⁿ⁺ ions and the analysis of aminoethanethiol as a reducing agent were possible by capillary electrophoresis. In the newly developed non-cyanide-based electroless Au plating solution, it was confirmed that Auⁿ⁺ ions exist in the form of Au⁺ having a charge of +1, and that thiomalic acid and Au⁺ are combined in a molar ratio of 2 : 1. In addition, it was confirmed that aminoethanethiol can form a complex by combining with Au⁺ ions depending on conditions as well as acting as a reducing agent.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.20 no.8
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• pp.534-540
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• 2008

In this paper, the optimal bang-bang control problem of an air-conditioning system with slab thermal storage was formulated by gradient method. Furthermore, the numeric solution obtained by gradient method algorithm was compared with the analytic solution obtained on the basis of maximum principle. The control variable is changed uncontinuously at the start time of thermal storage operation in an analytic solution. On the other hand, it is showed as a continuous solution in a numeric solution. The numeric solution reproduces the analytic solution when a tolerance for convergence is applied severely. It is conceivable that gradient method is effective in the analysis of the optimal bang-bang control of the large-scale system like an air-conditioning system with slab thermal storage.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.1
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• pp.99-104
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• 2002

This paper presents a method of sensitivity analysis for the infeasible interior point method when a new variable is introduced. For the sensitivity analysis in introducing a new variable, we present a method to find an optimal solution to the modified problem. If dual feasibility is satisfied, the optimal solution to the modified problem is the same as that of the original problem. If dual feasibility is not satisfied, we first check whether the optimal solution to the modified problem can be easily obtained by moving only dual solution to the original problem. If it is possible, the optimal solution to the modified problem is obtained by simple modification of the optimal solution to the original problem. Otherwise, a method to set an initial solution for the infeasible interior point method is presented to reduce the number of iterations required. The experimental results are presented to demonstrate that the proposed method works better.