• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.677-693
• /
• 2018

In this work, we generalize a family of optimal eighth order weighted-Newton methods to Banach spaces and study its local convergence to approximate a locally-unique solution of a system of nonlinear equations. The convergence in this study is shown under hypotheses only on the first derivative. Our analysis avoids the usual Taylor expansions requiring higher order derivatives but uses generalized Lipschitz-type conditions only on the first derivative. Moreover, our new approach provides computable radius of convergence as well as error bounds on the distances involved and estimates on the uniqueness of the solution based on some functions appearing in these generalized conditions. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives which may not exist or may be very expensive or impossible to compute. The convergence order is computed using computational order of convergence or approximate computational order of convergence which do not require usage of higher derivatives. This technique can be applied to any iterative method using Taylor expansions involving high order derivatives. The study of the local convergence based on Lipschitz constants is important because it provides the degree of difficulty for choosing initial points. In this sense the applicability of the method is expanded. Finally, numerical examples are provided to verify the theoretical results and to show the convergence behavior.

• Journal of computational fluids engineering
• /
• v.15 no.4
• /
• pp.25-31
• /
• 2010

Interface tracking of two phase is significant to analyze multi-phase phenomena. The VOF(Volume of Fluid) and level set are well known interface tracking method. However, they have limitations to solve compressible flow and incompressible flow at the same time. CIP(Cubic Interpolate Propagation) method is appropriate for considering compressible and incompressible flow at once by solving the governing equation which is divided up into advection and non-advection term. In this article, we analyze the droplet impingement according to various We number using improved CIP method which treats nonlinear term once more comparison with original CIP method. Furthermore, we compare spread radius after droplet impingement on the wall with the experimental data and original CIP method. The result using improved CIP method shows the better result of the experiments, comparison with result of original CIP method, and it reduces the mass conservation error which is generated in the numerical analysis comparison with original CIP method.

• Proceedings of the KSME Conference
• /
• 2002.08a
• /
• pp.365-368
• /
• 2002

The design of industrial arc plasma systems is still largely based on trial and error although the situation is rapidly improving because of the available computational power at a cost which is still fast coming down. The desire to predict the behavior of arc plasma system, thus reducing the development cost, has been the motivation of arc research. To interrupt fault current, the most enormous duty of a circuit breaker, is achieved by separating two contacts in a interruption medium, $SF_{6}$ gas or air etc., and arc plasma is inevitably established between the contacts. The arc must be controlled and interrupted at an appropriate current zero. In order to analyze arc behavior in $SF_{6}$ gas circuit breakers, a numerical calculation method combined with flow field and electromagnetic field has been developed. The method has been applied to model arc generated in the Aachen nozzle and compared the results with the experimental results. Next, we have simulated the unsteady flow characteristics to be induced by arcing of AC cycle, and conformed that the method can predict arc behavior in account of thermal transport to $SF_{6}$ gas around the arc, such as increase of arc voltage near current zero and dependency of arc radius on arc current to maintain constant arc current density.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.7
• /
• pp.1029-1037
• /
• 2004

High-speed/precision servomechanisms have been widely used in the manufacturing and semiconductor industries. In order to ensure the required high-speed and high-precision specifications in servomechanisms, an integrated design methodology is required, where the interactions between mechanical and electrical subsystems will have to be considered simultaneously. For the first step of the integrated design process, it is necessary to obtain not only strict mathematical models of separate subsystems but also formulation of an integrated design problem. A two-degree-of-freedom controller described in the discrete-time domain is considered as an electrical subsystem in this paper. An accurate identification process of the mechanical subsystem is conducted to verify the obtained mathematical model. Mechanical and electrical constraints render the integrated design problem accurate. Analysis of the system performance according to design and operating parameters is conducted for better understanding of the dynamic behavior and interactions of the servomechanism. Experiments are performed to verify the validity of the integrated design problem in the x-Y positioning system.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1996.04a
• /
• pp.119-124
• /
• 1996

End milling operation is very important in machining precision components. Deterioration of surface roughness and surface geometry will cause more process for surface finishing. According to the feed rate and the cutting edge geometry, the cusp which is geometrically uncut surface is determined. To reduce the cost for dinishing operation after end milling, the cusp must be remaianed in small size as possible. Due to the cylindrical type of the end mill, tool deflection is one of the main problems in surface generation. The cutting resistance and the rigidity of the end mill will determine the size of tool deflection. One more important factor which deteriorate surface quality comes from the error in manufacturing end mills. Run-out of end mill which is the difference of the radius of each cutting edges will produce the difference of the cusp size in every rotation of end mill. These three major factors to the surface quality will be analized and the result will be compared with experimental ressult.

• Structural Engineering and Mechanics
• /
• v.60 no.1
• /
• pp.111-130
• /
• 2016

Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.

• Journal of the Institute of Electronics Engineers of Korea SD
• /
• v.47 no.9
• /
• pp.24-29
• /
• 2010

This paper presents the RF modeling for silicon nanowire MOSFET with 30 nm channel length and 5 nm channel radius. Equations for analytical parameter extraction are derived by analysis of Y-parameter. Accuracies of the new model and extracted parameters have been verified by 3-dimensional device simulation data up to 100 GHz. The model verifications are performed under conditions of saturation region ($V_{gs}$ = $_{ds}$ = 1 V) and linear region ($V_{gs}$ = 1 V, $V_{ds}$ = 0.5 V). The RMS modeling error of Y-parameters was calculated to be 1 %.

• Transactions of Materials Processing
• /
• v.26 no.6
• /
• pp.341-347
• /
• 2017

Flexibly-reconfigurable roll forming (FRRF) is a novel sheet metal forming technology conducive to produce multi-curvature surfaces by controlling strain distribution along longitudinal direction. Reconfigurable rollers could be arranged to implement a kind of punch die set. By utilizing these reconfigurable rollers, desired curved surface can be formed. In FRRF process, three-dimensional surface is formed from two-dimensional curve. Thus, it is difficult to predict the forming result. In this study, a regression analysis was suggested to construct a predictive model for a longitudinal curvature of FRRF process. To facilitate investigation, input parameters affecting the longitudinal curvature of FRRF were determined as maximum compression value, curvature radius in the transverse direction, and initial blank width. Three-factor three-level full factorial experimental design was utilized and 27 experiments using FRRF apparatus were performed to obtain sample data of the regression model. Regression analysis was carried out using experimental results as sample data. The model used for regression analysis was a quadratic nonlinear regression model. Determination factor and root mean square root error were calculated to confirm the conformity of this model. Through goodness of fit test, this regression predictive model was verified.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.8 no.5
• /
• pp.1654-1675
• /
• 2014

In practical wireless systems, the erroneous channel state information (CSI) sometimes deteriorates the performance drastically. This paper focuses on robust design of coordinated set planning of coordinated multi-point (CoMP) transmission, with respect to the feedback delay and link error. The non-ideal channel models involving various uncertainty conditions are given. After defining a penalty factor, the robust net ergodic capacity optimization problem is derived, whose variables to be optimized are the number of coordinated base stations (BSs) and the divided area's radius. By the maximum minimum criterion, upper and lower bounds of the robust capacity are investigated. A practical scheme is proposed to determine the optimal number of cooperative BSs. The simulation results indicate that the robust design based on maxmin principle is better than other precoding schemes. The gap between two bounds gets smaller as transmission power increases. Besides, as the large scale fading is higher or the channel is less reliable, the number of the cooperated BSs shall be greater.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 2001.05a
• /
• pp.186-189
• /
• 2001

In keeping with the needs of the times for energy and labor saving and simplifying production processes, interests has been growing in warm forging. Moreover, it is interested in increasing the material usage and production amounts. To improve the productivity and material usage, it is studied the process design of warm forging for socket. Until now, socket is manufactured by hot forging in hammer. The percentage of material usage is under $60\%$ in hammer forging. On the other han4 the percentage can be increased over $90\%$ in warm forging. To change the process from hot forging to warm forging, process designs must be performed. In this time, by using the FEM package, DEFORM-3D, we could get the shape of 1st process and minimum sealing pressure. They are very essential design data to decrease the trial and error. Practically, the overlap defect could be detected and eliminated with design modification of rib height and fillet radius. Moreover, forging load and minimum sealing pressure was defined by the 3D FEM analysis.