• East Asian mathematical journal
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• v.26 no.1
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• pp.59-67
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• 2010

In this paper, we suggest and analyze some three step iterative scheme for finding the common elements of the set of the solutions of the extended general variational inequalities involving three operators and the set of the fixed points of nonexpansive mappings. We also consider the convergence analysis of suggested iterative schemes under some mild conditions. Since the extended general variational inequalities include general variational inequalities and several other classes of variational inequalities as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as a refinement and improvement of the previously known results.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1067-1082
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• 2022

This paper presents a new optimal three-step eighth-order family of iterative methods for finding multiple roots of nonlinear equations. Different from the all existing optimal methods of the eighth-order, the new iterative scheme is constructed using one function and three derivative evaluations per iteration, preserving the efficiency and optimality in the sense of Kung-Traub's conjecture. Theoretical results are verified through several standard numerical test examples. The basins of attraction for several polynomials are also given to illustrate the dynamical behaviour and the obtained results show better stability compared to the recently developed optimal methods.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.

• International Journal of Control, Automation, and Systems
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• v.3 no.4
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• pp.640-645
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• 2005

Closed-loop model-free optimization of positive feedback time delay controllers for dominant time delay systems is presented. Iterative feedback tuning (IFT) is applied to the tuning of positive feedback time delay controller. Three experiments are carried out to perform the model-free gradient descent optimization. The initial controller parameters and duration in specifying the cost function are suggested. The effects of step size, filter function and time weighting function on the performance of the optimized controlled are given. Simulation and experimental studies are included to demonstrate the effectiveness of the tuning scheme.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.28 no.7
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• pp.293-298
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• 2016

A three-dimensional (3D) numerical model of the vertical ground-coupled heat exchanger is useful for analyzing the modern ground source heat pump system. Furthermore, a detailed description of the inner side of the exchanger allows to account for the effects of the thermal capacity. Thus, both methods are included in the proposed numerical model. For the ground portion, a FDM (Finite Difference Method) scheme has been applied using the Cartesian coordinate system. Cylindrical grids are applied for the borehole portion, and the U-tube configuration is adjusted at the grid, keeping the area and distance unchanged. Two sub-models are numerically coupled at each time-step using an iterative method for convergence. The model is validated by a reference 3D model under a continuous heat injection case. The results from a periodic heat injection input show that the proposed thermal capacity model reacts more slowly to the changes, resulting in lower borehole wall temperatures, when compared with a thermal resistance model. This implies that thermal capacity effects may be important factors for system controls.

• Proceedings of the IEEK Conference
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• 2001.06b
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• pp.365-368
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• 2001

This paper described a design and implementation of the division/square-root for a redundant floating point binary number using high-speed quotient selector. This division/square-root used the method of a redundant binary addition with 25MHz clock speed. The addition of two numbers can be performed in a constant time independent of the word length since carry propagation can be eliminated. We have developed a 16-bit VLSI circuit for division and square-root operations used extensively in each iterative step. It peformed the division and square-root by a redundant binary addition to the shifted binary number every 16 cycles. Also the circuit uses the nonrestoring method to obtain a quotient. The quotient selection logic used a leading three digits of partial remainders in order to be implemented in a simple circuit. As a result, the performance of the proposed scheme is further enhanced in the speed of operation process by applying new quotient selection addition logic which can be parallelly process the quotient decision field. It showed the speed-up of 13% faster than previously presented schemes used the same algorithms.

• Journal of the Korean Society for Marine Environment & Energy
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• v.7 no.4
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• pp.216-223
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• 2004

A nonlinear sloshing problem is numerically simulated. During excessive sloshing the sloshinginduced impact load can cause a critical damage on the tank structure. A three-dimensional free-surface flow in a tank is formulated in the scope of potential flow theory. The exact nonlinear free-surface condition is satisfied numerically. A finite-element method based on Hamiltons principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The computations are made through an iterative method at each time step. The hydrodynamic loading on the pillar in the tank is computed.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.37 no.5
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• pp.7-16
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• 2000

This paper described a design and implementation of the division/square-root for a redundant floating point binary number using high-speed quotient selector. This division/square-root used the method of a redundant binary addition with 25MHz clock speed. The addition of two numbers can be performed in a constant time independent of the word length since carry propagation can be eliminated. We have developed a 16-bit VLSI circuit for division and square-root operations used extensively in each iterative step. It performed the division and square-toot by a redundant binary addition to the shifted binary number every 16 cycles. Also the circuit uses the nonrestoring method to obtain a quotient. The quotient selection logic used a leading three digits of partial remainders in order to be implemented in a simple circuit. As a result, the performance of the proposed scheme is further enhanced in the speed of operation process by applying new quotient selection addition logic which can be parallelly process the quotient decision field. It showed the speed-up of 13% faster than previously presented schemes used the same algorithms.

• Geophysics and Geophysical Exploration
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• v.7 no.3
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• pp.207-212
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• 2004

This article reviews recent developments in three-dimensional (3-D) magntotelluric (MT) imaging. The inversion of MT data is fundamentally ill-posed, and therefore the resultant solution is non-unique. A regularizing scheme must be involved to reduce the non-uniqueness while retaining certain a priori information in the solution. The standard approach to nonlinear inversion in geophysis has been the Gauss-Newton method, which solves a sequence of linearized inverse problems. When running to convergence, the algorithm minimizes an objective function over the space of models and in the sense produces an optimal solution of the inverse problem. The general usefulness of iterative, linearized inversion algorithms, however is greatly limited in 3-D MT applications by the requirement of computing the Jacobian(partial derivative, sensitivity) matrix of the forward problem. The difficulty may be relaxed using conjugate gradients(CG) methods. A linear CG technique is used to solve each step of Gauss-Newton iterations incompletely, while the method of nonlinear CG is applied directly to the minimization of the objective function. These CG techniques replace computation of jacobian matrix and solution of a large linear system with computations equivalent to only three forward problems per inversion iteration. Consequently, the algorithms are efficient in computational speed and memory requirement, making 3-D inversion feasible.

• Journal of Korean Society of Steel Construction
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• v.20 no.1
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• pp.151-163
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• 2008

A formulation of three-dimensional model of articulated train-b ridge dynamic interaction has been made for the Korean eXpress Train (KTX). Semi-periodic profiles of rail irregularities consisting of elevation, alignment, cross and gauge irregularities have also been proposed using FRA maximum tolerable rail deviations. The effects of rail joints and sleeper step were also included. The resulting system matrices of train and bridge are very spare, and thus, are stored in one-dimensional arrays, yielding a time-efficient solution. A numerical algorithm for computing bridge-train response including an iterative scheme is also formulated. A program simulating train-bridge interaction and solving this problem using the new algorithm is implemented as new modules for the f inite element analysis software named XFINAS. Computed results using the new program are then checked by that of the validated 2-D bridge-train interaction model. This new 3D analysis provides more detailed train responses such as swaying, bouncing, rolling, pitching and yawing accelerations, which are useful inevaluating passenger riding comfort. Train operation safety and derailment could also be directly investigated by relative wheel displacements computed from this program.