• Computational Structural Engineering
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• v.1 no.2
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• pp.121-130
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• 1988

Adaptive reinements yield a large sparse system of equations. In order to solve such a system, the core storage requirement is an important consideration. Accordingly, an iterative method which minimizes the core storage and provides a high rate of convergence is called for. In this paper the conjugate gradient algorithms with various preconditionings including the incomplete Cholesky decomposition are examined.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.45-63
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• 2006

This paper is concerned with a boundary control problem for the vorticity minimization, in which the flow is governed by the stationary two dimensional Stokes equations. We wish to find a mathematical formulation and a relevant process for an appropriate control along the part of the boundary to minimize the vorticity due to the flow. After showing the existence and uniqueness of an optimal solution, we derive the optimality conditions. The differentiability of the state solution in regard to the control parameter shall be conjunct with the necessary conditions for the optimal solution. For the minimizer, an algorithm based on the conjugate gradient method shall be proposed.

• Journal of the Society of Naval Architects of Korea
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• v.39 no.4
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• pp.17-23
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• 2002

The present paper describes the optimum inverse design of 2-D linear cascade airfoil. The pressure coefficient of an airfoil surface is taken as the objective function, and non-orthogonal incompressible Navier-Stokes equation is applied to calculate the pressure coefficient. Both of steepest descent and conjugate gradient method have been used to make the objective function go to zero. The 1st order finite differential method is applied to the searching direction and the golden section method is used to compute the searching distance. As a result of the present work, a good convergence to the target airfoil has been obtained.

• Journal of computational fluids engineering
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• v.19 no.4
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• pp.20-28
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• 2014

An efficient solution algorithm for simulating free surface problem is presented. Navier-Stokes equations for variable density incompressible flow are employed as the governing equation on Cartesian meshes. In order to describe the free surface motion efficiently, VOF(Volume Of Fluid) method utilizing THINC(Tangent of Hyperbola for Interface Capturing) scheme is employed. The most time-consuming part of the current free surface flow simulations is the solution step of the linear system, derived by the pressure Poisson equation. To solve a pressure Poisson equation efficiently, the PCG(Preconditioned Conjugate Gradient) method is utilized. This study showed that the proper application of the preconditioner is the key for the efficient solution of the free surface flow when its pressure Poisson equation is solved by the CG method. To demonstrate the efficiency of the current approach, we compared the convergence histories of different algorithms for solving the pressure Poisson equation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.2100-2107
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• 2000

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.4
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• pp.566-576
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• 1995

A Computational code has been developed in order to design axial fans by the numerical optimization techniques incorporated with flow analysis code solving three-dimensional Navier-Stokes equation. The steepest descent method and the conjugate gradient method are used to look for the search direction in the design space, and the golden section method is used for one-dimensional search. To solve the constrained optimization problem, sequential unconstrained minimization technique, SUMT, is used with imposed quadratic extended interior penalty functions. In the optimization of two-dimensional cascade design, the ratio of drag coefficient to lift coefficient is minimized by the design variables such as maximum thickness, maximum ordinate of camber and chord wise position of maximum ordinate. In the application of this numerical optimization technique to the design of an axial fan, the efficiency is maximized by the design variables related to the sweep angle distributed by quadratic function along the hub to tip of fan.

• Journal of the Korea Computer Industry Society
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• v.6 no.3
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• pp.447-456
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• 2005

This paper describes iterative restoration method of restoring blurred images using the LOG compansion function and Conjugate Gradient method. Conventional restoration methods results satisfy the requirement performance for restoring blurred images. but iteration number and convergence velocity increase. This paper proposed an opmtimised iteration restoration method for the images degraded by blurring effect, using the LOG compansion function and Conjugate Gradient method. Here, the LOG compansion function used to improve local properties of the image being restored, made the visual character and convergence velocity of the restored image improved. Throught the simulation results, the author showed that proposed algorithm produced superior performance results by conventional methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.10
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• pp.1048-1054
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• 2004

The Passive acoustic control is used in various fields, such as structures, automobiles, aircraft and so on. It is used in variety of acoustic field with the absorbing material, as one of the methods which can control the acoustic in optional space. In that case of passive control using this absorption material, it would be important to maximize the control performance of material property, numbers, geometry shape and the attached location of boundary area of the absorbing material. But realistically these variables, specially material Property, have no broad choice. Therefore, the position of absorbing material is the most important variable. In this study, we use the optimization method to minimize acoustic energy of optional space in the interest frequency attaching some absorbing materials to the boundary area. For analysis and optimization, this study uses the FEA and the conjugate gradient method. This optimization process is very efficient and useful in the passive acoustic control.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4604-4622
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• 2015

It is not easy to reconstruct the geometrical characteristics of the distorted images captured by the devices. One of the most popular optimization methods is fast iterative shrinkage/ thresholding algorithm. In this paper, to deal with its approximation error and the turbulence of the decrease process, an adaptive proximal conjugate gradient (APCG) framework is proposed. It contains three stages. At first stage, a series of adaptive penalty matrices are generated iterate-to-iterate. Second, to trade off the reconstruction accuracy and the computational complexity of the resulting sub-problem, a practical solution is presented, which is characterized by solving the variable ellipsoidal-norm based sub-problem through exploiting the structure of the problem. Third, a correction step is introduced to improve the estimated accuracy. The numerical experiments of the proposed algorithm, in comparison to the favorable state-of-the-art methods, demonstrate the advantages of the proposed method and its potential.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.9 no.5
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• pp.640-647
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• 1998

Microstrip patch antennas are analyzed by a multiresolution wavelet method. The spectral Green's dyad of the structure is obtained and its joint spatial-spectral domain representations are presented. Based on the joint spatial-spectral domain representation, we show that the spectral-domain wavelets are useful in the analysis of this problem. We obtain the matrix equations of the integral equations of this Green's dyad by using the method of moment(MoM), and efficiently solve the problem using the spectral domain wavelet transform concepts in conjuction with the conjugate gradient method. The results for a single-layered square patch are compared with those of conventional MoM and CG-FFT.