• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.83-90
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• 2004

Substructuring methods are usually used in finite element structural analyses. In this study a multi-level substructuring algorithm is developed and proposed as a possible candidate for incompressible fluid solves. Finite element formulation for incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et.al.[5]. The present algorithm consists of four stages such as a gathering stage, a condensing stage, a solving stage and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At highest level, each subdomain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each subdomain has been replaced by a sequential static condensation. The global algebraic system arising feom the assembly of each subdomains is solved using Conjugate Gradient Squared(CGS) method. In this case, pre-conditioning techniques usually accompanied by iterative solvers are not needed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1335-1342
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• 2000

Three-dimensional flow analysis and numerical optimization methods are presented for the design of an axial-flow fan. Steady, incompressible, three-dimensional Reynolds-averaged Navier-Stokes equations are used as governing equations, and standard k- ${\varepsilon}$ turbulence model is chosen as a turbulence model. Governing equations are discretized using finite volume method. Steepest descent method, conjugate gradient method and BFGS method are compared to determine the searching directions. Golden section method and quadratic fit-sectioning method are tested for one dimensional search. Objective function is defined as a ratio of generation rate of the turbulent kinetic energy to pressure head. Two variables concerning sweep angle distribution are selected as the design variables. Performance of the final fan designed by the optimization was tested experimentally.

• Journal of Electrical Engineering and Technology
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• v.1 no.1
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• pp.92-97
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• 2006

This paper presents the characteristic analysis and the optimal design of a permanent magnetic actuator (PMA) for a vacuum circuit breaker (VCB) using a two-dimensional finite element analysis. The purpose of this research about a PMA is to minimize the breaking time and the volume of the permanent magnet within the limits of the holding force and maximum current in the coil. The conjugate gradient method is used as an optimization algorithm. The node moving technique is iteratively implemented until the design variables of the PMA are optimized. In this paper, the optimal design of a PMA is accomplished to improve the conventional design methods.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.317-330
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• 2018

We first provide how to apply the global preconditioned conjugate gradient ($G{\ell}-PCG$) method with Kronecker product preconditioners to image deblurring problems with nearly separable point spread functions. We next provide a coarse-grained parallel image deblurring algorithm using the $G{\ell}-PCG$. Lastly, we provide numerical experiments for image deblurring problems to evaluate the effectiveness of the $G{\ell}-PCG$ with Kronecker product preconditioner by comparing its performance with those of the $G{\ell}-CG$, CGLS and preconditioned CGLS (PCGLS) methods.

• Proceedings of the KIEE Conference
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• 1987.11a
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• pp.421-424
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• 1987

Recently, the problem associated with the achievement of desired trajectories for non-linear robotic manipulatory systems are researched. The control system which is designed for this robot manipulator, poses a number of severe problem. The methods proposed to deal with the problem fall loosely into three main classes : "direct" "adaptive", "anthropomorphic". Besides there is an approach which is described based upon the application of optimal control theory. In this paper, using the optimal theory, we choose error-coordinate, between the desired trajectories and the practical as the state values, and determine the control law U which minimize a corresponding performance criterion. Let's consider the robotic arm proposed by Freund and set up the deviations of it's trajectory as a measure of performance. To find the optimal control law $U^*$ and the next state value which need to obtain $U^*$ here, we should introduced the conjugate gradient algorithm and the Runge Kutta method.

• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.467-480
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• 2008

An aggregation multigrid method (AMM) is a leading iterative solver in solid mechanics. Recently, AMM is applied for solving Schur Complement system in the FE analysis of shell structures. In this work, an extended application of AMM for solving Schur Complement system in the FE analysis of continuum elements is presented. Further, the performance of the proposed AMM in multiple load cases, which is a challenging problem for an iterative solver, is studied. The proposed method is developed by combining the substructuring and the multigrid methods. The substructuring method avoids factorizing the full-size matrix of an original system and the multigrid method gives near-optimal convergence. This method is demonstrated for the FE analysis of several elastostatic problems. The numerical results show better performance by the proposed method as compared to the preconditioned conjugate gradient method. The smaller computational cost for the iterative procedure of the proposed method gives a good alternative to a direct solver in large systems with multiple load cases.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.134-136
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• 1993

This paper presents a novel and efficient method to calculate the critical point of voltage collapse. Conjugate gradient and modified Newton-Raphson methods are employed to calculate two pairs of multiple load flow solutions for two operating conditions, i.e., both +mode and -mode voltages for two loading conditions respectively. Then these four voltage magnitude-load data sets of the bus which is most susceptible to voltage collapse, are fitted to third order polynomial using Lagrangian interpolation in order to represent approximate nose curve (P-V curve). This nose curve locates first estimate of the critical point of voltage collapse. The procedure described above is repeated near the critical point and the new estimate will be very close to the critical point. The proposed method is tested for the eleven bus Klos-Kerner system, with good accuracy and fast computation time.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.3 s.246
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• pp.270-277
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• 2006

Inverse radiation problems were solved for estimating boundary temperature distribution in a way of function estimation approach in an axisymmetric absorbing, emitting and scattering medium, given the measured radiative data. In order to reduce the computational time fur the calculation of sensitivity matrix, automatic differentiation and Broyden combined method were adopted, and their computational precision and efficiency were compared with the result obtained by finite difference approximation.. In inverse analysis, the effects of the precision of sensitivity matrix, the number of measurement points and measurement error on the estimation accuracy had been inspected using quasi-Newton method as an inverse method. Inverse solutions were validated with the result acquired by additional inverse methods of conjugate-gradient method or Levenberg-Marquardt method.

• Korean Journal of Remote Sensing
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• v.1 no.1
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• pp.39-51
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• 1985

The study was emphasized on application of the digital image processing techniques for lineament analysis. The major lineament of the study area belongs to Choogaryong faults which many geologists have studied since 1903. Also the lineament is so significant in geological views, because the lineament runs through Seoul area. The several image processing methods such as gradient, Laplacian and spatial filter have been applied, and the spatial filtering is most suitable method for lineament analysis among them. The lineaments distribute predominently in the N20.deg.-30.deg.E trend and N80.deg.-90.deg.W trend which have the conjugated relationship each other, and it coincides with the Gyeongsang conjugate system. The circular structure of study area was developed by cooling circular joint.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.435-443
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• 2007

Computing the interior spectrum of large sparse generalized eigenvalue problems $Ax\;=\;{\lambda}Bx$, where A and b are large sparse and SPD(Symmetric Positive Definite), is often required in areas such as structural mechanics and quantum chemistry, to name a few. Recently, CG-type methods have been found useful and hence, very amenable to parallel computation for very large problems. Also, as in the case of linear systems proper choice of preconditioning is known to accelerate the rate of convergence. After the smallest eigenpair is found we use the orthogonal deflation technique to find the next m-1 eigenvalues, which is also suitable for parallelization. This offers advantages over Jacobi-Davidson methods with partial shifts, which requires re-computation of preconditioner matrx with new shifts. We consider as preconditioners Incomplete LU(ILU)(0) in two variants, ever-relaxation(SOR), and Point-symmetric SOR(SSOR). We set m to be 5. We conducted our experiments on matrices from discretizations of partial differential equations by finite difference method. The generated matrices has dimensions up to 4 million and total number of processors are 32. MPI(Message Passing Interface) library was used for interprocessor communications. Our results show that in general the Multi-Color ILU(0) gives the best performance.