• The KSFM Journal of Fluid Machinery
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• v.2 no.1 s.2
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• pp.29-34
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• 1999

To develop the efficient numerical optimization method for the design of an airfoil, an evaluation of various methods coupled with two-dimensional Naviev-Stokes analysis is presented. Simplex method and Hook-Jeeves method we used as direct search methods, and steepest descent method, conjugate gradient method and DFP method are used as indirect search methods and are tested to determine the search direction. To determine the moving distance, the golden section method and cubic interpolation method are tested. The finite volume method is used to discretize two-dimensional Navier-Stokes equations, and SIMPLEC algorithm is used for a velocity-pressure correction method. For the optimal design of two-dimensional airfoil, maximum thickness, maximum ordinate of camber line and chordwise position of maximum ordinate are chosen as design variables, and the ratio of drag coefficient to lift coefficient is selected as an objective function. From the results, it is found that conjugate gradient method and cubic interpolation method are the most efficient for the determination of search direction and the moving distance, respectively.

• Investigative Magnetic Resonance Imaging
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• v.13 no.1
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• pp.15-21
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• 2009

Purpose : A method to estimate a real k-space trajectory based on a circuit model of the gradient system is proposed for spiral imaging. The estimated k-space trajectory instead of the ideal trajectory is used in the reconstruction to improve the image quality in the spiral imaging. Materials and Methods : Since the gradient system has self resistance, capacitance, and inductance, as well as the mutual inductance between the magnet and the gradient coils, the generated gradient fields have delays and transient responses compared to the input waveform to the gradient system. The real gradient fields and their trajectory in k-space play an important role in the reconstruction. In this paper, the gradient system is modeled with R-L-C circuits, and real gradient fields are estimated from the input to the model. An experimental method to determine the model parameters (R, L, C values) is also suggested from the quality of the reconstructed image. Results : The gradient fields are estimated from the circuit model of the gradient system at 1.5 Tesla MRI system. The spiral trajectory obtained by the integration of the estimated gradient fields is used for the reconstruction. From experiments, the reconstructed images using the estimated trajectory show improved uniformity, reduced overshoots near the edges, and enhanced resolutions compared to those using the ideal trajectory without model. Conclusion : The gradient system was successfully modeled by the R-L-C circuits. Much improved reconstruction was achieved in the spiral imaging using the trajectory estimated by the proposed model.

• Proceedings of the Korean Information Science Society Conference
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• 2004.10b
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• pp.697-699
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• 2004

Stochastic Neighbor Embedding(SNE) is a probabilistic method of mapping high-dimensional data space into a low-dimensional representation with preserving neighbor identities. Even though SNE shows several useful properties, the gradient-based naive SNE algorithm has a critical limitation that it is very slow to converge. To overcome this limitation, faster optimization methods should be considered by using trust region method we call this method fast TR SNE. Moreover, this paper presents a couple of useful optimization methods(i.e. conjugate gradient method and Newton's method) to embody fast SNE algorithm. We compared above three methods and conclude that TR-SNE is the best algorithm among them considering speed and stability. Finally, we show several visualizing experiments of TR-SNE to confirm its stability by experiments.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.609-619
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• 2014

Nonsmooth equations with finitely many maximum functions is often used in the study of complementarity problems, variational inequalities and many problems in engineering and mechanics. In this paper, we consider the global convergence methods for nonsmooth equations with finitely many maximum functions. The steepest decent method and the smoothing gradient method are used to solve the nonsmooth equations with finitely many maximum functions. In addition, the convergence analysis and the applications are also given. The numerical results for the smoothing gradient method indicate that the method works quite well in practice.

• Journal of Power System Engineering
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• v.9 no.4
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• pp.202-208
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• 2005

The genetic algorithm (GA) which is one of the popular optimum algorithm has been used to solve a variety of optimum problems. Because it need not require the gradient of objective function and is easier to find global solution than gradient-based optimum algorithm using the gradient of objective function. However optimum method using the GA and the finite element method (FEM) takes many computational time to solve the optimum structural design problem which has a great number of design variables, constraints, and system with many degrees of freedom. In order to overcome the drawback of the optimum structural design using the GA and the FEM, the author developed a computer program which can optimize frame structures by using the GA and the generalized transfer stiffness coefficient method. In order to confirm the effectiveness of the developed program, it is applied to optimum design of plane frame structures. The computational results by the developed program were compared with those of iterative design.

• Bulletin of the Korean Chemical Society
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• v.15 no.11
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• pp.953-957
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• 1994

Pseudospectral Hartree-Fock(PSHF) gradient calculations with $6-31G^{**}$ basis set have been carried out to determine the structure of D-Asparagine molecule $(C_4N_2O_3H_8)$ with improved grids and with the BFGS method. The modified PSHF method, despite partial optimization of the gradient code, turned out to be still faster than the conventional ab initio method, GAUSSIAN 90 program by more than twice. The optimum geometry of D-Asparagine obtained by the PSHF method is in good agreement with those calculated by the GAUSSIAN 90 program (within 0.0036 ${\AA}$ for bond lengths, 0.8 degrees for bond angles, and 1.6 degrees for torsional angles) except for three torsional angles. Here, rather large discrepancy of these three torsional angles (5-6 degrees) is attributed to the small differences in the optimum bond lengths and angles between the PSHF and GAUSSIAN 90 calculations.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.3.1-3
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• 2003

We show how the minimization can be used to solve the quadratic matrix equattion. We then compare two different types of conjugate gradient method and show Polak and Ribire version converge more rapidly than Fletcher and Reeves version in several examples.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.5 s.305
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• pp.41-46
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• 2005

Deinterlacing is the conversion from interlaced to progressive scan image that is considered to be 2 times image interpolation. In this paper, the simple and effective deinterlacing method is proposed based on the local gradient information of neighborhood pixels. In the proposed method, the weights for directions around the pixel to be interpolated are estimated, and the weighted sum for the neighborhood pixels is the final intensity value of the pixel to be interpolated. The proposed method has the structure suitable to practical implementation and can avoid the artifacts due to the wrong detection of edge direction. In the simulation, it showed improved subjective and objective performance than the ELA method and comparable performance compared with the variation of ELA method which has more complex structure and requires a couple of parameters that is determined by experience.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.9
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• pp.1041-1050
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• 2011

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

• Nuclear Engineering and Technology
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• v.42 no.4
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• pp.442-449
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• 2010

Recently, the neutron irradiation for large diameter silicon (Si)-ingots of more than 8" diameter is requested to satisfy the demand for the neutron transmutation doping silicon (NTD-Si). By increasing the Si-ingot diameter, the radial non-uniformity becomes larger due to the neutron attenuation effect, which results in a limit of the feasible diameter of the Si-ingot. The current evaluation method has a certain limit to precisely evaluate the radial uniformity of Si-ingot because the current evaluation method does not consider the effect of the Si-ingot diameter on the radial uniformity. The objective of this study is to propose a new evaluation method of radial uniformity by improving the conventional evaluation approach. To precisely predict the radial uniformity of a Si-ingot with large diameter, numerical verification is conducted through comparison with the measured data and introducing the new evaluation method. A new concept of a gradient is introduced as an alternative approach of radial uniformity evaluation instead of the radial resistivity gradient (RRG) interpretation. Using the new concept of gradient, the normalized reaction rate gradient (NRG) and the surface normalized reaction rate gradient (SNRG) are described. By introducing NRG, the radial uniformity can be evaluated with one certain standard regardless of the ingot diameter and irradiation condition. Furthermore, by introducing SNRG, the uniformity on the Si-ingot surface, which is ignored by RRG and NRG, can be evaluated successfully. Finally, the radial uniformity flattening methods are installed by the stainless steel thermal neutron filter and additional Si-pipe to reduce SNRG.