• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.19-30
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• 2011

In [21], we compared the Newton-Krylov method and some high-order methods to solve nonlinear systems. In this paper, we propose high-order Newton-Krylov methods combining the Newton-Krylov method with some high-order iterative methods to solve systems of nonlinear equations. We provide some numerical experiments including comparisons of CPU time and iteration numbers of the proposed high-order Newton-Krylov methods for several nonlinear systems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.9
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• pp.1276-1282
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• 2013

This paper presents a demosaicking method based on high-order interpolation with parameters. Demosaicking is an essential process in capturing color images through a single sensor-array. Thus, a lot of methods including the Hamilton-Adams(HA) method has been studied in this literature. However, the image quality depends on various factors such as contrast and correlation in color space; existing algorithms depend on test images in use. Consequently, a new test image set was suggested to develop demosaicking algorithms properly. According to previous studies, the HA method shows high performances with the new test data set. In this paper, we improve the HA method using high-order interpolation with parameters. Also, we provide an analysis and formulations for the proposed method. To evaluate our method, we compare our method with the existing methods both objectively and subjectively. The experimental results indicate that the proposed method is superior to the existing methods.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.2
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• pp.412-434
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• 2023

This study discusses the high-order diffusion method in the wavelet domain. It aims to improve the edge protection capability of the high-order diffusion method using wavelet coefficients that can reflect image information. During the first step of the proposed diffusion method, the wavelet packet decomposition is a more refined decomposition method that can extract the texture and structure information of the image at different resolution levels. The high-frequency wavelet coefficients are then used to construct the edge detection function. Subsequently, because accurate wavelet coefficients can more accurately reflect the edges and details of the image information, by introducing the idea of state weight, a scheme for recovering wavelet coefficients is proposed. Finally, the edge detection function is constructed by the module of the wavelet coefficients to guide high-order diffusion, the denoised image is obtained. The experimental results showed that the method presented in this study improves the denoising ability of the high-order diffusion model, and the edge protection index (SSIM) outperforms the main methods, including the block matching and 3D collaborative filtering (BM3D) and the deep learning-based image processing methods. For images with rich textural details, the present method improves the clarity of the obtained images and the completeness of the edges, demonstrating its advantages in denoising and edge protection.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.29-40
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• 2007

An implicit discontinuous Galerkin method for the two-dimensional Euler equations was developed on unstructured triangular meshes. The method can achieve high-order spatial accuracy by using hierachical basis functions based on Legendre polynomials. Numerical tests were conducted to estimate the convergence order of numerical solutions to the Ringleb flow and the supersonic vortex flow for which analytic solutions are available. Also, the flows around a 2-D circular cylinder and an NACA0012 airfoil were numerically simulated. The numerical results showed that the implicit discontinuous Galerkin methods couples with a high-order representation of curved solid boundaries can be an efficient method to obtain very accurate numerical solutions on unstructured meshes.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.261-265
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• 2011

An adaptive wavelet transformation method with high order accuracy is proposed to allow efficient and accurate flow computations. While maintaining the original numerical accuracy of a conventional solver, the scheme offers efficient numerical procedure by using only adapted dataset. The main algorithm includes 3rd order wavelet decomposition and thresholding procedure. After the wavelet transformation, 3rd order of spatial and temporal accurate high order interpolation schemes are executed only at the points of the adapted dataset. For the other points, high order of interpolation method is utilized for residual evaluation. This high order interpolation scheme with high order adaptive wavelet transformation was applied to unsteady Euler flow computations. Through these processes, both computational efficiency and numerical accuracy are validated even in case of high order accurate unsteady flow computations.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.43 no.2 s.308
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• pp.87-92
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• 2006

In array signal processing, high order statistics can be used to estimate parameters from signal of sums of complex exponential. This paper presents a high order Matrix Pencil method(MPM) using the fourth order cumulant. Since the fourth order cumulant can suppress the Gaussian noise, the response of MPM has better noise immunity than the conventional approaches. We successfully formulate the high order MPM with all the benefits of MPM along with higher accuracy. In the numerical simulations we demonstrated that the proposed method with forth order cumulant has better resolution to find degree of arrival(DOA) in the presence of the Gaussian noise.

• Journal of the Korean earth science society
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• v.36 no.5
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• pp.476-483
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• 2015

The high-order Laplacian-type filter, which is capable of providing isotropic and sharp cut-off filtering on the spherical domain, is essential in processing geophysical data. In this study, a spherical high-order filter was designed by combining the Fourier method with finite difference-method in the longitude and latitude, respectively. The regular grid system was employed in the filter, which has uniform angular spacing including the poles. The singularity at poles was eliminated by incorporating variable transforms and continuity-matching boundary conditions across poles. The high-order filter was assessed using the Rossby-Haurwitz wave, the observed geopotential, and observed wind field. The performance of the filter was found comparable to the filter based on the Galerkin procedure. The filter, employing the finite difference method, can be designed to give any target order of accuracy, which is an important advantage being unavailable in other methods. The computational complexity is represented with 2n-1 diagonal matrices solver with n being the target order of accuracy. Along with the availability of arbitrary target-order, it is also advantageous that the filter can adopt the reduced grid to increase computational efficiency.

• Nuclear Engineering and Technology
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• v.53 no.7
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• pp.2084-2094
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• 2021

Delta-form-based methods for solving high order spatial discretization schemes are introduced into the reactor S_N transport equation. Due to the nature of the delta-form, the final numerical accuracy only depends on the residuals on the right side of the discrete equations and have nothing to do with the parts on the left side. Therefore, various high order spatial discretization methods can be easily adopted for only the transport term on the right side of the discrete equations. Then the simplest step or other robust schemes can be adopted to discretize the increment on the left hand side to ensure the good iterative convergence. The delta-form framework makes the sweeping and iterative strategies of various high order spatial discretization methods be completely the same with those of the traditional S_N codes, only by adding the residuals into the source terms. In this paper, the flux limiter method and weighted essentially non-oscillatory scheme are used for the verification purpose to only show the advantages of the introduction of delta-form-based solving methods and other high order spatial discretization methods can be also easily extended to solve the S_N transport equations. Numerical solutions indicate the correctness and effectiveness of delta-form-based solving method.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.382-385
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• 2006

A high-order spectral/boundary-element method is newly adapted as an efficient numerical tool. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved fly using the high-order spectral method and body potential is solved fly using the high-order boundary element method. Through the combination of these two methods, the wave-making problems fly a submerged sphere moving with the large amplitude oscillation are solved in time-domain. With the example calculations, nonlinear effects on free-surface profiles and hydrodynamic forces are shown and discussed.

• Structural Engineering and Mechanics
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• v.34 no.6
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• pp.779-799
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• 2010

In order to consider high-order effects on the actual limit state function, a new response surface method is proposed for structural reliability analysis by the use of high-order approximation concept in this study. Hermite polynomials are used to determine the highest orders of input random variables, and the sampling points for the determination of highest orders are located on Gaussian points of Gauss-Hermite integration. The cross terms between two random variables, only in case that their corresponding percent contributions to the total variation of limit state function are significant, will be added to the response surface function to improve the approximation accuracy. As a result, significant reduction in computational cost is achieved with this strategy. Due to the addition of cross terms, the additional sampling points, laid on two-dimensional Gaussian points off axis on the plane of two significant variables, are required to determine the coefficients of the approximated limit state function. All available sampling points are employed to construct the final response surface function. Then, Monte Carlo Simulation is carried out on the final approximation response surface function to estimate the failure probability. Due to the use of high order polynomial, the proposed method is more accurate than the traditional second-order or linear response surface method. It also provides much more efficient solutions than the available high-order response surface method with less loss in accuracy. The efficiency and the accuracy of the proposed method compared with those of various response surface methods available are illustrated by five numerical examples.