• Title, Summary, Keyword: high order

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HIGH-ORDER NEWTON-KRYLOV METHODS TO SOLVE SYSTEMS OF NONLINEAR EQUATIONS

  • Darvishi, M.T.;Shin, Byeong-Chun
    • 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 ADAPTIVE WAVELET FOR HIGH ORDER ACCURATE AND EFFICIENT COMPUTATIONAL FLUID DYNAMICS (고차정확도 및 효율적인 전산유체해석을 위한 Adaptive Wavelet)

  • Lee, Do-Hyung
    • 한국전산유체공학회:학술대회논문집
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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.

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AN ACCURATE AND EFFICIENT CALCULATION OF HIGH ENTHALPY FLOWS USING A HIGH ORDER NEW LIMITING PROCESS

  • Noh, Sung-Jun;Lee, Kyung-Rock;Park, Jung-Ho;Kim, Kyu-Hong
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.15 no.1
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    • pp.67-82
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    • 2011
  • Calculation of accurate wall heat flux for high enthalpy flows requires a dense grid system, which leads to significantly large computational time. A high-order scheme can improve the efficiency of calculation because wall heat flux can be obtained accurately even with a relatively coarse grid system. However, conventional high order schemes have some drawbacks such as oscillations near a discontinuity and instability in multi-dimensional problem. To resolve these problems, enhanced Multi-dimensional Limiting Process(e-MLP) was applied as a high-order scheme. It could provide robust and accurate solutions with high order accuracy in calculation of high enthalpy flows within a short time. We could confirm the efficiency of the high order e-MLP scheme through grid convergence tests with different grid densities in a hypersonic blunt nose problem.

FE Lubrication Analyses of High-Speed Gas-Levitation Applications using High-Order Shape Function (고차 형상함수를 이용한 고속 가스부상 FE 윤활해석)

  • 이안성;김준호
    • Tribology and Lubricants
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    • v.20 no.1
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    • pp.14-20
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    • 2004
  • In high-speed gas-levitation applications a high compressibility number may bring a numerical difficulty in predicting generated pressure profiles accurately as it causes erroneous sudden pressure overshoot and oscillation in the trailing-edge. To treat the problem, in this study an exact exponential high-order shape function is introduced in the FE lubrication analyses. It is shown by various example applications that the high-order shape function scheme can successfully subdue undesired pressure overshoot and oscillation.

A Finite Element Galerkin High Order Filter for the Spherical Limited Area Model

  • Lee, Chung-Hui;Cheong, Hyeong-Bin;Kang, Hyun-Gyu
    • Journal of the Korean earth science society
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    • v.38 no.2
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    • pp.105-114
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    • 2017
  • Two dimensional finite element method with quadrilateral basis functions was applied to the spherical high order filter on the spherical surface limited area domain. The basis function consists of four shape functions which are defined on separate four grid boxes sharing the same gridpoint. With the basis functions, the first order derivative was expressed as an algebraic equation associated with nine point stencil. As the theory depicts, the convergence rate of the error for the spherical Laplacian operator was found to be fourth order, while it was the second order for the spherical Laplacian operator. The accuracy of the new high order filter was shown to be almost the same as those of Fourier finite element high order filter. The two-dimension finite element high order filter was incorporated in the weather research and forecasting (WRF) model as a hyper viscosity. The effect of the high order filter was compared with the built-in viscosity scheme of the WRF model. It was revealed that the high order filter performed better than the built in viscosity scheme did in providing a sharper cutoff of small scale disturbances without affecting the large scale field. Simulation of the tropical cyclone track and intensity with the high order filter showed a forecast performance comparable to the built in viscosity scheme. However, the predicted amount and spatial distribution of the rainfall for the simulation with the high order filter was closer to the observed values than the case of built in viscosity scheme.

Evaluation of High Order Statistical Parameter for Electrochemical Noise Analysis

  • Kim, Jong Jip
    • Corrosion Science and Technology
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    • v.7 no.5
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    • pp.296-299
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    • 2008
  • High order statistical parameters were evaluated using the electrochemical noise data collected during corrosion of type 430 stainless steel coupled to a inert, platinum electrode in 3.5% NaCl solution. High order statistical parameters are shown to predict uniform corrosion properly. However, Localization index, skewness of current, kurtosis and skewness of potential are capable of predicting pitting corrosion only when the transients are large with long life time. Of the high order statistical parameters evaluated, kurtosis of current is found to be the most sensitive parameter for detecting uniform and pitting corrosion.

A HIGH-ORDER MODEL FOR SPIKE AND BUBBLE IN IMPULSIVELY ACCELERATED INTERFACE

  • Sohn, Sung-Ik
    • Korean Journal of Mathematics
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    • v.20 no.3
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    • pp.323-331
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    • 2012
  • We present a high-order potential ow model for the motion of the impulsively accelerated unstable interface of infinite density jump. The Layzer model for the evolution of the interface is extended to high-order. The time-evolution solutions of the bubble and the spike in the interface are obtained from the high-order model. We show that the high-order model gives improvement on the prediction of the evolution of the bubble and the spike.

A new high-order response surface method for structural reliability analysis

  • Li, Hong-Shuang;Lu, Zhen-Zhou;Qiao, Hong-Wei
    • 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.

A Comparison of Estimation Approaches of Structural Equation Model with Higher-Order Factors Using Partial Least Squares (PLS를 활용한 고차요인구조 추정방법의 비교)

  • Son, Ki-Hyuk;Chun, Young-Ho;Ok, Chang-Soo
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.36 no.4
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    • pp.64-70
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    • 2013
  • Estimation approaches for casual relation model with high-order factors have strict restrictions or limits. In the case of ML (Maximum Likelihood), a strong assumption which data must show a normal distribution is required and factors of exponentiation is impossible due to the uncertainty of factors. To overcome this limitation many PLS (Partial Least Squares) approaches are introduced to estimate the structural equation model including high-order factors. However, it is possible to yield biased estimates if there are some differences in the number of measurement variables connected to each latent variable. In addition, any approach does not exist to deal with general cases not having any measurement variable of high-order factors. This study compare several approaches including the repeated measures approach which are used to estimate the casual relation model including high-order factors by using PLS (Partial Least Squares), and suggest the best estimation approach. In other words, the study proposes the best approach through the research on the existing studies related to the casual relation model including high-order factors by using PLS and approach comparison using a virtual model.

2.5 GHZ SECOND-AND FOURTH-ORDER INDUCTORLESS RF BANDPASS FILTERS

  • Thanachayanont, Apinunt
    • Proceedings of the IEEK Conference
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    • pp.86-89
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    • 2002
  • A new design approach for realising low-power low-voltage high-Q high-order RE bandpass filter is proposed. Based on the gyrator-C inductor topology, a 2$\^$nd/-order biquadratic bandpass filter can be realised by adding a series capacitor to the input port of the gyrator. High-Q 2$\^$nd/-order and 4$\^$th/-order fully differential RF bandpass filters operating in the 2.4-㎓ ISM (Industrial, scientific and medical) frequency band under a 2-V single power supply voltage with low power dissipation are reported.

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