• 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.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.181-193
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• 1998

The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.

• Journal of computational fluids engineering
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• v.19 no.2
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• pp.58-65
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• 2014

The adaptive wavelet method is studied for the enhancement of computational efficiency of three-dimensional flows. For implementation of the method for three-dimensional Euler equation, wavelet decomposition process is introduced based on the previous two-dimensional adaptive wavelet method. The order of numerical accuracy of an original solver is preserved by applying modified thresholding value. In order to assess the efficiency of the proposed algorithm, the method is applied to the computation of flow field around ONERA-M6 wing in transonic regime with 4th and 6th order interpolating polynomial respectively. Through the application, it is confirmed that the three-dimensional adaptive wavelet method can reduce the computational time while conserving the numerical accuracy of an original solver.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.42-49
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• 2008

A wavelet method is presented in order to improve the computational efficiency of two dimensional unsteady flow problems while maintaining the order of accuracy of conventional CFD schemes. First, by using the interpolating wavelet transformation including decomposition and thresholding, an adaptive dataset to a solution is constructed. Then, inviscid and viscous fluxes are calculated only at the points within an adaptive dataset, which enhances the computational efficiency. Second, thresholding step is modified to maintain the spatial and temporal accuracy of conventional CFD schemes automatically by selecting the threshold value between user-defined value and the magnitude of spatial or temporal truncation error. The wavelet method suggested in this study is successfully applied to various unsteady flow problems and it is shown that the computational efficiency is enhanced with maintaining the computational accuracy of CFD schemes.

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.42-49
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• 2008

A wavelet method is presented in order to improve the computational efficiency of two dimensional unsteady flow problems while maintaining the order of accuracy of conventional CFD schemes. First, by using the interpolating wavelet transformation including decomposition and thresholding, an adaptive dataset to a solution is constructed. Then, inviscid and viscous fluxes are calculated only at the points within an adaptive dataset, which enhances the computational efficiency. Second, thresholding step is modified to maintain the spatial and temporal accuracy of conventional CFD schemes automatically by selecting the threshold value between user-defined value and the magnitude of spatial or temporal truncation error. The wavelet method suggested in this study is successfully applied to various unsteady flow problems and it is shown that the computational efficiency is enhanced with maintaining the computational accuracy of CFD schemes.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.279-294
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• 2013

We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.

• The KIPS Transactions:PartC
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• v.12C no.5 s.101
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• pp.665-672
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• 2005

We present a novel pilot-aided channel estimation method for OFDM (Orthogonal Frequency Division Muitiplexing) system using WT(Wavelet transform) and interpolation. Due to excellent AWGN (Additive White Gaussian Noise) cancellation capability of n, pilot channels are estimated quite exactly and then, Dey are used in 2-degree polynomial interpolating the other remaining data symbol channels. The simulation results for Short WATM (Wireless Asynchronous Transfer Mode) channel show that the degradation in BER (Bit Error Ratio) performance of OFDM system iか this estimator is negligible compared to the case of perfect knowledge of CSI (Channel State Information).

• Korean Journal of Computational Design and Engineering
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• v.12 no.1
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• pp.27-38
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• 2007

This paper describes a multiresidual approximation method for scattered volumetric data modeling. The approximation method employs a volumetric NURBS or VNURBS as a data interpolating function and proposes two multiresidual methods as a data modeling algorithm. One is called as the residual series method that constructs a sequence of VNURBS functions and their algebraic summation produces the desired approximation. The other is the residual merging method that merges all the VNURBS functions mentioned above into one equivalent function. The first one is designed to construct wavelet-type multiresolution models and also to achieve more accurate approximation. And the second is focused on its improvement of computational performance with the save fitting accuracy for more practical applications. The performance results of numerical examples demonstrate the usefulness of VNURBS approximation and the effectiveness of multiresidual methods. In addition, several graphical examples suggest that the VNURBS approximation is applicable to various applications such as surface modeling and fitting problems.

• Geophysics and Geophysical Exploration
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• v.21 no.2
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• pp.103-111
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• 2018

The recent research aim of seismic trace interpolation is to effectively interpolate the data with spatial aliasing. Among various interpolation methods, the Matching Pursuit interpolation, that finds the proper combination of basis functions which can best recover traces, has been developed. However, this method cannot interpolate aliased data. Thus, the multi-component Matching Pursuit interpolation and moveout correction method have been proposed for interpolation of spatially aliased data. It is difficult to apply the multi-component Matching Pursuit interpolation to interpolating the OBC (Ocean Bottom Cable) data which is the multi-component data obtained at the ocean bottom because the isolation of P wave component is required in advance. Thus, in this study, we dealt with an effective single-component matching Pursuit interpolation method in OBC data where P-wave and S-wave are mixed and spatial aliasing is present. To do this, we proposed the Ricker wavelet based single-component Matching Pursuit interpolation workflow with moveoutcorrection and systematically investigated its effectiveness. In this workflow, the spatial aliasing problem is solved by applying constant value moveout correction to the data before the interpolation is performed. After finishing the interpolation, the inverse moveout correction is applied to the interpolated data using the same constant velocity. Through the application of our workflow to the synthetic OBC seismic data, we verified the effectiveness of the proposed workflow. In addition, we showed that the interpolation of field OBC data with severe spatial aliasing was successfully performed using our workflow.