• 대한기계학회논문집A
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• 제24권8호
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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.

• 대한수학회논문집
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• 제13권1호
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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.

• 한국전산유체공학회지
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• 제19권2호
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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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• 한국전산유체공학회 2008년도 학술대회
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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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• 한국전산유체공학회 2008년 추계학술대회논문집
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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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• 제17권4호
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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.

• 정보처리학회논문지C
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• 제12C권5호
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• pp.665-672
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• 2005

본 논문에서는 웨이블릿 변환과 보간법을 이용하여 OFDM(Orthogonal Frequency Division Multiplexing)시스템을 위한 새로운 파일럿 지원 채널 추정 기법을 소개한다. 웨이블릿 변환의 AWGN(Additive White Gaussian Noise) 감쇄능력이 뛰어남으로 인해 파일럿 채널은 아주 정확하게 추정될 수 있고, 이렇게 추정된 파일럿 데이터는 남아있는 다른 데이터 심볼 채널에 대해 2차 다항식 보간법을 하는데 사용된다. Short WATM(Wireless Asynchronous Transfer Mode)채널에 대한 모의실험 결과를 통해, 이 추정기를 쓴 OFDM 시스템의 성능은 완벽한 CSI(Channel State Information)에서 발생하는 BER(Bit Error Ratio) 성능과 거의 비슷한 것을 확인할 수 있다.

• 한국CDE학회논문집
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• 제12권1호
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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.

• 지구물리와물리탐사
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• 제21권2호
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• pp.103-111
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• 2018

탄성파 내삽 기법의 최근 연구방향은 공간적 알리아싱이 존재하는 자료에서의 내삽을 효과적으로 수행하는 것이다. 다양한 내삽 기법 중 기저함수를 정의하여 트레이스를 가장 잘 복원할 수 있는 기저함수의 조합을 찾아내는 Matching Pursuit 내삽 기법이 개발된 바 있다. 그러나 이 방법은 공간적 알리아싱 문제를 해결하지 못하는데 이를 해결하기 위해 다성분 Matching Pursuit 방법이 제안되었고 또한 시간차 보정(moveout correction) 방법도 소개된 바 있다. 다성분을 이용한 방법은 P파만을 갖는 다성분 자료가 획득되어야 하는데 해저면에서 다성분을 측정하는 OBC (Ocean Bottom Cable) 자료의 경우에는 P파 성분만을 분리하는 작업이 어려워 현장자료 적용이 힘들게 된다. 따라서 이 연구에서는 P파와 S파가 혼재하고 공간적 알리아싱이 존재하는 OBC 탐사 자료에서의 효과적인 단일성분 Matching Pursuit 내삽 기법을 다룬다. 이를 위해 시간차 보정을 포함하는 리커 요소파 기반의 단일성분 Matching Pursuit 내삽 기법 작업흐름도를 제안하고 그 효과를 체계적으로 살펴보았다. 이 작업흐름도는 내삽을 적용하기 전에 시간차 보정을 적용하고 다시 역 시간차 보정을 적용하여 공간적 알리아싱 문제를 해결하였다. 제안한 작업흐름도를 OBC 측정을 가정한 합성탄성파탐사 자료에 적용하여 그 효과를 검증하였고 현장자료에 적용함으로써 공간적 알리아싱이 심한 경우에도 내삽이 가능함을 확인하였다.