• Title, Summary, Keyword: Pseudo-spectral method

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NUMERICAL SOLUTIONS OF BURGERS EQUATION BY REDUCED-ORDER MODELING BASED ON PSEUDO-SPECTRAL COLLOCATION METHOD

  • SEO, JEONG-KWEON;SHIN, BYEONG-CHUN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.2
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    • pp.123-135
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    • 2015
  • In this paper, a reduced-order modeling(ROM) of Burgers equations is studied based on pseudo-spectral collocation method. A ROM basis is obtained by the proper orthogonal decomposition(POD). Crank-Nicolson scheme is applied in time discretization and the pseudo-spectral element collocation method is adopted to solve linearlized equation based on the Newton method in spatial discretization. We deliver POD-based algorithm and present some numerical experiments to show the efficiency of our proposed method.

PSEUDO-SPECTRAL LEAST-SQUARES METHOD FOR ELLIPTIC INTERFACE PROBLEMS

  • Shin, Byeong-Chun
    • Journal of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1291-1310
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    • 2013
  • This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

Trajectory Optimization for a Supersonic Air-Breathing Missile System Using Pseudo-Spectral Method

  • Park, Jung-Woo;Tahk, Min-Jea;Sung, Hong-Gye
    • International Journal of Aeronautical and Space Sciences
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    • v.10 no.1
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    • pp.112-121
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    • 2009
  • This paper deals with supersonic air-breathing missile system. A supersonic air-breathing missile system has very complicated and incoherent thrust characteristics with respect to outer and inner environment during operation. For this reason, the missile system has many maneuver constraints and is allowed to operate within narrow flight envelope. In this paper, trajectory optimization of the missile is accomplished. The trajectory optimization problem is formulated as a discrete parameter optimization problem. For this formulation, Legendre Pseudo-Spectral method is introduced. This method is based on calculating the state and control variables on Legendre-Gauss-Lobatto (LGL) points. This approach helps to find approximated derivative and integration quantities simply. It is shown that, for this trajectory optimization, trend analysis is performed from thrust characteristics on various conditions so that the trajectory optimization is accomplished with fine initial guess with these results.

Eigenvalue Analysis of Double-span Timoshenko Beams by Pseudo spectral Method

  • Lee, Jin-Hee
    • Journal of Mechanical Science and Technology
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    • v.19 no.9
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    • pp.1753-1760
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    • 2005
  • The pseudo spectral method is applied to the free vibration analysis of double-span Timoshenko beams. The analysis is based on the Chebyshev polynomials. Each section of the double-span beam has its own basis functions, and the continuity conditions at the intermediate support as well as the boundary conditions are treated separately as the constraints of the basis functions. Natural frequencies are provided for different thickness-to-length ratios and for different span ratios, which agree with those of Euler-Bernoulli beams when the thickness-to-length ratio is small but deviate considerably as the thickness-to-length ratio grows larger.

Spectral Element modeling for the one-dimensional blood flow analysis (일차원 혈류해석을 위한 스펙트럴 요소 모델링)

  • Jang, In-Joon;Lee, U-Sik
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.152-155
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    • 2008
  • The blood flow characteristics have been closely related to various cardiovascular diseases, it is very important to predict them accurate enough in an efficient way. Thus, this paper proposes a one-dimensional spectral element model for the blood flow through blood vessels. The spectral element model is formulated by using the variational method. The nonlinear terms in spectral element model are all treated as the pseudo-force and an iterative solution method is applied in the frequency domain.

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SAR Image Processing Using SVD-Pseudo Spectrum Technique (SAR에 적용된 SVD-Pseudo Spectrum 기술)

  • Kim, Binhee;Kong, Seung-Hyun
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.3
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    • pp.212-218
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    • 2013
  • This paper presents an SVD(Singular Value Decomposition)-Pseudo Spectrum method for SAR (Synthetic Aperture Radar) imaging. The purpose of this work is to improve resolution and target separability of SAR images. This paper proposes SVD-Pseudo Spectrum method whose advantages are noise robustness, reduction of sidelobes and high resolution of spectral estimation. SVD-Pseudo Spectrum method uses Hankel Matrix of signal components and SVD (Singular Value Decomposition) method. In this paper, it is demonstrated that the SVD-Pseudo Spectrum method shows better performance than the matched filtering method and the conventional super-resolution based multiple signal classification (MUSIC) method in SAR image processing. The targets to be separated are modeled, and this modeled data is used to demonstrate the performance of algorithms.

Optimal Trajectory Design of Descent/Ascent phase for a Lunar Lander With Considerable Sub-Phases (Sub-Phase를 고려한 달착륙선의 Descent/Ascent phase 최적 궤적 생성)

  • Jo, Sung-Jin;Min, Chan-Oh;Lee, Dae-Woo;Cho, Kyeum-Rae
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.38 no.12
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    • pp.1184-1194
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    • 2010
  • The descent and ascent phases for a lunar lander are composed of several phases. Accordingly, the constraints and control values adequate for each phase are required in order to generate optimal lander's trajectory. The optimal trajectories for descent and ascent phases are generated by the cost function to minimize fuel consumption & attitude variation rates. In this paper, the optimal control problem to make trajectory uses Gauss pseudo-spectral method which is one of the direct approach method. This problem generates lander's reference trajectory, states and controls.

Time Domain Acoustic Propagation Analysis Using 2-D Pseudo-spectral Modeling for Ocean Environment (해양환경에서 2차원 유사 스펙트럴 모델링을 이용한 시간 영역 음 전달 해석)

  • Kim Keesan;Lee Keunhwa;Seong Woojae
    • The Journal of the Acoustical Society of Korea
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    • v.23 no.8
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    • pp.576-582
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    • 2004
  • A computer code that is based on the Pseudo-spectral finite difference algorithm using staggered grid is developed for the wave propagation modeling in the time domain. The advantage of a finite difference approximation is that any geometrically complicated media can be modeled. Staggered grids are advantageous as it provides much more accuracy than using a regular grid. Pseudo-spectral methods are those that evaluate spatial derivatives by multiplying a wavenumber by the Fourier transform of a pressure wave-field and performing the inverse Fourier transform. This method is very stable and reduces memory and the number of computations. The synthetic results by this algorithm agree with the analytic solution in the infinite and half space. The time domain modeling was implemented in various models. such as half-space. Pekeris waveguide, and range dependent environment. The snapshots showing the total wave-field reveals the Propagation characteristic or the acoustic waves through the complex ocean environment.

An Efficient Design Method of Linear-Phase Prototype Lowpass Filter for Near-Perfect Reconstruction Pseudo-QMF Banks (근접 완전재생 Pseudo-QMF 뱅크를 위한 선형위상 프로토타입 저역통과 필터의 효율적인 설계 방법)

  • Jeon, Joon-Hyeon
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.33 no.3C
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    • pp.271-280
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    • 2008
  • M channel near-perfect-reconstruction(NPR) pseudo-QMF banks are a hybrid of conventional pseudo-QMF design and spectral factorization approach where the analysis and synthesis filters are cosine-modulated versions of the prototype-lowpass filter(p-LPF). However, p-LPF H(z) does not have linear-phase symmetry as well as magnitude-distortion optimization since it is obtained by spectral factorization of $2M^{-th}$ band filter $G(z)=z^{-(N-1)}H(z^{-1})H(z)$. A fair amount of attention, therefore, has been focused on the design of filter banks for reducing only alias-cancellation distortion without reconstructed-amplitude distortion. In this paper, we propose a new method for designing linear-phase p-LPF in NPR pseudo-QMF banks, which is based on Maxflat(maximally flat) FIR filters with closed-form transfer function. In addition, p-LPF H(z) is optimized in this approach so that the 2M-channel overall distortion response represented with $G(z)=H^2(z)$ approximately becomes an unit magnitude response. Through several examples of NPR pseudo-QMF banks, it is shown that the peek ripple of the overall magnitude distortion is less than $3.5{\times}10^{-4}\;({\simeq}-70dB)$ and analysis/synthesis filters have the sharp monotone-stopband attenuation exceeding 100 dB.

2-D Forward Modeling on an Explosion Data in Korea (한반도의 폭파자료에 대한 2-D 수치 모델링 연구)

  • Kang, Ik-Bum;Cho, Kwang-Hyun
    • 한국방재학회:학술대회논문집
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    • pp.137-139
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    • 2007
  • To enhance capability on discerning local and regional seismic phases, such as, Pn, Pg, Sn, Rg, etc, within the crust, 2-D numerical forward modeling will be applied to the data obtained from local seismic stations by simulating almost all waves including not only body wave but also surface wave generated without having to explicitly include them under consideration of Q factor. In this study, after getting rid of instrumental response by deconvolution, pseudo-spectral method instead of relying on typical numerical methods, such as, FEM(Finite Element Method) and FDM(Finite Difference Method), will be implemented for 2-D numerical forward modeling by considering velocities of P-wave and S-wave, density, and Q factors. Ultimately, the Power of reaching the enhanced capability on discerning local and regional seismic phases will make it easier for us to identify the seismic source, whether it is originated from man-made explosion or pure earthquake.

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