Relevant bibliographies by topics / Fourier pseudo-spectral method

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Academic literature on the topic 'Fourier pseudo-spectral method'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Fourier pseudo-spectral method"

1

Waxler, Roger, and Doru Velea. "Modeling infrasound propagation using the Fourier pseudo‐spectral method." Journal of the Acoustical Society of America 129, no. 4 (2011): 2444. http://dx.doi.org/10.1121/1.3588004.

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2

Jia-dong, Zheng, Zhang Ru-fen, and Guo Ben-yu. "The Fourier pseudo-spectral method for the SRLW equation." Applied Mathematics and Mechanics 10, no. 9 (1989): 843–52. http://dx.doi.org/10.1007/bf02013752.

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3

Ito, Izumi. "A New Pseudo-Spectral Method Using the Discrete Cosine Transform." Journal of Imaging 6, no. 4 (2020): 15. http://dx.doi.org/10.3390/jimaging6040015.

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The pseudo-spectral (PS) method on the basis of the Fourier transform is a numerical method for estimating derivatives. Generally, the discrete Fourier transform (DFT) is used when implementing the PS method. However, when the values on both sides of the sequences differ significantly, oscillatory approximations around both sides appear due to the periodicity resulting from the DFT. To address this problem, we propose a new PS method based on symmetric extension. We mathematically derive the proposed method using the discrete cosine transform (DCT) in the forward transform from the relation between DFT and DCT. DCT allows a sequence to function as a symmetrically extended sequence and estimates derivatives in the transformed domain. The superior performance of the proposed method is demonstrated through image interpolation. Potential applications of the proposed method are numerical simulations using the Fourier based PS method in many fields such as fluid dynamics, meteorology, and geophysics.
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4

Rashid, Abdur. "The Pseudo-Spectral Collocation Method for Resonant Long-Short Nonlinear Wave Interaction." Georgian Mathematical Journal 13, no. 1 (2006): 143–52. http://dx.doi.org/10.1515/gmj.2006.143.

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Abstract A pseudo-spectral collocation method for a class of equations describing resonant long-short wave interaction is studied. Semi-discrete and fully discrete Fourier pseudo-spectral collocation schemes are given. In fully discrete case we establish a three-level explicit scheme which is convenient and saves time in real computation. We use energy estimation methods to obtain error estimates for the approximate solutions.
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5

Gong, Yuezheng, Qi Wang, Yushun Wang, and Jiaxiang Cai. "A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation." Journal of Computational Physics 328 (January 2017): 354–70. http://dx.doi.org/10.1016/j.jcp.2016.10.022.

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6

Rashid, Abdur, and Ahmad Izani Bin Md Ismail. "A Fourier Pseudospectral Method for Solving Coupled Viscous Burgers Equations." Computational Methods in Applied Mathematics 9, no. 4 (2009): 412–20. http://dx.doi.org/10.2478/cmam-2009-0026.

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AbstractThe Fourier pseudo-spectral method has been studied for a one- dimensional coupled system of viscous Burgers equations. Two test problems with known exact solutions have been selected for this study. In this paper, the rate of con- vergence in time and error analysis of the solution of the first problem has been studied, while the numerical results of the second problem obtained by the present method are compared to those obtained by using the Chebyshev spectral collocation method. The numerical results show that the proposed method outperforms the conventional one in terms of accuracy and convergence rate.
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7

Zhang, Jun, Shimin Lin, and JinRong Wang. "Stability and convergence analysis of Fourier pseudo-spectral method for FitzHugh-Nagumo model." Applied Numerical Mathematics 157 (November 2020): 563–78. http://dx.doi.org/10.1016/j.apnum.2020.07.009.

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8

Qiang, Yicheng, and Weihua Li. "Accelerated Pseudo-Spectral Method of Self-Consistent Field Theory via Crystallographic Fast Fourier Transform." Macromolecules 53, no. 22 (2020): 9943–52. http://dx.doi.org/10.1021/acs.macromol.0c01974.

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9

Zhang, Y., X. B. Hu, and H. W. Tam. "Integrable discretization of nonlinear Schrödinger equation and its application with Fourier pseudo-spectral method." Numerical Algorithms 69, no. 4 (2014): 839–62. http://dx.doi.org/10.1007/s11075-014-9928-7.

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10

Sabetghadam, Fereidoun, and Elshan Soltani. "Simulation of solid body motion in a Newtonian fluid using a vorticity-based pseudo-spectral immersed boundary method augmented by the radial basis functions." International Journal of Modern Physics C 26, no. 05 (2015): 1550053. http://dx.doi.org/10.1142/s0129183115500539.

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The moving boundary conditions are implemented into the Fourier pseudo-spectral solution of the two-dimensional incompressible Navier–Stokes equations (NSE) in the vorticity-velocity form, using the radial basis functions (RBF). Without explicit definition of an external forcing function, the desired immersed boundary conditions are imposed by direct modification of the convection and diffusion terms. At the beginning of each time-step the solenoidal velocities, satisfying the desired moving boundary conditions, along with a modified vorticity are obtained and used in modification of the convection and diffusion terms of the vorticity evolution equation. Time integration is performed by the explicit fourth-order Runge–Kutta method and the boundary conditions are set at the beginning of each sub-step. The method is applied to a couple of moving boundary problems and more than second-order of accuracy in space is demonstrated for the Reynolds numbers up to Re = 550. Moreover, performance of the method is shown in comparison with the classical Fourier pseudo-spectral method.
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