Multi-Symplectic Fourier Pseudospectral Method for the Kawahara Equation

2014 ◽  
Vol 16 (1) ◽  
pp. 35-55 ◽  
Author(s):  
Yuezheng Gong ◽  
Jiaxiang Cai ◽  
Yushun Wang
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Pseudospectral Method ◽  
Kawahara Equation ◽  
Fourier Pseudospectral Method ◽  
Numerical Examples ◽  
Fourier Pseudospectral ◽  
Energy And Momentum ◽  
The Relationship ◽  
Pseudospectral Scheme

AbstractIn this paper, we derive a multi-symplectic Fourier pseudospectral scheme for the Kawahara equation with special attention to the relationship between the spectral differentiation matrix and discrete Fourier transform. The relationship is crucial for implementing the scheme efficiently. By using the relationship, we can apply the Fast Fourier transform to solve the Kawahara equation. The effectiveness of the proposed methods will be demonstrated by a number of numerical examples. The numerical results also confirm that the global energy and momentum are well preserved.

scholarly journals Prediction of Dynamic Stability Using Mapped Chebyshev Pseudospectral Method

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Jae-Young Choi ◽  
Dong Kyun Im ◽  
Jangho Park ◽  
Seongim Choi
Keyword(s):  
Unsteady Flow ◽  
Three Dimensional ◽  
Pseudospectral Method ◽  
Accurate Method ◽  
Spectral Approach ◽  
Fourier Pseudospectral Method ◽  
Chebyshev Pseudospectral Method ◽  
Fourier Pseudospectral ◽  
Chebyshev Pseudospectral ◽  
Good Agreement

A mapped Chebyshev pseudospectral method is extended to solve three-dimensional unsteady flow problems. As the classical Chebyshev spectral approach can lead to numerical instabilities due to ill conditioning of the spectral matrix, the Chebyshev points are evenly redistributed over the domain by an inverse sine mapping function. The mapped Chebyshev pseudospectral method can be used as an alternative time-spectral approach that uses a Chebyshev collocation operator to approximate the time derivative terms in the unsteady flow governing equations, and the method can make general applications to both nonperiodic and periodic problems. In this study, the mapped Chebyshev pseudospectral method is employed to solve three-dimensional periodic problem to verify the spectral accuracy and computational efficiency with those of the Fourier pseudospectral method and the time-accurate method. The results show a good agreement with both of the Fourier pseudospectral method and the time-accurate method. The flow solutions also demonstrate a good agreement with the experimental data. Similar to the Fourier pseudospectral method, the mapped Chebyshev pseudospectral method approximates the unsteady flow solutions with a precise accuracy at a considerably effective computational cost compared to the conventional time-accurate method.

scholarly journals A study of acoustic characteristics of voluntary expiratory sounds produced before and immediately after swallowing

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Shoma Hattori ◽  
Shinji Nozue ◽  
Yoshiaki Ihara ◽  
Koji Takahashi
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Time Window ◽  
Maximum Amplitude ◽  
Comparison Method ◽  
Window Length ◽  
Acoustic Characteristics ◽  
The Mean ◽  
Time Waveform ◽  
The Relationship

AbstractTo evaluate the expiratory sounds produced during swallowing recorded simultaneously with videofluorographic examination of swallowing (VF) using fast Fourier transform (FFT), and to examine the relationship between dysphagia and its acoustic characteristics. A total of 348 samples of expiratory sounds were collected from 61 patients with dysphagia whose expiratory sounds were recorded during VF. The VF results were evaluated by one dentist and categorized into three groups: safe group (SG), penetration group (PG), and aspiration group (AG). The duration and maximum amplitude of expiratory sounds produced were measured as the domain characteristics on the time waveform of these sounds and compared among the groups. Time window-length appropriate for FFT and acoustic discriminate values (AD values) of SG, PG, and AG were also investigated. The groups were analyzed using analysis of variance and Scheffé's multiple comparison method. The maximum amplitude of SG was significantly smaller than those of PG and AG. The mean duration in SG (2.05 s) was significantly longer than those in PG (0.84 s) and AG (0.96 s). The AD value in SG was significantly lower than those in PG and AG. AD value detects penetration or aspiration, and can be useful in screening for dysphagia.

Sign in / Sign up

Export Citation Format

Share Document