A Legendre-Galerkin spectral method for constructing atmospheric acoustic normal modes

2018 ◽  
Vol 143 (6) ◽  
pp. 3595-3601 ◽  
Author(s):  
Richard B. Evans ◽  
Xiao Di ◽  
Kenneth E. Gilbert
Keyword(s):  
Spectral Method ◽  
Normal Modes ◽  
Galerkin Spectral Method

scholarly journals A Chebyshev-Tau spectral method for normal modes of underwater sound propagation with a layered marine environment

2021 ◽  
Vol 492 ◽  
pp. 115784
Author(s):  
Houwang Tu ◽  
Yongxian Wang ◽  
Qiang Lan ◽  
Wei Liu ◽  
Wenbin Xiao ◽  
...  
Keyword(s):  
Spectral Method ◽  
Marine Environment ◽  
Sound Propagation ◽  
Normal Modes ◽  
Underwater Sound

scholarly journals A unified Petrov–Galerkin spectral method for fractional PDEs

2015 ◽  
Vol 283 ◽  
pp. 1545-1569 ◽  
Author(s):  
Mohsen Zayernouri ◽  
Mark Ainsworth ◽  
George Em Karniadakis
Keyword(s):  
Spectral Method ◽  
Fractional Pdes ◽  
Galerkin Spectral Method

scholarly journals The Convergence of the Legendre–Galerkin Spectral Method for Constructing Atmospheric Acoustic Normal Modes

2020 ◽  
Vol 28 (03) ◽  
pp. 2050002
Author(s):  
Richard B. Evans
Keyword(s):  
Legendre Polynomials ◽  
Normal Modes ◽  
Sobolev Norm ◽  
Linear Operators ◽  
Basis Sets ◽  
Spectral Approximation ◽  
Spectral Approximations ◽  
Potential Applications ◽  
Galerkin Spectral Method ◽  
Theoretical Results

The asymptotic rate of convergence of the Legendre–Galerkin spectral approximation to an atmospheric acoustic eigenvalue problem is established, as the dimension of the approximating subspace approaches infinity. Convergence is in the [Formula: see text] Sobolev norm and is based on the existing theory [F. Chatelin, Spectral Approximations of Linear Operators (SIAM, 2011)]. The assumption is made that the eigenvalues are simple. Numerical results that help interpret the theory are presented. Eigenvalues corresponding to acoustic modes with smaller [Formula: see text] norms are especially accurately approximated, even with lower dimensioned basis sets of Legendre polynomials. The deficiencies in the potential applications of the theoretical results are noted in connection with the numerical examples.

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