Wave operators and asymptotic solutions of wave propagation problems of classical physics

1966 ◽  
Vol 22 (1) ◽  
pp. 37-76 ◽  
Author(s):  
Calvin H. Wilcox
Keyword(s):  
Wave Propagation ◽  
Asymptotic Solutions ◽  
Classical Physics ◽  
Wave Operators

scholarly journals Completeness of the wave operators for scattering problems of classical physics

1971 ◽  
Vol 77 (5) ◽  
pp. 777-783 ◽  
Author(s):  
John R. Schulenberger ◽  
Calvin H. Wilcox
Keyword(s):  
Scattering Problems ◽  
Classical Physics ◽  
Wave Operators

DFT MODAL ANALYSIS OF SPECTRAL ELEMENT METHODS FOR ACOUSTIC WAVE PROPAGATION

2008 ◽  
Vol 16 (04) ◽  
pp. 531-561 ◽  
Author(s):  
GÉZA SERIANI ◽  
SAULO POMPONET OLIVEIRA
Keyword(s):  
Wave Propagation ◽  
Plane Waves ◽  
Spectral Element ◽  
Numerical Dispersion ◽  
Spectral Elements ◽  
Spectral Element Methods ◽  
Wave Operators ◽  
Safe Level ◽  
Novel Approach ◽  
2D And 3D

Spectral element methods are now widely used for wave propagation simulations. They are appreciated for their high order of accuracy, but are still used on a heuristic basis. In this work we present the numerical dispersion of spectral elements, which allows us to assess their error limits and to devise efficient numerical simulations, particularly for 2D and 3D problems. We propose a novel approach based on a discrete Fourier transform of both the probing plane waves and the discrete wave operators. The underlying dispersion relation is estimated by the Rayleigh quotients of the plane waves with respect to the discrete operator. Together with the Kronecker product properties, this approach delivers numerical dispersion estimates for 1D operators as well as for 2D and 3D operators, and is well suited for spectral element methods, which use nonequidistant collocation points such as Gauss–Lobatto–Chebyshev and Gauss–Lobatto–Legendre points. We illustrate this methodology with dispersion and anisotropy graphs for spectral elements with polynomial degrees from 4 to 12. These graphs confirm the rule of thumb that spectral element methods reach a safe level of accuracy at about four grid points per wavelength.

On wave propagation in an inhomogeneous non–stationary medium with an inhomogeneous non-stationary flow

2005 ◽  
Vol 461 (2055) ◽  
pp. 701-710
Author(s):  
Arthur D. Gorman
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Stationary Flow ◽  
Asymptotic Solutions ◽  
Scalar Wave ◽  
Space And Time ◽  
Stationary Medium ◽  
Approximate Wave ◽  
Hamiltonian Properties ◽  
Moving Fluid

An approximate wave equation that models scalar wave propagation in a moving fluid whose ambient properties and flow are inhomogeneous both in space and time is considered. Asymptotic solutions for both non–caustic and caustic regions and some Hamiltonian properties of the equation in both non–caustic and caustic regions are developed.

Eigenfunction expansions and scattering theory for wave propagation problems of classical physics

1972 ◽  
Vol 46 (4) ◽  
pp. 280-320 ◽  
Author(s):  
John R. Schulenberger ◽  
Calvin H. Wilcox
Keyword(s):  
Wave Propagation ◽  
Scattering Theory ◽  
Eigenfunction Expansions ◽  
Classical Physics

scholarly journals A Local Compactness Theorem for Wave Propagation Problems of Classical Physics

1972 ◽  
Vol 22 (5) ◽  
pp. 429-433 ◽  
Author(s):  
John Schulenberger
Keyword(s):  
Wave Propagation ◽  
Compactness Theorem ◽  
Classical Physics ◽  
Local Compactness

Intramural wave propagation in cardiac tissue: Asymptotic solutions and cusp waves

2004 ◽  
Vol 70 (6) ◽  
Author(s):  
O. Bernus ◽  
M. Wellner ◽  
A. M. Pertsov
Keyword(s):  
Wave Propagation ◽  
Cardiac Tissue ◽  
Asymptotic Solutions

Spectral representation and scattering theory for the wave equation with two unbounded media

1993 ◽  
Vol 113 (2) ◽  
pp. 423-447 ◽  
Author(s):  
G. F. Roach ◽  
Bo Zhang
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Stationary Phase ◽  
Scattering Theory ◽  
Spectral Representation ◽  
Fourier Transforms ◽  
Eigenfunction Expansions ◽  
Wave Operators ◽  
Unbounded Media ◽  
Generalized Eigenfunction

AbstractIn this paper, we establish the generalized eigenfunction expansions for wave propagation in inhomogeneous, penetrable media in ℝn(n ≥ 2) with an unbounded interface. We then use them together with the method of stationary phase to prove the existence of the wave operators and to obtain the representations of the wave operators in terms of the generalized Fourier transforms.

The scattering theory of lax and phillips and wave propagation problems of classical physics†‡

1973 ◽  
Vol 3 (1) ◽  
pp. 57-77 ◽  
Author(s):  
James A. La vita ◽  
John R. Schulenberger ◽  
Calvin H. Wilcox
Keyword(s):  
Wave Propagation ◽  
Scattering Theory ◽  
Classical Physics
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