Further Developments on the Solution of the Transient Scalar Wave Equation

1985 ◽  
pp. 87-123 ◽  
Author(s):  
W. J. Mansur ◽  
C. A. Brebbia
Keyword(s):  
Wave Equation ◽  
Scalar Wave ◽  
Scalar Wave Equation

Seismic scalar wave equation with variable coefficients modeling by a new convolutional differentiator

2010 ◽  
Vol 181 (11) ◽  
pp. 1850-1858 ◽  
Author(s):  
Xiaofan Li ◽  
Tong Zhu ◽  
Meigen Zhang ◽  
Guihua Long
Keyword(s):  
Wave Equation ◽  
Variable Coefficients ◽  
Scalar Wave ◽  
Scalar Wave Equation

scholarly journals MOTION OF MASSIVE AND MASSLESS TEST PARTICLES IN DYADOSPHERE GEOMETRY

2009 ◽  
Vol 24 (16) ◽  
pp. 1277-1287 ◽  
Author(s):  
B. RAYCHAUDHURI ◽  
F. RAHAMAN ◽  
M. KALAM ◽  
A. GHOSH
Keyword(s):  
Wave Equation ◽  
Test Particle ◽  
Massless Particle ◽  
Jacobi Method ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Test Particles

Motion of massive and massless test particle in equilibrium and nonequilibrium case is discussed in a dyadosphere geometry through Hamilton–Jacobi method. Scalar wave equation for massless particle is analyzed to show the absence of superradiance in the case of dyadosphere geometry.

Modal methods for the scalar wave equation

1983 ◽  
pp. 640-655 ◽  
Author(s):  
Allan W. Snyder ◽  
John D. Love
Keyword(s):  
Wave Equation ◽  
Scalar Wave ◽  
Scalar Wave Equation

An average-derivative optimal scheme for frequency-domain scalar wave equation

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. T201-T210 ◽  
Author(s):  
Jing-Bo Chen
Keyword(s):  
Wave Equation ◽  
Frequency Domain ◽  
Waveform Inversion ◽  
Scalar Wave ◽  
Scalar Wave Equation ◽  
Optimal Scheme ◽  
Phase Velocity Dispersion ◽  
Point Scheme ◽  
Sampling Intervals ◽  
Average Derivative

Forward modeling is an important foundation of full-waveform inversion. The rotated optimal nine-point scheme is an efficient algorithm for frequency-domain 2D scalar wave equation simulation, but this scheme fails when directional sampling intervals are different. To overcome the restriction on directional sampling intervals of the rotated optimal nine-point scheme, I introduce a new finite-difference algorithm. Based on an average-derivative technique, this new algorithm uses a nine-point operator to approximate spatial derivatives and mass acceleration term. The coefficients can be determined by minimizing phase-velocity dispersion errors. The resulting nine-point optimal scheme applies to equal and unequal directional sampling intervals, and can be regarded a generalization of the rotated optimal nine-point scheme. Compared to the classical five-point scheme, the number of grid points per smallest wavelength is reduced from 13 to less than four by this new nine-point optimal scheme for equal and unequal directional sampling intervals. Three numerical examples are presented to demonstrate the theoretical analysis. The average-derivative algorithm is also extended to a 2D viscous scalar wave equation and a 3D scalar wave equation.

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