Chebyshev pseudospectral method for wave equation with absorbing boundary conditions that does not use a first order hyperbolic system

2010 ◽  
Vol 80 (11) ◽  
pp. 2124-2133 ◽  
Author(s):  
F.S.V. Bazán
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Hyperbolic System ◽  
Pseudospectral Method ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Chebyshev Pseudospectral Method ◽  
First Order ◽  
Chebyshev Pseudospectral

Optimized first-order absorbing boundary conditions for anisotropic elastodynamics

2019 ◽  
Vol 350 ◽  
pp. 719-749 ◽  
Author(s):  
Daniel Rabinovich ◽  
Shmuel Vigdergauz ◽  
Dan Givoli ◽  
Thomas Hagstrom ◽  
Jacobo Bielak
Keyword(s):  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
First Order

Stability of wide‐angle absorbing boundary conditions for the wave equation

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1153-1163 ◽  
Author(s):  
R. A. Renaut ◽  
J. Petersen
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wide Angle ◽  
Courant Number ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Artificial Boundaries

Numerical solution of the two‐dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approximations to the one‐way wave equation and is commonly called an absorbing boundary. Here we investigate order 2 absorbing boundary conditions which include the standard paraxial approximation. Absorption properties are compared analytically and numerically. Our numerical results confirm that the [Formula: see text] or Chebychev‐Padé approximations are best for wide‐angle absorption and that the Chebychev or least‐squares approximations are best for uniform absorption over a wide range of incident angles. Our results also demonstrate, however, that the boundary conditions are stable for varying ranges of Courant number (ratio of time step to grid size). We prove that there is a stability barrier on the Courant number specified by the coefficients of the boundary conditions. Thus, proving stability of the interior scheme is not sufficient. Furthermore, waves may radiate spontaneously from the boundary, causing instability, even if the stability bound on the Courant number is satisfied. Consequently, the Chebychev and least‐squares conditions may be preferred for wide‐angle absorption also.

scholarly journals Absorbing boundary conditions for wave‐equation migration

Geophysics ◽  
1980 ◽  
Vol 45 (5) ◽  
pp. 895-904 ◽  
Author(s):  
Robert W. Clayton ◽  
Björn Engquist
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Final Section ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Seismic Section ◽  
Difference Wave ◽  
Different Types ◽  
Almost All ◽  
The Cost

The standard boundary conditions used at the sides of a seismic section in wave‐equation migration generate artificial reflections. These reflections from the edges of the computational grid appear as artifacts in the final section. Padding the section with zero traces on either side adds to the cost of migration and simply delays the inevitable reflections. We develop stable absorbing boundary conditions that annihilate almost all of the artificial reflections. This is demonstrated analytically and with synthetic examples. The absorbing boundary conditions presented can be used with any of the different types of finite‐difference wave‐equation migration, at essentially no extra cost.

Enhancing the PML absorbing boundary conditions for the wave equation

2005 ◽  
Vol 53 (3) ◽  
pp. 1242-1246 ◽  
Author(s):  
Y.S. Rickard ◽  
N.K. Nikolova
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary

Conformal absorbing boundary conditions for the vector wave equation

1993 ◽  
Vol 6 (16) ◽  
pp. 886-889 ◽  
Author(s):  
A. Chatterjee ◽  
J. L. Volakis
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Vector Wave ◽  
Vector Wave Equation
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