scholarly journals A uniformly controllable and implicit scheme for the 1-D wave equation

2005 ◽  
Vol 39 (2) ◽  
pp. 377-418 ◽  
Author(s):  
Arnaud Münch
Keyword(s):  
Wave Equation ◽  
Implicit Scheme ◽  
D Wave

A Widely Convergent Generalized Pulse- Spectrum Methods for 2-D Wave Equation Inversion

2003 ◽  
Vol 46 (2) ◽  
pp. 373-380 ◽  
Author(s):  
Guofeng FENG ◽  
Bo HAN ◽  
Jiaqi LIU
Keyword(s):  
Wave Equation ◽  
Pulse Spectrum ◽  
D Wave

3‐D wave‐equation prestack imaging under salt

2000 ◽  
Author(s):  
Biondo Biondi ◽  
Louis Vaillant
Keyword(s):  
Wave Equation ◽  
D Wave

Multipoint Explicit Differencing (MED) for Time Integrations of the Wave Equation

2007 ◽  
Vol 135 (11) ◽  
pp. 3862-3875 ◽  
Author(s):  
Celal S. Konor ◽  
Akio Arakawa
Keyword(s):  
Wave Equation ◽  
Finite Number ◽  
Multilevel Models ◽  
Horizontal Resolution ◽  
Explicit Scheme ◽  
Implicit Scheme ◽  
Courant Number ◽  
Time Step ◽  
Wide Range ◽  
Grid Points

Abstract For time integrations of the wave equation, it is desirable to use a scheme that is stable over a wide range of the Courant number. Implicit schemes are examples of such schemes, but they do that job at the expense of global calculation, which becomes an increasingly serious burden as the horizontal resolution becomes higher while covering a large horizontal domain. If what an implicit scheme does from the point of view of explicit differencing is looked at, it is a multipoint scheme that requires information at all grid points in space. Physically this is an overly demanding requirement because wave propagation in the real atmosphere has a finite speed. The purpose of this study is to seek the feasibility of constructing an explicit scheme that does essentially the same job as an implicit scheme with a finite number of grid points in space. In this paper, a space-centered trapezoidal implicit scheme is used as the target scheme as an example. It is shown that an explicit space-centered scheme with forward time differencing using an infinite number of grid points in space can be made equivalent to the trapezoidal implicit scheme. To avoid global calculation, a truncated version of the scheme is then introduced that only uses a finite number of grid points while maintaining stability. This approach of constructing a stable explicit scheme is called multipoint explicit differencing (MED). It is shown that the coefficients in an MED scheme can be numerically determined by single-time-step integrations of the target scheme. With this procedure, it is rather straightforward to construct an MED scheme for an arbitrarily shaped grid and/or boundaries. In an MED scheme, the number of grid points necessary to maintain stability and, therefore, the CPU time needed for each time step increase as the Courant number increases. Because of this overhead, the MED scheme with a large time step can be more efficient than a usual explicit scheme with a smaller time step only for complex multilevel models with detailed physics. The efficiency of an MED scheme also depends on how the advantage of parallel computing is taken.

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