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numerical dispersion
Genetic algorithm in reduction of numerical dispersion of 3-D ADI-FDTD method
      
A new method to reduce the numerical dispersion of the three-dimensional Alternating Direction Implicit Finite-Difference Time-Domain (3-D ADI-FDTD) method is proposed.
      
Firstly, the numerical formulations of the 3-D ADI-FDTD method are modified with the artificial anisotropy, and the new numerical dispersion relation is derived.
      
In addition the reduction of the numerical dispersion is investigated as the objective function of the AGA.
      
This paper presents the calculation of truncation errors, namely numerical diffusion and numerical dispersion for various finite difference schemes.
      
The difficulties arise from the vast computer resources needed to discretize the entire region of interest and the accumulation of numerical dispersion error.
      
The trial results for the salt model show that the numerical dispersion is decreased to a minimum extent, the accuracy high and diffracted waves abundant.
      
The new scheme has high resolution in sharp discontinuities, and avoids the "distortion" due to the stronger numerical dispersion in the relatively more smooth region.
      
We point out the existence of purely numerical parasitic phenomena and quantify the numerical dispersion relative to guided waves.
      
Numerical dispersion analysis shows that these two schemes are non-dissipative.
      
To avoid large numerical dispersion and dissipation, different grid sizes are used for different material layers so that the CFL number in each layer can be set to one in the limit.
      
Detailed analyses on stability, numerical dissipation and numerical dispersion are also given.
      
Moreover the paper demonstrates how to suppress numerical dispersion and therewith how to use finite difference approximations in general settings.
      
For tracer-transport calculations, we have used a semianalytic transit-time algorithm which is fast, accurate, and free of numerical dispersion.
      
The numerical tests show that the method is nearly numerical dispersion free and permits accurate calculations even for simulations of low-concentration transport.
      
It is also shown that all the three Galerkin methods have restricted ranges of wave numbers and circular frequencies over which the numerical dispersion relation matches with the physical dispersion relation - a central requirement for wave problems.
      
The numerical dispersion and the insertion of lossy media in the One-Step method are evaluated.
      
One of these is the difference in horizontal and vertical scales in natural situations; other difficulties encountered are numerical dispersion and the flow near singularities.
      
Numerical dispersion is suppressed by particle tracking.
      
Simulations performed showed that Schumann's subgrid eddy viscosity was sufficient to spreads out sharp ripples which appeared in the numerical solution due to numerical dispersion.
      
 

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