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首页> 外文期刊>Microwave and optical technology letters >NUMERICAL VALIDATION OF DISPERSION RELATIONS USING A CYLINDRICAL WAVE FOR 2D FDTD METHODS
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NUMERICAL VALIDATION OF DISPERSION RELATIONS USING A CYLINDRICAL WAVE FOR 2D FDTD METHODS

机译：二维FDTD方法使用圆柱波的色散关系的数值验证

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摘要

The numerical dispersion of a proposed new FDTD scheme is often evaluated and compared with that of well-established FDTD methods. Because there may be a theoretical deficiency in the dispersion analysis, numerical experimentation is often used to validate the dispersion relation. This paper describes the "matching method" for validation using a cylindrical wave in the two-dimensional (2D) case. The matching method is demonstrated by evaluating the numerical dispersion of Yee 's FDTD and ADI-FDTD. The result is compared with the analytical numerical dispersion relation, and excellent agreement is obtained, The difference between the theoretical value for the numerical dispersion and that from numerical experiments using the matching method is 10{sup}(-5)for Yee's FDTD and 10{sup}(-4)-10{sup}(-5) for ADI-FDTD, The numerical velocity obtained from the matching method satisfies the theoretical dispersion relation with residual errors to the order of W6. Such accuracy is sufficient to conclude that a numerical dispersion relation is correct. Although the matching method uses a cylindrical wave to test the numerical dispersion relation, the cylindrical wave is not a solution of the difference equations, thus it cannot be used to derive a theoretical dispersion relation.
机译：经常对提议的新FDTD方案的数值离散进行评估，并将其与完善的FDTD方法进行比较。由于色散分析可能存在理论上的不足，因此经常使用数值实验来验证色散关系。本文介绍了在二维（2D）情况下使用圆柱波进行验证的“匹配方法”。通过评估Yee的FDTD和ADI-FDTD的数值色散来证明匹配方法。将结果与解析的数值色散关系进行比较，并获得了极好的一致性，数值色散的理论值与使用匹配方法的数值实验所得的值之间的差异对于Yee FDTD为10 {sup}（-5），而对于10对于ADI-FDTD，{sup}（-4）-10 {sup}（-5），从匹配方法获得的数值速度满足理论色散关系，残余误差为W6量级。这样的精度足以得出数字色散关系正确的结论。尽管匹配方法使用圆柱波来测试数值色散关系，但是圆柱波不是差分方程的解，因此无法用于推导理论色散关系。

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