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n the paper, based on the theory of the remainder effects of difference schemes, some typical limiters are analysed and compared. For different limiters, the different strength of numerical dissipation and dispersion of schemes is the reason why the schemes show obvious different characteristics. After analysing and comparing the numerical dissipation and dispersion of various schemes, a new kind of limiter is proposed. The new scheme has high resolution in sharp discontinuities, and avoids the “distortion”...

n the paper, based on the theory of the remainder effects of difference schemes, some typical limiters are analysed and compared. For different limiters, the different strength of numerical dissipation and dispersion of schemes is the reason why the schemes show obvious different characteristics. After analysing and comparing the numerical dissipation and dispersion of various schemes, a new kind of limiter is proposed. 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. Numerical experiments show that the scheme has good properties.

本文利用差分方法余项效应理论,分析比较了一些典型的限制因子·对不同的限制因子,格式的表现明显差异主要是由其数值耗散性、色散性强弱不同所致·在分析比较格式的数值耗散性、色散性之后,本文提出了一种新的限制因子,得到的格式在解的剧烈变化区具有更高的分辨率,在光滑区避免了由于数值色散性较强导致的失真·数值试验表明该格式具有较好的性质·

It is constructed the Liao′s absorbing boundary condition for the finite difference time domain method with four order difference in space ((2,4)FDTD).The effectiveness of the new method whose numerical velocity error is much less than the ordinary finite difference time domain method with two order difference in both time and space domain has been proved.The method makes the (2,4) FDTD suitable for practical application,especially for simulating devices with harger structures,such as optical fiber waveguides....

It is constructed the Liao′s absorbing boundary condition for the finite difference time domain method with four order difference in space ((2,4)FDTD).The effectiveness of the new method whose numerical velocity error is much less than the ordinary finite difference time domain method with two order difference in both time and space domain has been proved.The method makes the (2,4) FDTD suitable for practical application,especially for simulating devices with harger structures,such as optical fiber waveguides.

建立了在空间上用四阶差分的时域有限差分法的 L iao氏吸收边界 ,证明了四阶差分具有比二阶差分更小的数值色散 .空间上用四阶差分的时域差分法将有助于人们对尺寸较大的物体如光纤等光波导的数值分析 .

 
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