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首页> 美国政府科技报告 >Uniform in Time Asymptotic and Numerical Methods for Propagation in Dielectric Exhibiting Fractional Relaxation and Efficient and Accurate Impedance Boundary Conditions for High-Order Numerical Schemes for the Time- Dependent Maxwell Equations
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Uniform in Time Asymptotic and Numerical Methods for Propagation in Dielectric Exhibiting Fractional Relaxation and Efficient and Accurate Impedance Boundary Conditions for High-Order Numerical Schemes for the Time- Dependent Maxwell Equations

机译：电导传播的均匀时间渐近和数值方法表示时间依赖麦克斯韦方程组的高阶数值格式的分数弛豫和高效精确的阻抗边界条件

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In this paper we examine the small- and large-depth response of a Cole-Cole dielectric half-space subjected to a prescribed incident pulse; the case of delta-function incidence is employed to determine and analyze the resulting impulse response. Our purpose is to contrast our findings to the corresponding ones obtained for the Debye model in order to ascertain whether the time-domain waveforms obtained in a TDR experiment could serve as a means for selecting the most appropriate frequency-domain model for the experimentally obtained dielectric data. Our approach involves both asymptotic and numerical methods. We find that the Cole-Cole model's impulse response is in find that the Cole-Cole model's impulse response is infinitely smooth at the wavefront (small-depth), and determine its shape. It follows that sawtooth and square-pulse waveforms, and all other realistic waveforms, become smooth after travelling a brief time in any Cole-Cole model. This is in contrast to the case of the Debye impulse response which is discontinuous at the wavefront.

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