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An enhanced higher-order FDTD technique for the construction of efficient reflectionless PMLs in 3-D generalized curvilinear coordinate systems

机译：增强的高阶FDTD技术，用于在3-D广义曲线坐标系中构造有效的无反射PML

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摘要

A systematic implementation of reflectionless split and unsplit-field PMLs in 3-D nonorthogonal curvilinear coordinates via a novel higher-order FDTD methodology, is presented. The technique, which introduces both conventional and nonstandard schemes, incorporates a higher-order rendition of the covariant and contravariant vector component theory. Enhanced attenuation performance and levels of accuracy are achieved by means of new conductivity profiles and efficient ABCs terminating the PML, region. Moreover, a progressively expanding curvilinear discretization algorithm leads to a significant reduction of the absorbers' necessary thickness. In the temporal variable, the four-stage Runge-Kutta integrator is invoked, whereas the wider spatial increments near absorbing walls are effectively limited through the use of properly modified compact operators. Numerical verification demonstrates that the proposed higher order curvilinearly structured PMLs offer a considerable decrease in dispersion errors and can be imposed very close to the scatterer, thus attaining notable savings in computational resources.
机译：通过新颖的高阶FDTD方法，系统地实现了3-D非正交曲线坐标系中无反射分裂和非分裂场PML的系统实现。引入常规和非标准方案的技术结合了协变和反协矢量分量理论的高阶表示。通过新的电导率曲线和终止PML区域的高效ABC，可实现增强的衰减性能和精确度。此外，逐渐扩展的曲线离散算法导致吸收器所需厚度的显着减小。在时间变量中，调用了四级Runge-Kutta积分器，而通过使用适当修改的紧致算子，有效地限制了吸收壁附近较宽的空间增量。数值验证表明，提出的高阶曲线结构的PML可以大大降低色散误差，并且可以将其强加在散射体附近，从而显着节省了计算资源。

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