This paper proposes a scattered field formulation of the finite-difference time domain method (S-FDTD) combining with a time-domain electric field integral equation (TD-EFIE) based on surface equivalence theorem. The scattered field formulation enables us to reduce computation cost effectively forthe case that scatterers are located at a far distance from field sources of electromagnetic wave since we need to calculate the scattered field component only on the region in the vicinity of the scatterers. Then it is required for the use of the scattered field formulation that the field source for the incident field component has to be expressed by any analytical solutions such as a point dipole source, plane wave, and so on. In this work, the scattered field formulation of the FDTD method is applied to cases that there are no analytical expressions of the field sources, in which the field source contains conductors such as antennas, combining with the TD-EFIE on a virtual surface which encloses the field sources. Then, it is known that calculation of the TD-EFIE itself is time consuming. This paper considers speed-up of the S-FDTD simulation based on the TD-EFIE using a spherical harmonic expansion of Green’s function of Helmholtz equation, additionally.

中文翻译：

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利用格林函数的球谐展开加快时域EFIE与FDTD方法的散射场公式的加速

本文提出了一种基于表面等效定理的时域电场积分方程（TD-EFIE），结合时域有限差分时域方法（S-FDTD）和时域电场积分方程（TD-EFIE）的散射场公式。散射场公式使我们能够有效地降低散射体与电磁波场源距离较远的情况下的计算成本，因为我们仅需要在散射体附近的区域上计算散射场分量。然后，对于使用散射场公式，要求入射场分量的场源必须通过任何分析解决方案来表示，例如点偶极子源，平面波等。在这项工作中 FDTD方法的散射场公式适用于没有场源解析表达式的情况，其中场源包含导体（如天线），并与TD-EFIE结合在包围场源的虚拟表面上。然后，已知TD-EFIE本身的计算是耗时的。此外，本文还考虑了基于TD-EFIE的S-FDTD仿真的加速，并使用了亥姆霍兹方程的格林函数的球谐展开。