XFDTD中外部边界条件的设置

原文地址：XFDTD中外部边界条件的设置作者：浜嗕簡闈炰簡XFDTD中默认的外部边界条件是二阶稳定Liao辐射边界条件。

它可以将辐射或散射的电磁波几乎完全吸收，只有很少的反射。

XFDTD中还有完全匹配层（PML）外部边界条件、完全电导体（PEC）和完全磁导体（PMC）边界条件。

在同一个计算中，不能将Liao和PML边界混合使用。

而且，PML不能和PMC混用，Liao不能和PEC混用。

不恰当的边界条件可能导致不稳定的计算结果。

Liao BoundaryIt is important to understand the differences between the Liao and PML options. Liao is an estimation method. By looking into the FDTD space and back in time, it estimates the electric fields just outside the limits of the FDTD mesh. These estimated values are then used in the FDTD equations inside the space. The Liao estimation assumes that waves are allowed to travel outward from the space but not reflect back in. The Liao method works well provided that there is enough space between the radiating geometry and the outer boundary. Typical limits are at least 15 cells spacing.A homogeneous dielectric may be located against the Liao boundary. For example, in a lossy earth or strip line calculation, the earth or dielectric layer may touch the outer boundary. Liao will usually function well in this situation provided that there are no air gaps within 5 cells of the Liao boundary. Liao assumes homogeneous material within 5 cells, and if this is not the case then the FDTD calculation will usually be unstable with rapidly rising field amplitudes.Since Liao is an estimation method, the size of the FDTD mesh is not increased by using it. Some storage is needed for saving electric values at previous time steps, but this is usually negligible in a typical calculation.PML BoundaryPML is an artificial absorbing material. It absorbs the incident energy as it propagates through the PML layers. Better absorption, that is, smaller reflection, is obtained by adding more layers at the expense of increasing the size of the FDTD mesh.PML 是人工吸波材料。

当波传播到PML 层时，入射能量被吸收。

通过添加更多的PML可以得到更好的吸收，即意味着较小的反射，代价是增加FDTD的网格大小。

For example, consider an FDTD calculation on a mesh using the Liao absorber that is 50 x 60 x 70 cells or a total of 210,000 cells. There is a 15 cell free space border all around the geometry so that the Liao boundaries can provide small reflections. If the Liao is changed to eight PML layers, the geometry mesh will not change. However, outside of this defined mesh region, eight additional FDTD mesh layers are added on each side of the geometry. This means that the actual number of FDTD cells that must be calculated grows to 66 x 76 x 86 or 431,000 cells, more than double. Since PML cells require more arithmetic operations than normal FDTD cells, the time penalty is actually greater.This time penalty for PML is also increased because the PML cells have special equations for both electric and magnetic fields. For an FDTD calculation with no magnetic materials present, the magnetic fields are computed very quickly. However, when PML is added, the magnetic field update equations are more complicated even when no actual magnetic fields are present and this adds to the time penalty.The benefit of using the PML layers is that they provide better absorption than Liao even with only a 5 cell border of free space, and perhaps only 6 PML layers would provide this. In such a situation calculation time would be saved. Making this comparison would require meshing the object again with a smaller free space margin to the outer boundary. This can be done easily in XFDTD using the mesh tab and choosing a smaller padding around the geometry.使用的PML 边界条件的好处是他们即使带有仅 5 单元格边框的自由空间，业比廖边界提供更好的吸收，也许只要6层PML 层就可以做到。

在这种情况将节省计算时间。

要做到这一点，需要重新对对象进行网格划分，在其外部边界上设置更小的自由空间。

这可以在XFDTD 使用Grid网格选项卡，通过选择较小的几何周围填充padding来实现。

Both PML and Liao are offered to provide flexibility. Both methods should provide similar results when properly used although in some cases, particularly when low frequencies (compared to the cell size) are used, PML is superior.PEC boundaryRadiation and scattering calculations require that all six outer boundaries be set as absorbing. In some situations there are advantages to terminating one or more faces of the FDTD geometry space with a perfect electric conductor (PEC). For example, the conducting ground plane of a micro strip could be located on one face of the FDTD space.辐射和散射计算要求外部边界的六个区域均要设置为吸收。

在某些情况下，将FDTD 几何空间的一个或多个面设置为完美的电导体(PEC) 是有利的。

例如，微带天线的导电平面可以置于FDTD 空间的一个面上。

If the outer boundary of the calculation is not free space, a plane wave should not be used to excite the calculation and thefar-zone transformations will not provide correct results for far-zone fields.如果计算域的外部边界不是自由空间，则不能使用平面波来进行计算，而且远场转换也不是远场区域的正确结果。