Singularity correction is a meshing option that accurately captures highly varying fields at the edges of both good conductor and PEC geometry.

## Background

## Controls

## Recommendations

Singularity correction should be enabled for critical, metallic design components in which strong and rapidly varying electric and magnetic fields are expected, such as antennas, transmission lines, and resonators. Automatic fixed point detection should also be enabled for such parts in order to place grid lines on the conductor edges.

As with many computational features, there is a certain degree of tradeoff between accuracy and performance. Generally, singularity correction enhances accuracy in the vicinity of every edge it is applied to, but results in a modest computational expense incurred by XF's meshing algorithm and FDTD engine. In most cases, this cost is more than compensated for with quality results from a coarser FDTD grid than would be possible without singularity correction enabled.

## Limitations

Singularity correction is available only for parts assigned either a PEC or good conductor material definition, and is only applied to part edges that are straight and axis-aligned over their entire length. Additionally, straight, axis-aligned edges must reside on an electric grid line in order for singularity correction to be applied during timestepping. Therefore, it is important to also enable automatic fixed point detection for any geometric object for which singularity correction is desired.

The following edges are not subject to singularity correction:

- Off-axis edges
- Curvilinear edges
- Infinitely thin wires
- Axis-aligned edges resulting from the staircase discretization of off-axis edges
- Edges that do not possess a constant wedge angle over their entire length
- Edges of curvilinear faces that result in an indeterminate wedge angle

## 60 GHz Example

To demonstrate singularity correction, S_{11} is computed for a 60 GHz microstrip antenna.

Three simulations are run with varied grid settings. The cells per wavelength determines the maximum cell size in the space and throughout the dielectric based on the frequency range of interest. The boundary refinement ratio determines the minimum cell size in the space and reduces the cell sizes around the conductor edges where there is high field variation. Each simulation utilizes a single NVIDIA K80 GPU.

Simulation 1 | Simulation 2 | Simulation 3 | |
---|---|---|---|

Singularity correction enabled | False | True | False |

Cells per wavelength | 60 | 60 | 150 |

Boundary refinement ratio | 7 | 7 | 9 |

Maximum cell size (um) | 73.3 | 73.3 | 29.4 |

Minimum cell size (um) | 9.2 | 9.2 | 3.3 |

Memory requirement (MB) | 274.6 | 274.7 | 1,184.4 |

Run time | 11 min 57 sec | 17 min 3 sec | 1 hr 52 min |