Variable Resolution/Coordinate Transformations

[mdfeinstein]

A topic of some interest, particularly for those interested in nano structures, is the ability to have a grid with variable resolution. For instance, there could be a simulation area around a nanostructure with much finer resolution than the rest of the cell, so that the nanostructure can be more accurately modeled while avoiding the computational costs for areas away from the nanostructure that don't need such high resolution. In addition, certain directions may require higher resolution than other directions. Such a feature is implemented in the commercial Lumerical/Ansys FDTD package.

While this feature does not exist in meep, a coordinate transformation method is mentioned in the docs. This method aims to increase the effective resolution of a simulation in a given region by transforming the space and the optical properties.

However, the method itself is not implemented with a python interface, and discussion of using this method is scattered across the Issues trackers (for example...). I hope that this post may become a hub for people to discuss their experience with this method, and to share what worked, didn't work, and any code that can make implementing this method easier. If there is a better forum for this topic, please let me know!