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Perfectly matched layer (PML) boundaries for the frequency-domain driven solver #916

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@krono-i2

The user guide lists PML boundaries as not yet implemented. Opening this as a tracking issue for the feature, and to describe a use case that depends on it.

Use case. Scattering and RCS problems in the driven solver (#690). With a known incident field injected on a Huygens surface (Love equivalence), the region outside that surface carries only the scattered field, which then has to leave the domain. A second-order Robin ABC works but its residual reflection is angle-dependent, which is exactly the wrong error to have when the quantity of interest is a bistatic RCS pattern at grazing angles. A PML would make the truncation error essentially independent of the observation angle, and would also help for open radiating structures (finite arrays, metasurfaces under oblique illumination) where the ABC has to be placed uncomfortably far from the source.

Prior work. I noticed there is a simlapointe/pml branch in the repo, so some of this may already exist. Is that work still active, and is there a plan to bring it forward? If it's stalled, I'd be happy to help..

Validation I can contribute either way:

  • reflection coefficient of the layer vs. thickness, profile order and incidence angle, against the analytic PML reflection estimate;
  • bistatic RCS of a PEC sphere, against the Mie series;
  • a regression test on a simple radiating case comparing PML against the existing second-order ABC.

Happy to split this into a separate issue if a PML tracking issue already exists somewhere I haven't found.

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