Non-central periodic operators?

[jlchan]

Would it be possible to support upwind/downwind stencils for periodic operators? For example, I am hoping to use the interior stencil of Mattsson2017(:minus/:plus) but for a periodic domain. I would very much like to take advantage of the specialized mul! if possible.

Thanks!

[ranocha]

That's already possible by specifying a left_offset, see https://ranocha.de/SummationByPartsOperators.jl/stable/api_reference/#SummationByPartsOperators.periodic_derivative_operator

[ranocha]

I'm on my phone right now so I can't check whether these give you exactly the same coefficients Ken Mattsson used in the interior but I think they should

[jlchan]

Thanks! Will try it out this afternoon.

[ranocha]

Please come back to me if there are any questions or problems. I should probably mention this feature a bit more prominently in the docs, too...

[jlchan]

The Q matrix entries indeed appear to be the same! The (non-boundary) mass matrix entries differ slightly between the operators, but I think that is to be expected. Thanks for the tip!

[ranocha]

Do you use the same number of nodes? To get equivalent results, you need to use one node less for periodic operators since the right boundary node is set by periodicity. Then, you should get the same D and M in the interior.

[jlchan]

That completely explains it. Thanks!