On 3/22/23 10:03, Lucas Myers wrote:
Thanks for the feedback! I have also not found any literature dealing with
this periodic boundary conditions problem -- I doubt I will try to get to the
bottom of it experimentally unless I run into technical issues solving my
particular problem. With both the lifting method and interior penalty method,
it appears that you need knowledge of adjacent cells in assembly; I suspect
this will be difficult (or at least annoying) with periodic boundaries if it's
not already implemented in deal.II.
Not difficult, that's all already there. Look at step-45.
For the triharmonic equation, this is the only thing I've been able to find
<https://nam10.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fpdf%2F1804.03793.pdf&data=05%7C01%7CWolfgang.Bangerth%40colostate.edu%7Cb3c80d79ce8c4a781f3d08db2aef01a8%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C0%7C638150979102895314%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=YRYTbpdtoyWdXhXdAUnasaVqsRd0x0kvTwMmwYCinq0%3D&reserved=0>. It seems quite similar to step-82.
In any case, I will try the method of introducing auxiliary variables (so that
it's just a bunch of coupled Laplace equations).
Yes, that would certainly be easiest if your boundary conditions allow it (and
periodic boundary conditions *should* allow it).
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
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