Hi Daniel and Wolfgang,
When I apply periodic boundary conditions only on velocities at all the
four sides of my unit square domain, then the rank of B (mxn) becomes
rank(B) = n-1, which I think is as you say due to the fact that the
pressure is up to a constant . However, when I try to impose periodic
boundary conditions for both velocities AND pressure, then the rank of B
becomes much less than the number of its columns and there comes my problem
with inverting the B^T (diag M)^{-1} B.
Any suggestions how to overcome this problem? I've tried to release some
nodes on the boundaries (i.e. have periodic b.c. on all the sides except
from 4 nodes - 1 free node per side) but still not working.
Thank you in advance!
Best,
Magda
On Thursday, January 17, 2019 at 7:17:25 PM UTC-5, Daniel Arndt wrote:
>
> Magda,
>
> [...]
>>
> B has rank much less than the number of columns which is due to the fully
>> periodic boundary conditions and the corresponding sparsity pattern. So I
>> don't know how I could solve this issue. Any ideas?
>>
> Can you identify the corresponding eigenvector of B^T B? I would still not
> be surprised if the pressure is only unique up to a constant implying that
> a vector representing a constant pressure is such an eigenvector.
>
> Best,
> Daniel
>
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