On 1/16/19 10:19 AM, [email protected] wrote:
>
> thanks for the reply. I'm working on Immersed Boundary Method and flagella
> swimming, and, more specifically, I'm trying to model a unit square domain,
> which is infinitely replicated in two dimensions, governed by the
> incompressible time-dependent stokes equations for low Reynolds number. For
> this reason I need periodic boundary conditions for velocity in both
> directions, but also for pressure. Therefore, for my unit square domain, I
> need to have *pure* periodicity, i.e.,
>
> \bold{u}_left = \bold{u}_left and p_left = p_right
>
> \bold{u}_bottom = \bold{u}_top and p_bottom = p_top
>
> Does that make sense to you?
Hm, I see. You are thinking of an infinite lattice of flagella at periodic
positions, all of which are swimming in synchrony. (They should make that an
Olympic sport!) You then just cut out one lattice square. I guess the boundary
conditions make sense then.
> My main problem with that is that when I'm trying to use the Block
> Preconditioner for the time-dependent Stokes (without convection), i.e. when
> I
> need to form the {\tilde{S}}^{-1} \approx [B^T (diag M)^{-1} B]^{-1} +
> \Delta{t}(\nu)M_p^{-1}, I have problems to invert the B^T (diag M)^{-1} B -
> it
> says not invertible. Any ideas?
The term
B^T (diag M)^{-1} B
is not invertible if one of the following three conditions is true:
* B is an n x m matrix where m>n, i.e., it is not "tall and skinny"
* B is an n x m matrix with n<=m but its column rank is less than n.
* (diag M) is not invertible.
You can now work your way down this list and check which condition is the
problem. For example, I would check that all diagonal entries of M are in fact
nonzero (you most likely want them to actually be positive as well).
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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