Hi Wolfgang, that's exactly the problem, 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?
Best, Magda On Wednesday, January 16, 2019 at 7:31:50 PM UTC-5, Wolfgang Bangerth wrote: > > On 1/16/19 10:19 AM, [email protected] <javascript:> 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. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: [email protected] > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
