[petsc-users] Block unstructured grid

[Pierre Jolivet]

> On 11 Mar 2021, at 2:48 PM, Mathieu Dutour <mathieu.dutour at gmail.com> wrote:
> 
> On Thu, 11 Mar 2021 at 13:52, Mark Adams <mfadams at lbl.gov <mailto:mfadams at lbl.gov>> wrote:
> Mathieu, 
> We have "FieldSplit" support for fields, but I don't know if it has ever been pushed to 1000's of fields so it might fall down. It might work.
> FieldSplit lets you manipulate the ordering, say field major (j) or node major (i).
> I just looked at it and FieldSplit appears to be used in preconditioner so not exactly relevant.
> 
> What was unsatisfactory?
> It sounds like you made a rectangular matrix A(1000,3e5) . Is that correct?
> That is incorrect. The matrix is of size (N, N) with N = 1000 * 3e^5. It is a square
> matrix coming from an implicit scheme.
> 
> Since the other answer appears to have the same misunderstanding, let me try
> to re-explain my point:
> --- In many contexts we need a partial differential equation that is not scalar.
> For example, the shallow water equation has b = 3 fields: H, HU, HV. There are other
> examples like wave modelling where we have something like b = 1000 fields (in a
> discretization).

I think what you want is MatBAIJ (https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreateBAIJ.html <https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatCreateBAIJ.html>) with bs = 1000, but just like Matt and Mark, I’m not quite sure I understand your notations from below 100%.

Thanks,
Pierre

> --- So, if we work with say an unstructured grid with N nodes then the total number
> of variables of the system will be N_tot = 3N or N_tot = 1000N.
> 
> The linear system has N_tot unknowns and N_tot equations. The entries 
> can be written as idx = (i , j) with 1 <= i <= b   and   1 <= j <= N.
> 
> Thus the non-zero entries in the matrix will be of two kinds:
> --- (idx1, idx2)   with idx1 = (i , j) and idx2 = (i' , j) , 1 <= i, i' <= b and 1 <= j <= N.
> Together those define a block in the matrix.
> 
> --- (idx1, idx2) with idx1 = (i , j) and idx2 = (i, j'), 1<= i <= b and 1<= j, j' <= N.
> For each unknown idx1, there will be about 6 unknowns idx2 of this form.
> 
> Otherwise, the block matrices do not have the same coefficients, so a tensor
> product approach does not appear to be workable.
> 
>   Mathieu

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