> On 11 Mar 2021, at 2:48 PM, Mathieu Dutour <[email protected]> wrote: > > On Thu, 11 Mar 2021 at 13:52, Mark Adams <[email protected] > <mailto:[email protected]>> 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
