[petsc-users] Solving subsystem using larger matrix

[Samuel Estes]

Hi,

I have a model in which we alternatively solve two submodels by the finite
element method both on the same unstructured mesh. The first model (call it
model 1) has three degrees of freedom per node while the second model
(model 2) is scalar (one degree of freedom). We are trying several
different implementations but one option that we would like to try is to
use the same matrix for both models. In other words, assuming we have n
nodes then we allocate a square matrix A to have 3*n rows, solve model 1,
and then reuse this matrix to solve model 2. So for model 2 any non-zeros
in the matrix A will be confined to the upper left ninth and the remaining
8/9ths of the matrix are irrelevant to the problem. I have several
questions about how best to implement something like this which I will list
below:

1. The solver requires that the matrix at least have some non-zeros in each
row, otherwise the solution ends up being all NANs. This makes sense as it
is solving the subsystem 0*x=0 which is clearly ill-defined. Is there any
way that I can communicate to PETSc, either through the solver or matrix
classes or some other way, that all I care about is a subsystem and that I
would like to use only a portion of the matrix A, the right hand side and
the solution vector? There are some routines involving submatrices in the
man pages but I'm not sure if they are appropriate for this problem or not.
In particular, the MatGetLocalSubMatrix routine might be what I need but
its not clear to me whether or not this actually copies the array of values
in the submatrix (not desirable due to memory concerns) or if it is just
essentially a pointer to the submatrix of values in the original matrix A
(ideal). Basically, the idea is to use a part of the matrix that we have
without allocating unnecessary extra memory.
2. Is there a way to use multiple local to global mappings for a single
matrix. I have a problem when I try to use the same local to global mapping
from model 1 in model 2. I understand why this is and can fix it but being
able to reset the local to global mapping without destroying the matrix
would be an ideal fix.
3. Any other input on the best way to approach solving a problem like this
using PETSc would be appreciated. I'm somewhat of a novice when it comes to
PETSc so I don't necessarily know all the tools which are available to me.
It seems clear that I've reached a point where the manual and man pages
aren't quite as helpful as they were for more basic operations.

I hope my explanation of the problem and my questions was clear. If not,
let me know and I can try to provide more details. Thanks!

Sam
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20210903/a148c352/attachment.html>