[petsc-users] PETSc with mesh refinement

[Zou, Ling]

Hi All,

I wonder if there is a good example on how PETSc should work with mesh
refinement. I have done some online search/PETSc-user email search, but did
not find a good one.

Here is my case. Currently, assuming NO mesh refinement (so I know exactly
the problem size, mesh connectivity, non-zero pattern of matrices, etc.)
In a transient simulation, my PETSc code looks like:

========================================================================
SetupVectors(); // unknown vec, old unknown, etc.
SetupResFunc(); // residual function, basically pointing to the discretized
PDE
SetupMatrices(); // allocate memory for preconditioning matrix based on
non-zero pattern (so it is mesh dependent)
                           // I also use finite differencing to get
preconditioning matrix, so there is another MatFDColoring object associated
with the matrix
for (int step = 0; step < max_step; step++)
{
  SNESSolve();
}
========================================================================

This setup works perfectly for my problems.
(I understand it is low efficient to use FD to get the preconditioning
matrix, but it is not a priority to me at this moment).

However, now I would like to do some mesh refinement, so the previous setup
would not work, because the problem size, non-zero pattern of the matrix
and MatFDColoring change with mesh size (and connectivity).
I suppose my code should be changed like this:

========================================================================
SetupVectors();
SetupResFunc();
SetupMatrices();

for (int step = 0; step < max_step; step++)
{
  MeshRefinement(); // I will manage my mesh

  AdjustVectors();   // resize vector
  AdjustMatrices(); // resize matrix, re-allocate memory, adjust non-zero
pattern, etc.

  SNESSolve();
}
========================================================================

The issue is that I understand one should not re-allocate memory to both
PETSc vector and matrix dynamically during simulation, which has been
discussed here:
https://scicomp.stackexchange.com/questions/373/is-it-possible-to-dynamically-resize-a-sparse-matrix-in-the-petsc-library

So, the final questions are:
1) Any good example on PETSc working with mesh refinement?
2) Any suggestion on my proposed code structure?

Best,

Ling
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