[petsc-users] indices into Vec/Mat associated to a DMPlex

[Matteo Semplice]

Hi.

I am struggling with indices into matrices associated to a DMPLex mesh. 
I can explain my problem to the following minimal example.

Let's say I want to assemble the matrix to solve an equation (say 
Laplace) with data attached to cells and the finite volume method. In 
principle I

- loop over the faces of the DMPlex (height=1)

- for each face, find neighbouring cells (say points i and j in the 
DMPlex) and compute the contributions coming from that face (in the 
example it would be something like (u_j-u_i)*<x_j-x_i,n> with 
x=centroids, n=scaled normal to face and <,> the inner product)

- insert the contributions +/-<x_j-x_i,n> in rows/columns n(i) and n(j) 
of the matrix where n(k) is the index into Vec/Mat of the unknown 
associated to the k-th cell

My problem is how to find out n(k). I assume that the Section should be 
able to tell me, but I cannot find the correct function to call. I see 
that FEM methods can use DMPlexMatSetClosure but here we'd need a 
DMPlexMatSetCone...

On a side note, I noticed that the grad field in PetscFVFaceGeom is not 
computed by DMPlexComputeGeometryFVM. Is it meant or could it be used to 
store the precomputed  <x_j-x_i,n> values? But even if so, this wouldn't 
sovle the problem of where to put the elements in the matrix, right?

Matteo