How to solve block matrix in fenics

General
1

How we can solve block matrix in FEniCS. Provide some reference.

a = inner(grad(u), grad(v)) * dx 
I have two set of nodes: Let us assume i have 5 nodes
I = {1,2,3}
J = {4,5}
[ a(I,I)  a(I,J)
  a(J,I)  a(J,J)]

Can i do this thing in FEniCS.

2

Yep, it’s entirely possible for subsets of DoFs, but rather esoteric and therefore you’d need to implement it yourself.

As a starting point you could consider the Stokes demo dolfinx/demo_stokes.py at main · FEniCS/dolfinx · GitHub and perhaps the static condensation demo dolfinx/demo_static-condensation.py at main · FEniCS/dolfinx · GitHub

A crude but effective way may be to assemble into a PETSc matrix, and then extract the sub blocks using an index set.