[petsc-users] Setting up a matrix for Lagrange multiplier

[Karthikeyan Chockalingam - STFC UKRI via petsc-users]

Hello,

I'm solving a problem using the Lagrange multiplier, the matrix has the form

K = [A P^T
       P   0]

I am familiar with constructing K using MATMPIAIJ. However, I would like to 
know if had [A], can I augment it with [P], [P^T] and [0] of type MATMPIAIJ? 
Likewise for vectors as well.

Can you please point me to the right resource, if it is a common operation in 
PETSc?

Many thanks.

Kind regards,
Karthik.