I am solving a problem
\begin{bmatrix}
\pmb{A} & \pmb{B}\\
\pmb{C} & \pmb{D}
\end{bmatrix}
\begin{pmatrix}
\pmb{x}\\
\pmb{y}
\end{pmatrix}
=
\begin{pmatrix}
\pmb{f_x}\\
\pmb{f_y}
\end{pmatrix}
and want to have
\pmb{K_y} = \pmb{D} - \pmb{C}\pmb{A}^{-1}\pmb{B}
\pmb{b_y} = \pmb{f_y} - \pmb{C}\pmb{A}^{-1}\pmb{f_x}
so that I can solve \pmb{K_y}\pmb{y}=\pmb{b_y}.
\pmb{A} is cell-wise block and so can be inverted in parallel cell-wise. I can do the cell-wise inversion (Cell-wise assembly in v10.0.0 - #2 by dokken) but I am unclear how to compile the cell-wise inverses into global inverse \pmb{A}^{-1}.