For 1D finite difference, the resulting linear system is tri-diagonal and can be solved in
O(n) using the Thomas algorithm.
I am trying to solve a finite difference system in 3D. Numerical Methods by Quarteroni et al goes over some theory behind extending the Thomas algorithm to block linear systems. This method seems to be ideal for me because it is still
From an algorithmic point of view however, I'm not sure how to proceed. Is there a reference that covers the implementation of this algorithm for a linear system such as the one resulting from 3D finite difference?