[chengdi]

AFAIK, renumbering works for sparse matrix to reduce its band width if it is stored as array of diagonals data structure. However, for lduMatrix format used by OpenFOAM, it seems meanlingless to use renumbering because it does not reduce the operations (at least for matrix-vector product) performed by the solvers.

From the point of view of linear algebra, reordering does not change the eigen value of matrix hence its condition number.

So I am confused that why renumbering works for LduMatrix?

We know that each algorithm is also working with data structure. For lduMatrix data structure, how can we find the optimality of its algorithm?