reordering

In reviewing the example of forced convection #162, some suggestions were made to reduce the five-minute run-time. These concern the Navier–Stokes solver rather than forced convection per se, so new issues are being launched to take them up. The first suggestion was:

Maybe precalculating Reverse Cuthill-McKee reordering for the rows and columns of self.S would help a bit but can’t say for sure.

Does reordering help in general? Does it help specifically with meshes imported from Gmsh and systems solved with scipy.sparse.linalg.solve? Does it depend on the block-structure of the matrix? (The Stokes problem as assembled in ex24 has the classic symmetric semidefinite saddle-point structure of the Taylor–Hood velocity–pressure mixed finite elements.) What about iterative solvers like GMRES as in the second suggestion?

The reordering is implemented in skfem.utils.rcm, but is not yet used in the examples.

[kinnala]

I suppose it could be possible to have an option to reorder mesh during initialization as an attempt to reduce fill in. However, I think it should not be enabled by default because it will cause surprising interpretation of the rows/cols of the resulting matrices.

[kinnala]

What you say is most certainly true, but I suppose scipy.sparse.linalg.solve will compute some (possibly better) reordering quite quickly before each solve anyways.