without using DoFRenumbering::Cuthill_McKee, but with using
DoFRenumbering::component_wise to ensure that degrees of freedom are
appropriately sorted into their corresponding blocks of the matrix and
-vector, then we get the following image after the first adaptive
+vector), then we get the following image after the first adaptive
refinement in two dimensions:
@image html step-22.2d.sparsity-nor.png
effects are also visible for the other blocks. In this case, the ILU
decomposition will be much closer to the full LU decomposition, which improves
the quality of the preconditioner. (It may be interesting to note that the
-sparse direct solver UMFPACK does some internal renumbering of the equations
+sparse direct solver UMFPACK does some %internal renumbering of the equations
before actually generating a sparse LU decomposition; that procedure leads to
a very similar pattern to the one we got from the Cuthill-McKee algorithm.)
// (and its block variant
// BlockCompressedSimpleSparsityPattern)
// has exactly the same interface, uses a
- // different internal data structure and
+ // different %internal data structure and
// is linear in the number of degrees of
// freedom and therefore much more
// efficient for large problems. As
// another alternative, we could also
// have chosen the class
// BlockCompressedSetSparsityPattern that
- // uses yet another strategy for internal
+ // uses yet another strategy for %internal
// memory management. Though, that class
// turns out to be more memory-demanding
// than
// abbreviations for the data structures
// that hold the local matrix, right
// hand side, and global
- // numbers of the degrees of freedom
+ // numbering of the degrees of freedom
// for the present cell.
template <int dim>
void StokesProblem<dim>::assemble_system ()