Pretty much the question. Given a general sparse, non-symmetric (both numerically and structurally) matrix, how important is the sparsity pattern (i.e. row/column permutation of matrix/vector) for iterative solvers? I can see it becomes important for direct solvers (LU) or preconditioners (ILU) by directly affecting the number of fill-ins.
For iterative solvers, however, it seems that the most important part is the MatVec operation which does not seem to care about the actual matrix pattern. Is there some component that could be depended on the pattern that I'm not considering here?
How about in parallel? I suspect the pattern could become important in the way the matrix and vectors are distributed and thus determines the communication volume/overhead but would like to see other thoughts and inputs.
I'm asking this both in general and also regarding PETSc's KSP solvers.