Abstract

CHAPTER 2. TEMPORAL INTEGRATION 43
finer grids, the Newton iteration converges to the solution, but the Newton steps are
computationally expensive, as shown by the large average number of Krylov iterations
on these grids.
The preconditioned method is much more efficient at solving this problem. The
largest number of Newton iterations needed is 11 for all the grids, the average number
of Krylov iteration is much lower than the unpreconditioned method and remains
fairly constant as the grids are refined, and there were no step reductions taken in
the preconditioned method.