[petsc-dev] New ILU, associativity changes

[Jed Brown]

I notice low-bit differences between the new ILU and versions from last
month.  From one of my tests:

  -Algebraic residual        |x|_1 9.35e-16  |x|_2 2.59e-16  |x|_inf 1.67e-16
  +Algebraic residual        |x|_1 1.09e-15  |x|_2 3.00e-16  |x|_inf 1.67e-16
  -Algebraic residual        |x|_1 6.18e-12  |x|_2 2.59e-13  |x|_inf 4.08e-14
  +Algebraic residual        |x|_1 6.19e-12  |x|_2 2.59e-13  |x|_inf 4.08e-14
  -Algebraic residual        |x|_1 4.85e-12  |x|_2 1.95e-13  |x|_inf 4.73e-14
  +Algebraic residual        |x|_1 4.84e-12  |x|_2 1.95e-13  |x|_inf 4.73e-14
  -Algebraic residual        |x|_1 3.36e-13  |x|_2 1.56e-14  |x|_inf 3.06e-15
  +Algebraic residual        |x|_1 3.32e-13  |x|_2 1.54e-14  |x|_inf 3.05e-15

I'm guessing this comes from traversing rows in the other order during
backsolve.  This is no problem at all since both are equally valid, I
just wanted to note that some rounding effects are visible.

Jed