

() explicit convection:  (solves faster, but goes unstable)fire %  main -f gr16 -parabolic -snes_monitor -snes_rtol 1e-3 ksp_rtol 1e-5 -Nsteps 20 -snes_atol 1e-10 -convection
iter = 0, SNES Function norm 3.52034e-14 
the number of its, 0
iter = 0, SNES Function norm 2.52743 
iter = 1, SNES Function norm 0.00500977 
iter = 2, SNES Function norm 3.1042e-06 
time step 0: the number of its, 2
iter = 0, SNES Function norm 7.34078 
iter = 1, SNES Function norm 0.0422274 
iter = 2, SNES Function norm 0.000139745 
time step 1: the number of its, 2
iter = 0, SNES Function norm 11.4669 
iter = 1, SNES Function norm 0.00227065 
time step 2: the number of its, 1
iter = 0, SNES Function norm 14.45 
iter = 1, SNES Function norm 0.00260553 
time step 3: the number of its, 1
iter = 0, SNES Function norm 16.0568 
iter = 1, SNES Function norm 0.00491542 
.
.
.
time step 9: the number of its, 1
iter = 0, SNES Function norm 40.379 
iter = 1, SNES Function norm 0.00552991 
time step 10: the number of its, 1
iter = 0, SNES Function norm 292.334 
iter = 1, SNES Function norm 0.0451294 
time step 11: the number of its, 1
iter = 0, SNES Function norm 4204.28 
iter = 1, SNES Function norm 0.886918 
time step 12: the number of its, 1
iter = 0, SNES Function norm 766937 
^Cp0_18

() fully implicit
lava % main -f gr16 -parabolic -snes_monitor -snes_rtol 1e-3 ksp_rtol 1e-5 -Nsteps 20 -snes_atol 1e-10
iter = 0, SNES Function norm 3.52034e-14 
the number of its, 0
iter = 0, SNES Function norm 2.52743 
iter = 1, SNES Function norm 0.00500977 
iter = 2, SNES Function norm 3.1042e-06 
time step 0: the number of its, 2
iter = 0, SNES Function norm 7.34078 
iter = 1, SNES Function norm 0.0422274 
iter = 2, SNES Function norm 0.000139745 
time step 1: the number of its, 2
iter = 0, SNES Function norm 11.4565 
iter = 1, SNES Function norm 0.110581 
iter = 2, SNES Function norm 0.00104253 
time step 2: the number of its, 2
iter = 0, SNES Function norm 14.4582 
iter = 1, SNES Function norm 0.19449 
iter = 2, SNES Function norm 0.00526199 
time step 3: the number of its, 2
iter = 0, SNES Function norm 16.0486 
iter = 1, SNES Function norm 0.261595 
iter = 2, SNES Function norm 0.0195697 
iter = 3, SNES Function norm 0.000430398 
time step 4: the number of its, 3
iter = 0, SNES Function norm 16.0712 
iter = 1, SNES Function norm 0.302527 
iter = 2, SNES Function norm 0.0284068 
iter = 3, SNES Function norm 0.000795864 
time step 5: the number of its, 3
iter = 0, SNES Function norm 14.526 
iter = 1, SNES Function norm 0.242367 
iter = 2, SNES Function norm 0.0156003 
iter = 3, SNES Function norm 0.000295574 
time step 6: the number of its, 3
iter = 0, SNES Function norm 11.5646 
iter = 1, SNES Function norm 0.148154 
iter = 2, SNES Function norm 0.00715777 
time step 7: the number of its, 2
iter = 0, SNES Function norm 7.48074 
iter = 1, SNES Function norm 0.0722093 
iter = 2, SNES Function norm 0.00227864 
time step 8: the number of its, 2
iter = 0, SNES Function norm 2.71068 
iter = 1, SNES Function norm 0.0225352 
iter = 2, SNES Function norm 0.000260134 
time step 9: the number of its, 2
iter = 0, SNES Function norm 2.56039 
iter = 1, SNES Function norm 0.00636855 

iter = 2, SNES Function norm 6.15769e-05 
time step 10: the number of its, 2
iter = 0, SNES Function norm 7.34132 
iter = 1, SNES Function norm 0.0170252 
iter = 2, SNES Function norm 0.000225053 
time step 11: the number of its, 2
iter = 0, SNES Function norm 11.4567 
iter = 1, SNES Function norm 0.0508961 
iter = 2, SNES Function norm 0.00163 
time step 12: the number of its, 2
iter = 0, SNES Function norm 14.459 
iter = 1, SNES Function norm 0.101844 
iter = 2, SNES Function norm 0.00579758 
time step 13: the number of its, 2
iter = 0, SNES Function norm 16.0492 
iter = 1, SNES Function norm 0.163147 
iter = 2, SNES Function norm 0.0134325 
time step 14: the number of its, 2
iter = 0, SNES Function norm 16.0708 
iter = 1, SNES Function norm 0.237434 
iter = 2, SNES Function norm 0.0127273 
time step 15: the number of its, 2
iter = 0, SNES Function norm 14.5221 
iter = 1, SNES Function norm 0.248871 
.
.
.
keeps on going well.


() What about.using the explicit method as a preconditioner for the fully implicit?
(the first two time steps are done implicitly)
would like to do a few explicit steps, then correct with implicit.  for now, one of each, but
double the time step
maybe half the dt, then take two explicit steps, then do one implicit solve

lava % main -f gr16 -parabolic -snes_monitor -snes_rtol 1e-3 ksp_rtol 1e-5 -Nsteps 80 -snes_atol 1e-10 -convection -precon:conv -matlab_graphics
iter = 0, SNES Function norm 3.52034e-14 
the number of its, 0
iter = 0, SNES Function norm 0.159188 
iter = 1, SNES Function norm 3.73316e-05 
time step 0: the number of its, 1
iter = 0, SNES Function norm 0.482153 
iter = 1, SNES Function norm 0.000301907 
time step 1: the number of its, 1
iter = 0, SNES Function norm 0.824025 
iter = 1, SNES Function norm 0.000166723 
time step 2: the number of its, 1
iter = 0, SNES Function norm 0.0679778 
iter = 1, SNES Function norm 6.74062e-05 
iter = 0, SNES Function norm 1.15711 
iter = 1, SNES Function norm 0.000208387 
time step 3: the number of its, 1
iter = 0, SNES Function norm 0.0114919 
iter = 1, SNES Function norm 1.50534e-05 
iter = 2, SNES Function norm 1.85386e-08 
iter = 0, SNES Function norm 1.49108 
iter = 1, SNES Function norm 0.000226239 


