uploading the implicit12 solver files

[maqsoodrajput]

I have designed a new solver that is faster than the default Rosenbrock solvers. This new solver is inspired by the IMEX solver. I developed it using the standard BE and Sdirk2a because an explicit method would not work for stiff problems. This new solver gave me a 5X speed-up when I used it with the ICON-ART model. The speed-up outweighed the minor loss in accuracy.

There are two files added:

• implicit12.f90
• implicit12.def

[yantosca]

Thanks @maqsoodrajput for this. I am at the International GEOS-Chem Conference this week so I may be slow to get to this PR. But this sounds like a great new feature for KPP. I can also try to set up the C-I tests for this integrator.

Also tagging @RolfSander @obin1 @msl3v @jimmielin

[msl3v]

@maqsoodrajput excellent!

[RolfSander]

Thanks @maqsoodrajput for providing the new KPP integrator! I will run it with my MECCA chemistry and compare it to Rosenbrock. Hopefully, I'll find the time next week for this...

[yantosca]

@maqsoodrajput @RolfSander: I have been running into an issue where the updated time isn't getting passed back via RSTATUS. I set up a test case with the small_strato mechanism.

   0.0%. T=0.432E+05  O1D= 0.9906E+02; O= 0.6624E+09; O3= 0.5326E+12; NO= 0.8725E+09; NO2= 0.2240E+09; O2= 0.1697E+17; 
 ### TIN, TOUT, in main    43200.000000000000        44100.000000000000 
 ### ierr:, in sdirk           0 
 ### tinitial, tfinal, in sdirk before calling sdirk_integrator:    43200.000000000000        44100.000000000000  
 ### RSTATUS in Sdirk:   0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000     
 ### RSTATE in Main    0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000        0.0000000000000000     
 ### T   0.0000000000000000 

I'm still digging but this means that the simulation is basically stuck in an infinite loop on the same timestep. Feedback greatly appreciated! My updates are in the feature/imex-solver branch.

[yantosca]

I'm still digging but this means that the simulation is basically stuck in an infinite loop on the same timestep. Feedback greatly appreciated! My updates are in the feature/imex-solver branch.

I've added the following code at the end of SDirk_Integrator, which solves the issue in the previous comment:

!~~~>  End of simplified Newton iterations

      ! Successful return
      Ierr  = 1

      ! Return updated time
      RSTATUS(Ntexit) = Tfinal
      RSTATUS(Nhexit) = H

      END SUBROUTINE SDIRK_Integrator

Let me know if you all think this isn't the right thing to do.

[RolfSander]

@maqsoodrajput: Would you like to write a few lines about your new solver which we can add to our KPP documentation? Probably somewhere here: https://kpp.readthedocs.io/en/stable/tech_info/07_numerical_methods.html#sdirk