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Contents

0. JFNK Solver (PETSc option)
1. Known Velocity
2. Petsc Nonlinear Solver [EXPERIMENTAL]
3. FASMGAMR [EXPERIMENTAL]
4. Python
5. Inverse Vertically Integrated Velocity Solver

BISICLES ice velocity

The ice velocity calculation depends at minimum on the ice sheet geometry and the in-ice and basal stresses. It may also depend on the thermodynamics and other factors that influence the in-ice and basal stresses.

If you have built the doxygen code documentation, the C++ class hierarchy underlying the ice velocity calculation is described at classIceVelocitySolver.html

An ice velocity model is specified at run time by setting

  amr.velocity_solver_type = < integer solver_type, default 1 >

Additional options include

  amr.velocity_solver_interval = < integer n, default 1 > recompute the velocity every n timesteps.
  amr.regrid_interval = < integer m, default 1 > recompute the mesh and velocity every m timesteps.

Options for < solver_type > are

0. Picard Solver [deprecated, because the JFNKSolver provides the same functionality]
1. JFNK Solver (the default) solves the vertically integrated (SSA, L1L2) stress equations using a matrix-free Newton method.
2. Known Velocity specifies a known velocity
3. Petsc Nonlinear Solver [EXPERIMENTAL] solves the vertically integrated (SSA, L1L2) stress equations using a PETSc SNES.
4. FASMGAMR [EXPERIMENTAL] A full-approximation storage solver for the vertically integrated (SSA, L1L2) stress equations.
5. Python specifies velocity through the python interface
6. Inverse Vertically Integrated Velocity Solver Estimates the basal friction and stiffness coefficients in order to provide a velocity field that fits observations.

JFNK Solver

BISICLES JFNK (Jacobian-free Newton-Krylov) solver solves the nonlinear vertically integrated (SSA, L1L2) stress equations using a matrix-free Newton method. It is the default for conventional (forward) simulations, and is also used by the Inverse Vertically Integrated Velocity Solver. BISICLES spends around 95% of its time solving the stress equations, and it is also the calculation most likely to fail. That said, it often fails or perform poorly when the input conditions - basal traction, ice thickness, boundary conditions - are incorrect in some way. For example, a region of floating ice unconnected to either grounded ice, a rocky wall, or a domain boundary with Dirichlet conditions does not have a unique solution - it is an ill-posed problem. So if you have problems - especially on time step 0 - check the input data first, especially the geometry and the basal traction.

However, problems that are in theory well-posed but ill-conditioned - for example the Drygalski ice tongue - can see their iterations diverge, and in those cases paying attention to the JFNKSolver options can be useful. The most useful course in such cases is to try the PETSc linear solvers

Option: PETSc linear solvers

By default, the JFNK solver uses the Chombo geometric multigrid (GMG) linear solvers to compute the Newton step. If you find that convergence of the velocity solver is stalling (or even diverging), you might want to try a PETSc algebraic multigrid (AMG) solver. To switch to the PETSc solvers,

1. You will need a .petsrc file to tell the PETSc solvers what to do. PETSc has an enormous range of options, but the important thing is to use a suitable preconditioner because the PETSc default does not work well in many cases. We usually find the HYPRE BoomerAMG solver. to work well. A minimal .petscrc file would be something like

   #.petsrc
   #use the hypre / boomeramg preconditioner
   -pc_type hypre
   -pc_hypre_type boomeramg
   #gmres is the safe (and default) option for a KSP method. bcgs is sometimes quicker
   -ksp_type gmres
   #this makes the output less confusing, but it is optional
   -ksp_norm_type unpreconditioned
   #sensible values? depends what you are doing
   -ksp_max_it 20
   -ksp_rtol 1.0e-4
   #include this to see log the PETSc solver progress in pout.X etc
   -ksp_monitor
       

2. Edit your BISICLES input file. There are two ways to use PETSC:
   • As a bottom solver in the Chombo GMG solver. (if you don't know what that means, don't worry -- suffice it to say that in many cases, this option occupies the middle ground between the Chombo native GMG solvers and a full AMR AMG solver.). Assuming you are using the JFNKSolver for your velocity solve, add the following line to your inputs file:

     JFNKSolver.bottom_solver_type = 1
     

   • If that doesn't help, then you're ready for the full AMR PETSc solver. Assuming once again that you're using the JFNKSolver, then change

      
       JFNKSolver.solverType = 0
       JFNKSolver.normType = 0
     

     to

      
       JFNKSolver.solverType = 4
       JNKKSolver.normType = 2
     

Known Velocity

Petsc Nonlinear Solver

FASMGAMR

Python

Inverse Vertically Integrated Velocity Solver