[petsc-users] preconditioning matrix-free newton-krylov

[Barry Smith]

> On Sep 23, 2017, at 12:48 PM, Mark W. Lohry <mlohry at princeton.edu> wrote:
> 
> I'm currently using JFNK in an application where I don't have a hand-coded jacobian, and it's working well enough but as expected the scaling isn't great.
> 
> What is the general process for using PC with MatMFFDComputeJacobian? Does it make sense to occasionally have petsc re-compute the jacobian via finite differences, and then recompute the preconditioner? Any that just need the sparsity structure?

 Mark

   Yes, this is a common approach. SNESSetLagJacobian -snes_lag_jacobian 

    The normal approach in SNES to use matrix-free for the operator and use finite differences to compute an approximate Jacobian used to construct preconditioners is to to create a sparse matrix with the sparsity of the approximate Jacobian (yes you need a way to figure out the sparsity, if you use DMDA it will figure out the sparsity for you). Then you use 

   SNESSetJacobian(snes,J,J, SNESComputeJacobianDefaultColor, NULL);

and use the options database option -snes_mf_operator


> Are there any PCs that don't work in the matrix-free context?

  If you do the above you can use almost all the PC since you are providing an explicit matrix from which to build the preconditioner

> Are there any example codes I overlooked?
> 
> Last but not least... can the Boomer-AMG preconditioner work with JFNK? To really show my ignorance of AMG, can it actually be written as a matrix P^-1(Ax-b)=0, , or is it just a linear operator?

  Again, if you provide an approximate Jacobian like above you can use it with BoomerAMG, if you provide NO explicit matrix you cannot use BoomerAMG or almost any other preconditioner.

   Barry

> 
> Thanks,
> Mark