[petsc-users] SNES + linesearch hackery?

[Andrew McRae]

I have a finite element discretisation of the following nonlinear equation:

m*(phi_xx * phi_yy - phi_xy^2) = const,

solving for phi.  Unfortunately, the function m depends on phi in a
complicated way -- let's assume I need to call my own function to handle
this.

I'm using PETSc's SNES  in Python via petsc4py, within the wider
environment of the software Firedrake.

Currently I'm hacking in the m update (and various output diagnostics) by
writing a Python function "fakemonitor" and calling
snes.setMonitor(fakemonitor).  This allows me to update m each nonlinear
iteration.

While this is better than nothing, there's still some problems: if I use
e.g. snes_linesearch_type: "l2", the fnorms for lambda = 1.0, 0.5 and 0.0
are calculated without updating m, and so the step length taken is
(seemingly) far from optimal.  I tried adding a damping parameter, but all
this does is change the lambdas used to generate the quadratic fit; it
doesn't actually make the step length smaller.

Is there some cleaner way to do what I want, perhaps by intercepting the
fnorm calculation to update m, rather than abusing a custom monitor routine?

Thanks,
Andrew
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