[petsc-users] Rescaling quantites to remove positivity constraints

[Matthew Knepley]

On Thu, Mar 13, 2014 at 6:12 PM, Mani Chandra <mc0710 at gmail.com> wrote:

> Hi,
>
> I'm trying to solve for fluid flows with large density and pressure
> variations using the theta method in the TS module. This inevitably leads
> to negative densities and pressures during the course of the evolution. In
> order to deal with this, I am trying to now solve for log(rho) and log(P)
> instead of rho and P. In order to do this, I changed my initial conditions
> for rho and P to log(rho) and log(P) and inside the residual evaluation
> function I keep the original code unchanged expect that I add the following
> lines above the original code:
>
> rho = exp(logrho)
> P = exp(logP)
>

You must d your scaling such that the output of your residual is log() of
your variables. If that is the case, it
will work.


> since I expect the solution vector x[j][i] to now have logrho and logP
> instead of rho and  P. I now run the simulation with a modified newton
> krylov method and lag the jacobian for every 100 linear solves. The
> jacobian assembly is using colored finite differences. This goes smoothly
> from the point I start the simulation to the first 100 linear solves after
> which it needs to assemble the jacobian again. At this point the nonlinear
> solver crashes and I think something is wrong with the jacobian assembly. I
> checked that the simulation runs till it has to assemble the jacobian the
> second time by varying the lagging by say 10, 20, 30, ... It fails
> everytime it has to assemble the second time.
>
>  When I view the solution using VecView inside TSMonitor during the time
> elasped when the simulation ran, the initial conditions are log(rho) and
> log(P) but the output of the vector actually has rho and P and not log(rho)
> and log(P) which I expect the solver to be solving for. However when I look
> at the .vts files generated by -ts_monitor_solution_vtk, the output is
> log(rho) and log(P).
>
> Should I be doing something else in order to rescale the quantities that
> TS/SNES should solve for instead of what I did above?
>
> The method suggesting that one rescales is described in this paper:
> "A newton-krylov solver for implicit solution of hydrodynamics in
> core-collapse supernova"
>
> http://iopscience.iop.org/1742-6596/125/1/012085/pdf/1742-6596_125_1_012085.pdf
>

I personally think this is a bad idea. They must have guesses that are very
close to the solutions, and
it messes with the accuracy of the discretization.

  Thanks,

     Matt

P.S I also tried the variational inequality SNES solver a while back but it
> didn't really work in enforcing the constraints.
>
> Thanks,
> Mani
>



-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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