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Add newton solver for VariationalDensityAdvection

Valentin Carlier requested to merge newton_density into devel

Solves the following issue(s):

Closes #253 (closed) partially closes #256 (closed) (the problem is now on VariationalMagFieldEvolve and will be solved in a future PR)

Core changes:

Updated the VariationalDensityAdvection propagator to use a Newton algorithm to solve the non-linear system instead of the previous Picard iteration. A smaller number of iteration is required (around 6) but a the moment they are quite costly because of the linear system to assemble and solve. I also changed for GMRES solver and use an adapted x0 in order to have better results.

At the moment the computation on simple geometries are slower then with Picard solver but the gain in stability might allow to use larger time steps and make possible the use of more complex geometries (for example Tokamak geometry is no longer a problem).

Update psydac to version 0.1.12 : add the possibility to use recycle flag in linear solvers and use it in Newton algorithm

Model-specific changes:

None

Documentation changes:

None

Edited by Valentin Carlier

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