dolfin team mailing list archive

[Johan Hake <johan.hake@xxxxxxxxx>]

On Tuesday 23 December 2008 18:11:59 Anders Logg wrote:
> On Tue, Dec 23, 2008 at 05:02:47PM +0000, Garth N. Wells wrote:
> > Anders Logg wrote:
> > > On Tue, Dec 23, 2008 at 03:28:44PM +0000, Garth N. Wells wrote:
> > >> Anders Logg wrote:
> > >>> Why is there a pseudo time-stepping algorithm built into
> > >>> NonlinearPDE::solve?
> > >>
> > >> So that the PDE can be solved with a series of Newton steps and
> > >> boundary conditions can functions of pseudo time t.
> > >>
> > >> Will it not converge if we just call the
> > >>
> > >>> NewtonSolver directly?
> > >>
> > >> Not always.
> > >
> > > ok.
> > >
> > >>> It would be better if the LinearPDE and NonlinearPDE only provided a
> > >>> layer between the forms and the linear/nonlinear solvers.
> > >>>
> > >>> If we need a pseudo time-stepping algorith, it can be built into
> > >>> NewtonSolver, or maybe another class?
> > >>
> > >> I wouldn't put it NewtonSolver. Best to keep NewtonSolver abstract
> > >> (i.e. unaware of PDEs) and just let it perform Newton solves. We could
> > >> create a class like NonlinearSolver or NonlinearPDESolver.
> > >
> > > NonlinearPDESolver would not be consistent with the current LinearPDE
> > > class which is in some sense is a solver for linear PDEs.
> > >
> > >> Most nonlinear PDEs are sufficiently complex and the solution methods
> > >> so diverse that for non-trivial problems I would expect that a user
> > >> will implement the solution procedure, and a NonlinearPDE class is not
> > >> very useful. Perhaps we could just provide more building blocks to
> > >> make the construction of nonlinear solvers easy?
> > >
> > > I would be inclined to just remove the NonlinearPDE class and
> > > implement the pseudo time-stepping directly in the demo:
> >
> > This is what I do in practice all the time, so removing NonlinearPDE is
> > fine with me.
>
> ok. I'll fix when I get a chance.
>
> > > while t < T:
> > >
> > >    A = assemble()
> > >    b = assemble()
> > >    bc.apply()
> > >
> > >    newton_solver.solve(...)
> > >
> > >    f.t = t
> > >    bc.t = t
> >
> > I added a Python class to take care of the time (it's in dolfin_time.py).
> >
> > >    t += dt
>
> Wouldn't it be simpler to just use a float? If one defines
>
>   f = Function(V, "t*sin(x[0])")
>
> then one may automatically change the variable t by
>
>   f.t = t
>
> thanks to some fancy magic Johan cooked up in the new Python Function
> class(es).

This cook up is all Martins original work, I only made it more easily 
accesable.

Johan

> > > I've also been thinking about the LinearPDE class. Perhaps we should
> > > rename it to VariationalProblem?
> >
> > Sounds good. Solving nonlinear PDEs usually involves solving a series of
> > variational problems, so we could later develop a design in which a
> > VariationalProblem can be sent to a nonlinear solver.
>
> ok. Should it be VariationalProblem or just VarProblem?