dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

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).

> > 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?

-- 
Anders

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