dolfin team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

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.

> 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



> 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.

Garth

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