dolfin team mailing list archive

["Garth N. Wells" <g.n.wells@xxxxxxxxxx>]

On Tue, 2006-02-21 at 16:09 +0100, Johan Hoffman wrote:
> This sounds like a good plan. But as we said, maybe we should wait to
> specify the format of the time dependent PDE's until we know how these
> will be handled (ODE timestepping or other...).
> 

Sure. I'll start with static linear and nonlinear PDEs.

Garth

> /Johan
> 
> 
> > On Tue, 2006-02-21 at 08:03 -0600, Anders Logg wrote:
> >> I suggest one class PDE that tries to be smart by looking at the
> >> arguments to the constructor and finds out what to do.
> >>
> >
> > Sure. We will still need to explicitly tell the PDE if it is nonlinear,
> > as for simple nonlinear functions, the constructor is the same (no extra
> > information is required). The only difference is the solve function.
> >
> > I've started PDE implementing as outlined below, modelled on the class
> > Function.
> >
> > Garth
> >
> >> Then we have specialized classes as subclasses of GenericPDE and PDE
> >> has a pointer to GenericPDE:
> >>
> >>     class PDE
> >>     {
> >>     public:
> >>
> >>     private:
> >>
> >>       GenericPDE* pde;
> >>
> >>     };
> >>
> >> Maybe the specialized classes at this point should be
> >>
> >>     StaticLinearPDE      (current solver in PDE class)
> >>     StaticNonlinearPDE   (Garth's new nonlinear solver)
> >>
> >> I expect we will add some automation for time-dependent PDEs at some
> >> point and use the ODE-solvers for adaptive time-stepping. Maybe we
> >> can then add
> >>
> >>     TimeDependentLinearPDE
> >>     TimeDependentNonlinearPDE
> >>
> >> Other options would be Transient (but I don't like it since it
> >> indicates something short-lived near t = 0) or Dynamic (which I don't
> >> really like either).
> >>
> >> Maybe we should also have a class called VariationalProblem that just
> >> is a copy of the current PDE class. This can be nice to have to set up
> >> variational problems for projections that are not really PDEs. Perhaps
> >> the StaticLinearPDE class can in turn define a VariationalProblem and
> >> solve it so that we don't have to duplicate the code.
> >>
> >> /Anders
> >>
> >>
> >> On Tue, Feb 21, 2006 at 11:27:07AM +0100, Garth N. Wells wrote:
> >> > Is it preferable to have objects LinearPDE, NonlinearPDE, etc, or just
> >> > one type, PDE, which knows (will be told) whether it is linear,
> >> > nonlinear, time-dependent, etc?
> >> >
> >> > Garth
> >> >
> >> > On Tue, 2006-02-21 at 11:19 +0100, Johan Hoffman wrote:
> >> > > Ok, sounds good. We had a similar structure in early versions of
> >> DOLFIN
> >> > > (StatProblem, TranProblem,...), which I think we removed since we
> >> wanted a
> >> > > more flat structure of PDE tools. But now we have the possibility to
> >> > > automate a lot of features within each class, so I think a
> >> resurrection is
> >> > > motivated.
> >> > >
> >> > > /Johan
> >> > >
> >> > >
> >> > > > I've added the class NonlinearPDE in src/kernel/nls, which has a
> >> very
> >> > > > similar interface to the class PDE, and has similar functionality
> >> for
> >> > > > solving.
> >> > > >
> >> > > > I think that Anders' suggestion to split-up PDE in the same
> >> fashion as
> >> > > > Function is good a good idea. I'm working in it now - at this
> >> stage for
> >> > > > linear and nonlinear PDE's.
> >> > > >
> >> > > > Garth
> >> > > >
> >> > > > On Fri, 2006-02-10 at 14:14 -0600, Anders Logg wrote:
> >> > > >> The new PDE class is now in place and takes care of some of the
> >> > > >> standard stuff you need to do to solve a static linear PDE:
> >> define
> >> > > >> vectors and matrices, assemble bilinear and linear forms, solve
> >> linear
> >> > > >> system and create a Function from the degrees of freedom.
> >> > > >>
> >> > > >> Here's the new version of the Poisson demo:
> >> > > >>
> >> > > >>   // Set up problem
> >> > > >>   UnitSquare mesh(16, 16);
> >> > > >>   Poisson::BilinearForm a;
> >> > > >>   Poisson::LinearForm L(f);
> >> > > >>   PDE pde(a, L, mesh, bc);
> >> > > >>
> >> > > >>   // Solve
> >> > > >>   Function u = pde.solve();
> >> > > >>
> >> > > >>   // Save function to file
> >> > > >>   File file("poisson.pvd");
> >> > > >>   file << u;
> >> > > >>
> >> > > >> This works for all linear static PDEs. I imagine that we can use
> >> the
> >> > > >> PDE class to automate the solution of static nonlinear PDEs,
> >> > > >> time-dependent etc. Depending on the arguments to the constructor
> >> > > >> (among other things), the PDE class would know what to do to
> >> solve the
> >> > > >> system. A first step would be to integrate Garth's Newton-solver
> >> with
> >> > > >> the PDE class. Perhaps we need to partition it in the same way as
> >> the
> >> > > >> Function class (GenericPDE, StaticLinearPDE etc) so it's easy to
> >> > > >> plugin a new solver.
> >> > > >>
> >> > > >> Note that as an alternative to
> >> > > >>
> >> > > >>   Function u = pde.solve();
> >> > > >>
> >> > > >> one can do
> >> > > >>
> >> > > >>   Function u;
> >> > > >>   pde.solve(u);
> >> > > >>
> >> > > >> which is slightly more efficient (avoids one copy of the vector
> >> of
> >> > > >> degrees of freedom).
> >> > > >>
> >> > > >> The PDE class i parametrized and has one parameter "solver", so
> >> you
> >> > > >> can do either
> >> > > >>
> >> > > >>   pde.set("solver", "direct"); // default option
> >> > > >>
> >> > > >> or
> >> > > >>
> >> > > >>   pde.set("solver", "iterative");
> >> > > >>
> >> > > >> /Anders
> >> > > >>
> >> > > >> _______________________________________________
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> >> > > >
> >> > > >
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> >> > > >
> >> > >
> >> > >
> >> > >
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> >
> >
> >
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> 
> 
> 
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-- 
Dr. Garth N. Wells
Faculty of Civil Engineering and Geosciences
Delft University of Technology
Stevinweg 1
2628 CN Delft
The Netherlands

tel.     +31 15 278 7922
fax.     +31 15 278 6383
e-mail   g.n.wells@xxxxxxxxxx
url      http://www.mechanics.citg.tudelft.nl/~garth