Solving equations with self-defined linear_solver

Sure, you just need to assemble the linear algebra objects, using
assemble. Then you pass the Matrix, A from the bilinear form and the
Vector, b from the linear form, to you linear solver.

johan

On 05/04/2012 02:45 PM, Gerd Wachsmuth wrote:
> New question #195998 on DOLFIN:
> https://answers.launchpad.net/dolfin/+question/195998
>
> Is it possible to solve an equation (a==L or F==0) by a self-defined linear solver?
>
> Assume we have
>
> Equation eq = (a==L);
> LinearSolver *solver = ...;
>
> Is there an easy (e.g. high-level) possibility to solve "eq" with "solver"? The same question applies for nonlinear equations and NewtonSolver.
>

On 05/05/2012 03:40 PM, Johan Hake wrote:
> Sure, you just need to assemble the linear algebra objects, using
> assemble. Then you pass the Matrix, A from the bilinear form and the
> Vector, b from the linear form, to you linear solver.

Sure, but this is a rather low-level implementation. I was thinking of a
_high-level_ method like solve( a==L, u, solver ). Maybe a constructor
like LinearVariationalSolver(problem, lin_solver) would be helpful.

But things are more difficult for nonlinear problems:
One can define a custom NewtonSolver by
      NewtonSolver(lin_solver, la_factory),
but this is more or less useless, since it cannot be passed to
NonlinearVariationalSolver. Instead, one has to _copy_ the class
NonlinearDiscreteProblem (because it is a private subclass). Here I
would propose to make NonlinearDiscreteProblem a sovereign class (such
that one could customizing it by inherited classes).

You can subclass NonlinearProblem, which NonlinearDiscreteProblem
subclasses, and pass that to a NewtonSolver. Is you point that the
present implementation of J and F in the NonlinearDiscreteProblem is so
general that it would be usefull to expose that class, so one can
subclass it and reuse J and F in one way or the other, within the
NonlinearVariationalSolver?

Johan

On 05/07/2012 08:35 AM, Gerd Wachsmuth wrote:
> Question #195998 on DOLFIN changed:
> https://answers.launchpad.net/dolfin/+question/195998
>
> Status: Answered => Open
>
> Gerd Wachsmuth is still having a problem:
> On 05/05/2012 03:40 PM, Johan Hake wrote:
>> Sure, you just need to assemble the linear algebra objects, using
>> assemble. Then you pass the Matrix, A from the bilinear form and the
>> Vector, b from the linear form, to you linear solver.
>
> Sure, but this is a rather low-level implementation. I was thinking of a
> _high-level_ method like solve( a==L, u, solver ). Maybe a constructor
> like LinearVariationalSolver(problem, lin_solver) would be helpful.
>
>
> But things are more difficult for nonlinear problems:
> One can define a custom NewtonSolver by
> NewtonSolver(lin_solver, la_factory),
> but this is more or less useless, since it cannot be passed to
> NonlinearVariationalSolver. Instead, one has to _copy_ the class
> NonlinearDiscreteProblem (because it is a private subclass). Here I
> would propose to make NonlinearDiscreteProblem a sovereign class (such
> that one could customizing it by inherited classes).
>

On 05/07/2012 09:05 AM, Johan Hake wrote:
> You can subclass NonlinearProblem, which NonlinearDiscreteProblem
> subclasses, and pass that to a NewtonSolver.
Do you mean something like

class MyNonlinearSolver : public Nonlinear Solver
{
 ...
 class MyNonlinearDiscreteProblem : public NonlinearDiscreteProblem
 {};
};

? Is it possible to inherit from a private subclass?

> Is you point that the
> present implementation of J and F in the NonlinearDiscreteProblem is so
> general that it would be usefull to expose that class, so one can
> subclass it and reuse J and F in one way or the other, within the
> NonlinearVariationalSolver?
I think it would be convenient in some situations. E.g. if you would
like to add "A.ident_zeros()" to F. Moreover, I have a situation, where
I have two possible initial guesses for the nonlinear problem - there it
would be convenient to have access to F in order to identify the best
initial guess (in terms of smallest initial residual).

However, for my problem concerning custom linear solvers it would also
be sufficient to add a new constructor
NonlinearVariationalSolver(problem, newton_solver).

Thanks Johan Hake, that solved my question.