dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Wed, Feb 25, 2009 at 10:32:19PM +0000, A Navaei wrote:
> 2009/2/25 Anders Logg <logg@xxxxxxxxx>:
> > On Wed, Feb 25, 2009 at 10:05:34PM +0000, A Navaei wrote:
> >> I'm not sure if I'm making sense here. Both of you suggested using
> >> assemble which requires Form which, if I'm not wrong, requires
> >> Function and that needs FunctionSpace which requires Mesh, but I
> >> emphasised that this is no FEM problem :) I'm just trying to get the
> >> best of available LA in dolfin.
> >>
> >> Let me give you a concrete example, have a look at Eq 12 of this paper:
> >>
> >> http://www.mia.uni-saarland.de/Publications/brox-eccv04-of.pdf
> >>
> >> Is it possible to use assemble() to extract A and b out of this
> >> equation? Many of the coefficients in the equation are image data, I
> >> guess I should convert the image data to Matrix and use Variable for
> >> the unknowns?
> >
> > Yes, this would be fine. You just need to set the values in the matrix
> > manually using A.set().
> 
> It's nice to know the automation is also available for non-FE
> approaches. I'll give it a try now.

I wouldn't call it automation if you are setting the entries manually,
but I agree it's good that it's possible to set the entries.

> >
> > But this looks a bit ugly. Why not apply finite elements to solve the
> > PDE?
> 
> I'm not sure if the available non-linear solvers are able to solve the
> highly non-linear Eq 7 directly, can they? The method suggested in the
> paper involves a double-linearisation which needs two nested loops,
> so, solving the final double-linearised equation inside this nested
> loops could be expensive.
> 
> I'm trying to compare the profiling of the finite-element approach and
> the approach in the paper, which could be classified as
> finite-difference as they approximate the equation, and then compare
> the speed and accuracy of the results.

What I mean is that there should be a way to do the same thing as in
the finite difference approximation except that you use FEM instead
for the space discretization. You should still be able to iterate in
the same fashion (but I haven't looked at it in detail).

-- 
Anders



> 
> -Ali
> 
> >
> >
> >
> >> -Ali
> >>
> >> 2009/2/25  <kent-and@xxxxxxxxx>:
> >> >
> >> > I'm not exactly sure what you are asking. But it is easy to obtain the
> >> > matrices
> >> > and vectors in the linear system to be solved.
> >> >
> >> > eg.
> >> > dolfin/demo/la/trilinos/python/demo.py
> >> >
> >> > shows how to solve the system using Trilinos. You can use dolfin
> >> > to make matrices and vectors in PETSc, uBlas, MTL, and Trilinos format.
> >> > You can choose to let dolfin solve it for you or you can get the underlying
> >> > matrix and solve it with the above LA libraries.
> >> >
> >> > Kent
> >> >
> >> >
> >> >
> >> >> Is the linear algebra support in dolfin capable of automatically
> >> >> generating the sparse linear system of equations? (I know that ffc
> >> >> effectively does this, but note that this question does not involve
> >> >> solving a PDE using FEM, but a linear system of equations).
> >> >>
> >> >> For example, assume we have some busy sets of linear equations and we
> >> >> wish to convert them to Ax = b so that we can feed them to the linear
> >> >> solvers. Is there any way of automatically obtaining A and b avoiding
> >> >> manual calculations and hard-coding?
> >> >>
> >> >>
> >> >> -Ali
> >> >> _______________________________________________
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> >> >>
> >> >
> >> >
> >> >
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