dolfin team mailing list archive

[Johan Hake <johan.hake@xxxxxxxxx>]

On Tuesday September 28 2010 09:39:57 Marie Rognes wrote:
> On 28. sep. 2010 18:18, Johan Hake wrote:
> > On Tuesday September 28 2010 09:08:01 Marie Rognes wrote:
> >> On 28. sep. 2010 17:16, Johan Hake wrote:
> >>> On Tuesday September 28 2010 04:46:30 Marie Rognes wrote:
> >>>> On 25. sep. 2010 22:02, Johan Hake wrote:
> >>>>> On Saturday September 25 2010 00:24:12 Marie E. Rognes wrote:
> >>>>>> On 25. sep. 2010, at 02:37, Johan Hake <johan.hake@xxxxxxxxx> wrote:
> >>>>>>> Hello!
> >>>>>>> 
> >>>>>>> I have been experimenting with forms including spaces of Real. I am
> >>>>>>> using the Real space to calculate average values of other species
> >>>>>>> across the boundaries. These values are then used to cacluate
> >>>>>>> derived values such as fluxes across a boundary. In this way I
> >>>>>>> manage to connect two sepatated meshes (stored in the same mesh)
> >>>>>>> via the calculated flux. As everything is contained in one form I
> >>>>>>> can linearize it an use it in a Newton solver, which converges
> >>>>>>> nicely.
> >>>>>>> 
> >>>>>>> In this procedure I have used unknowns of Reals to caluclate other
> >>>>>>> Reals. This is somewhat combersome when I have to express this
> >>>>>>> using an integral.
> >>>>>>> 
> >>>>>>> Consider:
> >>>>>>>  V = MixedFunctionSpace([FunctionSpace(mesh, "CG", 1)]+
> >>>>>>>  
> >>>>>>>                         [FunctionSpace(mesh, "R", 0)]*3)
> >>>>>>>  
> >>>>>>>  u, r0, r1, r2 = split(Function(V))
> >>>>>>>  v, v0, v1, v2 = TestFunctions(V)
> >>>>>>>  ...
> >>>>>>>  L0 = (r0-(r2-r1))*v0*ds(1)
> >>>>>>> 
> >>>>>>> Here I express r0 in terms of r1 and r2. However in the form I need
> >>>>>>> to integrate the expression over an arbitrary domain in the mesh. I
> >>>>>>> am not interested in this, as the value is not spatialy varying. Do
> >>>>>>> you have any suggestions of how to avoid this or to do it in some
> >>>>>>> other manner?
> >>>>>> 
> >>>>>> It is not entirely clear to me which values that are unknown above,
> >>>>>> but if everything is known or you are just operating on real
> >>>>>> numbers, I imagine that extracting the value of the Function using
> >>>>>> values() could be simpler?
> >>>>> 
> >>>>> r0, r1, and r2 are unknowns together with the field u. r1 and r2 are
> >>>>> the mean of the field across a boundary, and r0 are the flux between
> >>>>> the two distinct domains.
> >>>>> 
> >>>>> A more complete form would be:
> >>>>>   # Boundary forms
> >>>>>   L1 = (r1-u)/area[1]*v1*ds(1)
> >>>>>   L2 = (r2-u)/area[2]*v2*ds(2)
> >>>>>   L0 = (r0-(r2-r1))*v0*ds(1)
> >>>>>   Lu = r0*v*ds(1) - r0*v*ds(2)
> >>>>>   
> >>>>>   # Stiffnes + Boundary
> >>>>>   L = inner(grad(u),grad(v))*dx + L0 + L1 + L2 + Lu
> >>>>> 
> >>>>> My question relates to the algebraic relation of the reals in:
> >>>>>   L0 = (r0-(r2-r1))*v0*ds(1)
> >>>>> 
> >>>>> which really does not need an integral.
> >>>> 
> >>>> Do you really want:
> >>>>     r0 = (r2 - r1)
> >>> 
> >>> Yes.
> >>> 
> >>>> If yes, why not replace r0 by (r2 - r1)?
> >>> 
> >>> That is true but I figure I want to compute that value for book keeping
> >>> 
> >>> :P
> >> 
> >> So, you want a simpler way of doing it, but not a really simple way of
> >> doing it ;) ?
> > 
> > The point is that the flux quantity is nice to have computed, as I use it
> > for further computation. The above form works fine.
> 
> Ok.
> 
> >> I don't think I have any more suggestions at the moment -- could you
> >> remind me why the integration is a problem again? Or, what would you
> >> like to write?
> > 
> > No problem. Just overkill (I assume...). I am calculating a scalar
> > quantity (r0) from other scalar quantities (r1, r2) using a form. But
> > the only way I can use a form to evaluate these are by an integral. An
> > integral is over a spatial domain. r0, r1 and r2 are just values on R
> > not on the domain.
> 
> The are functions on the domain. Just constant ones:
> 
>     r0 : domain -> R
> 
> defined by
> 
>     r0(x) = r_0
> 
> for all x in domain, for some value r_0 \in R.

Ok.

> > Why
> > should I then have to integrate over the domain to calculate r0?
> 
> You need one equation to determine r_0, in particular an integral over
> some part of the domain will do.

Yes, and this is what I do. It just seemed pointless when everything is 
constant over the domain.

> > Because nothing else is implemented in UFL/UFC/DOLFIN. I am fine with
> > this, but it is a unintutive and it might be usefull to introduce some
> > other measure for these guys.
> 
> Introducing forms that are not defined using integrals sounds like it
> deserves its own thread.

Ok. But it is a minor request which probably cost more than it taste.

Johan

> >>> On a related topic:
> >>> The Real space can be used to compute ODEs coupled to PDEs by
> >>> expressing them using a form. I know several applications that this
> >>> might be usefull. But then we get the same "problem" when a scalar
> >>> value are computed by integrating over a domain.
> >> 
> >> Sounds like a bit of an overhead there, yes ...
> > 
> > Yes and the ODE solver can probably not be used to solve particular stiff
> > ODEs. BUT, and here comes the raisin in the hot dog, it can be included
> > in the automated linearization so you can get quadratic convergence in a
> > coupled ODE/PDE system.
> :
> :)
> 
> --
> Marie