dolfin team mailing list archive

[Marie Rognes <meg@xxxxxxxxx>]

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.

> 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.

>  
> 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.

>>> 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