dolfin team mailing list archive

[Marie Rognes <meg@xxxxxxxxx>]

On 20. okt. 2010 23:20, Johan Hake wrote:
> On Wednesday October 20 2010 14:16:13 Marie Rognes wrote:
>   
>> On 20. okt. 2010 22:40, Johan Hake wrote:
>>     
>>> On Wednesday October 20 2010 12:54:07 Marie Rognes wrote:
>>>       
>>>> On 20. okt. 2010 21:20, Johan Hake wrote:
>>>>         
>>>>> On Wednesday October 20 2010 10:39:11 Marie Rognes wrote:
>>>>>           
>>>>>> A while back (in connection with the blueprint
>>>>>> https://blueprints.launchpad.net/dolfin/+spec/solver-interfaces) there
>>>>>> was a discussion regarding the interface to VariationalProblem. Anders
>>>>>> and Marie have discussed this a bit further, in particular with regard
>>>>>> to the adaptive solution of variational problems, and suggest the
>>>>>> interface outlined below. (This suggestion involves a change in the
>>>>>> interface, and hence the double post to both the dolfin and
>>>>>> fenics-mailinglists)
>>>>>>             
>>>>> I guess this discussion comes on top of the previous one? Because that
>>>>> blueprint mentioned a lot more than what is mentioned here.
>>>>>           
>>>> Yes.
>>>>
>>>>         
>>>>> I also assume this is limited to the Python interface as doing stuff
>>>>> like derivative behind the scene is limited to PyDOLFIN?
>>>>>           
>>>> Yes and no.
>>>>
>>>> Using derivative is limited to Python (for now...). However, the
>>>> suggested change allows a clean common interface for c++ and Python,
>>>> incorporating the desired implicit derivative for Python users.
>>>>         
>>> Ok.
>>>
>>>       
>>>>>> >From Marie's perspective, the main reasons for changing the interface
>>>>>>             
>>>>>>> are
>>>>>>>
>>>>>>>               
>>>>>>     (a) The current "nonlinear=true" variable seems superfluous and
>>>>>>
>>>>>> suboptimal
>>>>>>
>>>>>>     (b) We should allow for automated computation of the Jacobian
>>>>>>     (when
>>>>>>
>>>>>> needed).
>>>>>>
>>>>>> For (nonlinear) variational problems, the interface should read
>>>>>>
>>>>>>       pde = VariationalProblem(Form F, Form jacobian=None, ...)
>>>>>>       pde.solve(u)
>>>>>>
>>>>>> where "F" is a Form of rank 1, "jacobian" is a Form of rank 2, and "u"
>>>>>> is a Function. Such a pde will be treated as a nonlinear variational
>>>>>> problem. The "jacobian" would be an optional argument. If not given,
>>>>>>
>>>>>>     jacobian = derivative(F, u)
>>>>>>
>>>>>> will be used for the nonlinear solve if needed (for instance as the
>>>>>> left-hand side of the Newton iteration).
>>>>>>
>>>>>> Additionally, we have the interface for linear problems (as before)
>>>>>>
>>>>>>       pde = VariationalProblem(Form a, Form L, ...)
>>>>>>       pde.solve(u) / u = pde.solve()
>>>>>>
>>>>>> where "a" is a Form of rank 2 and "L" is a form of rank 1. Such as pde
>>>>>> will be treated as a linear variational problem.
>>>>>>             
>>>>> Some wild thoughts...
>>>>>
>>>>> Couldn't we just lump a and L into one form F, and let
>>>>> VariationalProblem then figure out what kindoff problem the user would
>>>>> like to solve? Basically VariationalProblem then solve F=0.
>>>>>
>>>>> Differentiate F if the form is of rank 1, (or take an optional
>>>>> Jacobian), or split it into a linear problem using lhs and rhs?
>>>>>           
>>>> This is possible in the Python interface with the model suggested above.
>>>> (Just implies adding a bit more intelligence than indicated) However,
>>>> for the sake of the c++ interface (and many application codes), not
>>>> removing the (a, L) option seems like a good idea to me.
>>>>         
>>> Agree. However, I am not using VariationalProblem to anything :)
>>>
>>>       
>>>>>> Philosophical question: Should u be given as an argument to the
>>>>>>
>>>>>>   VariationalProblem instead of to the call to solve?
>>>>>>             
>>>>> It is more natural to give u to solve, as that is what you solve for.
>>>>> Then you can differentiate wrt to u in the solve function. However, it
>>>>> makes it more difficult to make u an optional argument to solve.
>>>>>           
>>>> I'm rather flexible at this point.
>>>>         
>>> Me too.
>>>
>>>       
>>>> Note that u is only an optional argument if the problem is linear,
>>>> right. For my purposes, no differentiation is needed in such cases (and
>>>> hence u can be created and not given).
>>>>         
>>> Sure, but how does a VariationalProblem know it is nonlinear so it can
>>> tell a user to provide u in solve?
>>>       
>> First, currently the VariationalProblem does not tell the user any such
>> thing (in Python). 
>>     
> Sure, we are talking about a Blueprint.
>
>   


Yes, but for there to be purpose to blueprints, some of them actually
have to be realized, occasionally ;)

>> Second, for the c++ interface (afaik), the u always
>> needs to be prescribed Third, if we want to tell the Python user, we
>> could either always require the input u if the
>>
>>     VariationalProblem(F, ...)
>>
>> version is used, or, add some quick UFL magic that checks F for
>> (non-)linearities and reports back if u is needed.
>>     
> Ok.
>
> For curiosity: 
>
>   How could you use ufl to figure out if a form is (non)linear?
>
>   


For the current situation, one could probably just check rank:

    rank == 1 => non-linear in the sense that u is required (F = F(u; v))
    max_rank >= 2 => linear in the sense that u is not required (F =
a(v, u) - L(v)).

?

--
Marie