On Thu, 23 Jan 2014 10:16:17 -0800 Nikolaus Rath <[email protected]> wrote:
> On 01/23/2014 10:02 AM, Jan Blechta wrote: > > On Thu, 23 Jan 2014 09:54:34 -0800 > > Nikolaus Rath <[email protected]> wrote: > > > >> On 01/23/2014 09:25 AM, Jan Blechta wrote: > >>> On Thu, 23 Jan 2014 18:19:45 +0100 > >>> Jan Blechta <[email protected]> wrote: > >>> > >>>> On Thu, 23 Jan 2014 08:53:13 -0800 > >>>> Nikolaus Rath <[email protected]> wrote: > >>>> > >>>>> On 01/23/2014 04:19 AM, Jan Blechta wrote: > >>>>>> On Wed, 22 Jan 2014 11:39:30 -0800 > >>>>>> Nikolaus Rath <[email protected]> wrote: > >>>>>> > >>>>>>> Hi Jan, > >>>>>>> > >>>>>>> It was my impression from the other thread that I could handle > >>>>>>> the problem of multiple solutions by giving the nullspace to > >>>>>>> the solver. But I'll try the Laplace constraint as well. > >>>>>>> > >>>>>>> But then, even with u constrained, I still need to somehow put > >>>>>>> the same constraint on the test functions, don't I? That's the > >>>>>>> part I'm struggling with. > >>>>>> > >>>>>> Sure. This is why it seems logical to me to constraint both > >>>>>> trial and test space by Laplace equation. Nevertheless I did > >>>>>> not think it over a much. > >>>>> > >>>>> > >>>>> For what it's worth, it seems logical to me as well... I just > >>>>> don't know how to impose the second constraint. > >>>> > >>>> Check > >>>> http://fenicsproject.org/documentation/dolfin/1.3.0/python/demo/documented/neumann-poisson/python/documentation.html > >>>> > >>>> Testing by (v, 0) and (v + c, 0) gives linearly dependent > >>>> equations - in fact, the same. Similar construction can apply to > >>>> your problem. > >>> > >>> Here, I meant (v, 0) and (v + arbitrary_constant, 0). And it holds > >>> because "the sufficient condition" > >>> \int f \dx + \int g \ds = c |\Omega| > >>> is fulfilled. > >> > >> > >> I'm afraid I'm completely lost. What do you mean with "Testing by > >> (v, 0) and (v + arbitrary_constant, 0)", and what is |\Omega|? The > >> sufficient condition on the above link doesn't have this term... > > > > "Testing by foo" means set test function in the equation to foo and > > observe... > > > > |\Omega| is a measure of \Omega. > > > > You get "the sufficient condition" > > \int f \dx + \int g \ds = c |\Omega| > > when testing by (v, d) := (1, 0). It is in quotes, as it is no > > longer a sufficient condition but rather a property of the > > solution. Actually, the value of the multiplier c. > > > Thanks, that makes sense to me now. But how does that relate to > imposing constraints on the test function? In this example, the problem does not see a shift of v by arbitrary constant. This is like when you were testing by for example v \ in {x + 10^42 \in V, \int x = 0} So effectively, test space is constrained. Jan > > > Best, > Nikolaus > > _______________________________________________ > fenics mailing list > [email protected] > http://fenicsproject.org/mailman/listinfo/fenics _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
