On Tue, Jun 10, 2014 at 10:58:38AM +0200, Martin Sandve Alnæs wrote:
> Maybe this term isn't quite like 'most DG formulations'?
> But another alternative which gives you avg * jump:
>
> inner(avg(grad(u)), outer(jump(v), n('+'))))
The problem with this one is that it seems to have a preferred
direction (+) which it shouldn't. That's the beauty of defining the
jump as something with n('+') + n('-'), that it does not have a
preferred direction.
--
Anders
> Based on:
>
> outer(v('+'), n('+')) + outer(v('-'), n('-'))
> = outer(v('+'), n('+')) - outer(v('-'), n('+'))
> = outer(v('+') - v('-'), n('+'))
> = outer(jump(v), n('+'))
>
> Martin
>
>
> On 10 June 2014 10:44, Anders Logg <[email protected]> wrote:
>
> On Tue, Jun 10, 2014 at 10:09:44AM +0200, Martin Sandve Alnæs wrote:
> > To clarify, Kristian talks about the jump(f,n) version:
> >
> > jump(scalar,n) is vector-valued
> > jump(vector,n) is scalar
> >
> > while I mixed up with the jump(f) version:
> >
> > jump(scalar) is scalar
> > jump(vector) is vector-valued
> >
> > The jump(f) version gives the difference of the full value, while
> > the jump(f,n) version gives the difference in normal component.
>
> I looked through the Unified DG paper that Kristian pointed to but
> couldn't see any examples of vector-valued equations.
>
> I also don't see the point in defining jump(v, n) for vector valued u
> as in the paper. If the result of jump(v, n) is a scalar quantity,
> there is no way to combine the normal n with the thing it should
> naturally be paired with, namely the flux (or grad(u)). It only works
> out in the special case of scalar elements.
>
> But perhaps adding tensor_jump() is the best solution since that paper
> is the standard reference for DG methods.
>
> (I'll ask Douglas Arnold about this, if he has not seen this
> already. Maybe I am missing something obvious.)
>
> > However, if I didn't mess up some signs I think you can write your term
> like
> >
> > 0.5*dot(jump(Dn(u)), jump(v))
> >
> > which seems much more intuitive to me (although I'm not that into DG
> scheme
> > terminology).
>
> Yes, that looks correct but I don't think it is intuitive since it
> does not involve the avg() operator which is naturally paired with the
> jump() operator in most DG formulations.
>
>
>
> > On 10 June 2014 09:05, Kristian Ølgaard <[email protected]> wrote:
> >
> >
> > On 9 June 2014 20:58, Martin Sandve Alnæs <[email protected]>
> wrote:
> >
> >
> > I object to changing definitions based on that it would work out
> nicely
> > for one particular equation. The current definition yields a
> scalar
> > jump for both scalar and vector valued quantities, and the
> definition
> > was chosen for a reason. I'm pretty sure it's in use. Adding a
> > tensor_jump on the other hand wouldn't break any older programs.
> >
> > Maybe Kristian has an opinion here, cc to get his attention.
> >
> >
> > I follow the list, but thanks anyway.
> >
> > The current implementation of the jump() operator follows the
> definition
> > often used in papers (e.g. UNIFIED ANALYSIS OF DISCONTINUOUS
> GALERKIN
> > METHODS
> > FOR ELLIPTIC PROBLEMS, arnold et al. http://epubs.siam.org/doi/abs/
> 10.1137/
> > S0036142901384162)
> >
> > where the jump of scalar valued function result in a vector, and the
> jump
> > of a vector valued function result in a scalar.
> >
> > Adding the tensor_jump() function seems like a good solution in this
> case
> > as I don't see a simple way of overloading the current jump()
> function to
> > return the tensor jump.
> >
> > Kristian
> >
> >
> >
> > Martin
> >
> > 9. juni 2014 20:16 skrev "Anders Logg" <[email protected]>
> følgende:
> >
> >
> > On Mon, Jun 09, 2014 at 11:30:09AM +0200, Jan Blechta wrote:
> > > On Mon, 9 Jun 2014 11:10:12 +0200
> > > Anders Logg <[email protected]> wrote:
> > >
> > > > For vector elements, the jump() operator in UFL is
> defined as
> > follows:
> > > >
> > > > dot(v('+'), n('+')) + dot(v('-'), n('-'))
> > > >
> > > > I'd like to argue that it should instead be implemented
> like
> > so:
> > > >
> > > > outer(v('+'), n('+')) + outer(v('-'), n('-'))
> > >
> > > This inconsistency has been already encountered by users
> > > http://fenicsproject.org/qa/359/
> > discontinuous-galerkin-jump-operators
> >
> > Interesting! I hadn't noticed.
> >
> > Are there any objections to changing this definition in UFL?
> >
> >
> >
> >
> >
>
>
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