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. -- Anders > 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? > > > > > _______________________________________________ fenics mailing list [email protected] http://fenicsproject.org/mailman/listinfo/fenics
