ffc team mailing list archive

[Bartosz Sawicki <sawickib@xxxxxxxxxxxxx>]

On 30/01/09 01:04 AM, Kristian Oelgaard wrote:
> Quoting Bartosz Sawicki <sawickib@xxxxxxxxxxxxx>:
>
> > I have a problem how to define form for integration over internal facets 
> > inside VectorElement("Discontinuous Lagrange", "tetrahedron", 0).
> > Having vector function "j" which is constant over element, I want to 
> > integrate over all internal facets term dot(j,n), where n is facet 
> > normal vector.
> >
> > Consider form:
> > =====
> > element = FiniteElement("Discontinuous Lagrange", "tetrahedron", 0)
> > vectorelement = VectorElement("Discontinuous Lagrange", "tetrahedron", 0)
> >
> > v = TestFunction(element)
> > e = TrialFunction(element)
> > j = Function(vectorelement)
> > n = FacetNormal("tetrahedron")
> >
> > a = v*e*dx
> > L = v*dot(j, n)*dS
> > =====
> >
> > Unfortunately it doesn't work. FFC communicates that "Integrand must be 
> > restricted ('+') or ('-') in an interior facet integral". That is 
> > confusing for me.
>
> Functions on interior facets can potentially be double valued (in your case they
> really are). So you need to tell FFC which value you want.
>
> Maybe you want something like:
>
> L = v*jump(j, n)*dS = v*(dot(j('+'), n('+')) + dot(j('-'), n('-')))*dS
>
> The discontinuous operators are explained in more detail in the FFC manual.

Thanks for your answer.

I've read FCC manual carefully, but there is "..., one _may_ restrict
expressions to the positive or negative side of the facet". What sugest
that I don't have to use restrictions.
It seems that, when using dS operator we _have to_ restrict every
function. Even your example doesn't compile, because v in not restricted.

Something what compiles correctly is:

a = v*e*dx
L = v('+')*dot(j('+'),n('+'))*dS + v('-')*dot(j('-'),n('-'))*dS

but I'm not sure if it is what I need. Moreover when I've tried to a 
solve the problem:

Function e;
VariationalProblem problem(a,L);
problem.solve(e);

I get runtime error "*** Error: Coefficient 1 has not been defined."
So something is definitely wrong with this form. :(

Have you got any other idea, how to describe separate integration for 
every cell?

regrs.
BArtek





> Kristian
>  
> > Maybe interior integration operator works differently?
> > So, would it be possible to use form language to describe such simple 
> > algorithm?
> >
> > iterate for every cell c:
> >    e_i = 0
> >    integrate for every facet in cell:
> >      e_i += dot(j,n)
> >    e(c) = e_i
> >
> >
> > regrds.
> > BArtek
> >
> >
> >
> >
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