[Dune] how does integrationOuterNormal work?

[Andreas Dedner]

Hi.
You should check out the definition of the 3 different geometries of the
intersection in detail.

Only intersection.geometry() maps into real space.
geometryInInside and geometryInOutsdide map between reference elements.
They map from the
reference element of the intersection into the reference element of the
inside/ouside entity. So
geometryInInside.global(x) is in fact a local coordinate within the
reference element of the inside entity.

If the global geometry is changed like in GeometryGrid then only the
geometries into real space need to be changed
the embeddings between different reference elements i.e.
geometryInInside do not have to be touched.

Best
Andreas

On 17/09/14 16:38, Aleksejs Fomins wrote:
> Dear Duners,
>
> I started dissecting the geometrygrid/intersection.hh today, and I am a
> bit puzzled how it works. Below I will provide my questions which will
> correspond to certain lines in the code
>
> Line 131:
> FieldVector< ctype, dimension > x( geometryInInside().global( local ) );
>
> Where can I find the implementation of
> hostIntersection().geometryInInside() ?
>
> --------------------------------------------------------
>
> Line 132:
> const typename ElementGeometryImpl::JacobianInverseTransposed &jit =
> insideGeo_.jacobianInverseTransposed( x );
>
> We have just defined x to be a global coordinate in the line 131,
> however in the element geometry implementations known to me (Affine and
> Multilinear) the jacobianInverseTransposed method is only defined for
> local coordinates. How does this work?
>
> --------------------------------------------------------
>
> Line 136/137:
>
> jit.mv( refNormal, normal );
> normal *= jit.detInv();
>
> We take a unit vector refNormal, multiply it by a matrix, and then
> multiply it by the value of the integration element. Why do we not
> normalize the vector normal after matrix multiplication?
>
>
>
> Regards,
> Aleksejs
>
>
>
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