# [Getdp] surface integrals

Christophe Geuzaine Christophe.Geuzaine at ulg.ac.be
Fri Oct 26 10:38:49 CEST 2001

```> Andri Nicolet wrote:
>
> Hello,
>

Hello Andre!

> 1) I still need surface integral (line integral in 2D in fact).
>
> I tried something like
>
> { Name Ampere ; Value { Integral { [ nu[] * {d a} ] ; Integration I1 ;
> In Dirichlet_a ; Jacobian Sur ; } } }
>
> in the postprocessing and get a : Unknown Jacobian Method : Sur  ...

You have to define 'Sur' as a Jacobian method, e.g. as

Jacobian {
{ Name Sur ;
Case { { Region All ; Jacobian Sur ; } }
}
}

Beware that the two 'Sur' have different meanings...

>
> What is wrong with it ?
>
> Integral on submanifolds are extremely useful and even necessary in
> some cases. What is available in GetDP on this today ?

In 3D, 'Vol' provides the classical 3x3 volume Jacobian; 'Sur' provides
the 2x3 surface Jacobian; 'Lin' provides a 1x3 line Jacobian. In 2D,
'Vol' provides the classical 2x2 "volume" Jacobian; 'Sur' provides the
1x2 "surface" Jacobian.

>
> 2) By the way, this kind of integral require the concept of trace e.g.
> tangential component of a 1-form and normal component of a 2-form. How
> is it dealt with in GetDP ?

By using the restriction of the volume mixed elements on surfaces/lines.
For example, to get the trace of a 1-form, you simply define BF_Edge as
the basis of your function space both in volume and on the surface (i.e.
you specify "Support Region[{Volume,Surface}]" in the FunctionSpace).
When dealing with submanifolds, the correct basis functions
(tetrahedral/hexahedral/prismatic curl-conforming elements in the
volume, triangular/quadrangular curl-conforming elements on the surface)
are thus automatically used to interpolate the unknowns.

>
> 3) I did not see the dot product (scalar product) among the operators
> (except its implicit use in the Galerkin command). Has it been
> forgotten ?

It's simply '*' (which thus has two meanings, depending of its
arguments... That's a shortcoming of the current syntax).

> As the exterior derivative d is available as a short cut
> and/or an explicit Hodge star operator ?

Yep, this is not done. These notions are hidden at the moment in the
'Galerkin[stuff,stuff]' notation.

Christophe

--
Christophe Geuzaine

Tel: 32 (0) 4 366 37 10    http://geuz.org
Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be

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