# [Getdp] integral quantities

Patrick Dular Patrick.Dular at ulg.ac.be
Fri Oct 5 17:38:12 CEST 2001

```Hello Andri,

> Andri Nicolet wrote:
>
> Hello,
>
> I would like to know how to compute integral quantities in order to be able to compute forces, energy, power, etc.
>
> I have modified Magnetostatic.pro this way in the postprocessing :
>
> { Name wm ; Value { Local { [ SquNorm[{d a}] * nu[] / 2.] ; In Domain ; Jacobian JVol ; } } }
>
> { Name Wmag ; Value { Integral { [ SquNorm[{d a}] * nu[] / 2.] ; In Domain ; Jacobian JVol ; } } }
>
> { Name lapfor ; Value { Local { [ Cross [ js[], {d a} ] ] ; In Domain_S ; Jacobian JVol ; } } }
>
> and then in test.pro
>
> Print[ wm, OnElementsOf Domain, File "energy.pos"];
>
> Print[ Wmag, OnRegion Domain, File "en.pos"];
>
> Print[ lapfor, OnElementsOf Domain_S, File "force.pos"];
>
> The first line computes the magnetic energy density and the second one is an attempt to compute the total energy. Unfortunately, it writes zeroes in the file en.pos.

You must add an Integration method for Wmag and, then, write

Print[ Wmag[DomainForIntegration], OnGlobal ];

where DomainForIntegration can be a subdomain of Domain (if DomainForIntegration is not included in Domain, the result will be zero).

> The third line gives the Laplace force density. How to integrate it on the conductors to get the total force ?

You should use the same syntax (with OnGlobal, and not OnElementsOf).

> How to integrate on the boundary of a region to get the forces by the Maxwell stress tensor or the energy with the Poynting vector ?

Coming soon...

>
> Thank you for your help !
>
> ********************************************
> Prof. Andri Nicolet
> Universiti d'Aix-Marseille III
> Dom. Univ. de Saint-Jirtme
> Service 162
> Institut Fresnel (UMR 6133)
> F-13397 Marseille cedex 20
> France
> tel +33 4 91 28 87 73
> fax +33 4 91 28 88 80
> secr +33 4 91 28 83 76
> mailto:andre.nicolet at fresnel.fr
> ********************************************

Patrick

--
Patrick Dular, Dr. Ir., Chercheur qualifii F.N.R.S. (Research associate)
Dipartement d'Electriciti Appliquie
Universiti de Lihge - Institut Montefiore - Bbt. B28 - Parking 32
B-4000 Lihge - Belgique - Tel. +32-4-3663710 - Fax +32-4-3662910
mailto:Patrick.Dular at ulg.ac.be

```