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Re: volume integration
Posted:
Sep 6, 2011 5:51 PM
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On Sep 6, 1:04 pm, "Bruno Luong" <b.lu...@fogale.findmycountry> wrote:
> Marios Karaoulis <marios.karaou...@gmail.com> wrote in message <8e295512-97e5-44e1-a95f-5e59af177...@o10g2000vby.googlegroups.com>...
> > Hi all,
>
> > I have two vector field J1 and J2, in 3D space (x,y,z) and calculated
> > at some discrete points (extracted in a txt file from comsol.
>
> > I need to volume integrate the
> > triple_integration of (J1 dot J2), which is expressed as
>
> > triple_integration ( J1(x)*J2(x) + J1(y)*J2(y) + J1(z)*J2(z) ).
>
> > I have found thathttp://www-users.math.umd.edu/~jmr/241/tripleint.html
> > , but in my case, I have no analytically expression of the funstion.
> > I guess I could interpolate using TriScatinterp, but is any other way
> > to do that?
>
> You could you partition the volume by Delaunay tetrahedron (help DelaunayTri). Over each tetrahedron Tj, approximate the integral by:
>
> Ij = |Tj|/4 sum(i) dot(J1,J2)(xi)
>
> where {xi}={x1,x2,x3,x4} are four corners of Tj. and |Tj| is the volume
>
> |Tj| = 1/6*abs(det [x2-x1 x3-x2 x4-x2 ]).
>
> Then sum Ij for all j to get the integral on the whole volume.
>
> Bruno
Thanks for the reply. I am not sure I get this, but I will give it a
shot.
By DelaunayTri, you create triangles. Should't I need delaunayn ?
Best
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