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Topic: volume integration
Replies: 11   Last Post: May 7, 2014 7:25 PM

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Bruno Luong

Posts: 8,813
Registered: 7/26/08
Re: volume integration
Posted: Sep 6, 2011 3:04 PM
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Marios Karaoulis <marios.karaoulis@gmail.com> wrote in message <8e295512-97e5-44e1-a95f-5e59af177653@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 that http://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



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