
Re: volume integration
Posted:
Sep 6, 2011 3:04 PM


Marios Karaoulis <marios.karaoulis@gmail.com> wrote in message <8e29551297e544e1a95f5e59af177653@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://wwwusers.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 [x2x1 x3x2 x4x2 ]).
Then sum Ij for all j to get the integral on the whole volume.
Bruno

