I need to integrate a rather complicated function on an ellipsoidal surface, specifically a prolate spheroid surface.
Im using the mathematica 10 feature of discretize the regions in mesh and pass the discretized region to NIntegrate.
However when i define the ellipsoidal surface region as:
region = BoundaryDiscretizeRegion[
Ellipsoid[{0, 0, 0}, {1, 0.125, 0.125}], MaxCellMeasure -> 0.1]
and i do
RegionDimension[region]
the answer is 3 so it is discretizing the whole volume not only the surface.
To confirm what seen above i computed the Integral in the case of a sphere:
NIntegrate[1, {x, y, z} ∈
BoundaryDiscretizeRegion[Ellipsoid[{0, 0, 0}, {1, 1, 1}],
MaxCellMeasure -> 0.01]]
whose result is 4.1798 that is $\approx \frac{4}{3} \pi$ confirming that he is performing the integration over the VOLUME not over the surface...
Am i doing something wrong?
Thanks in advance for the help
DiscretizeRegion
on theRegionBoundary
of your ellipsoid. If you look atBoundaryDiscretizeRegion
documentation you can see the result doesn't consist of the boundary alone... it's just that discretization occurs only on it. $\endgroup$ – kirma Jul 15 '15 at 15:51MaxCellMeasure
is not really reliable on pre-v10.2 versions; see mathematica.stackexchange.com/questions/54925/… . Also, you don't really need to perform discretization in many cases at all! $\endgroup$ – kirma Jul 15 '15 at 16:40