Integration of Current Density over Slice Intersection

The geometry is a 1m cube (subdomain 2) containing a component (subdomain 1) made of 4 joined cylindrical sections. (attached)



Boundariess: 5V/0V on the opposite faces of the cube that are perpendicular to the axes of the cylinders.

Once solved a YZ plane is cut through the current density (s_dc*sqrt(Vx^2+Vy^2+Vz^2) plot in the center (x=0.5)



I want to calculate two currents:
   1) the total current flowing into and out-of the cube by integrating the current density over one of the voltage boundaries

and

   2) the current flowing through each/both of the small connecting cylinders by integrating the current density over the two circular, planar intersections of the cut plane and the two small cylinders.



Which tutorials should I consult?  Is there other documentation other than the paragraph from /doc?

Boundary/Subdomain Integration
Integration of postprocessing expressions over subdomains Subdomain Integration... (calling intsubd) and boundaries Boundary Integration... (calling intbdr) can be performed by selecting the corresponding menu options. The integration dialog box allows for selecting predefined postprocessing or entering user defined expressions in the Integration Expression edit field. Numerical Integration Rule, Solution Number/Time, and Subdomain/Boundary: to integrate over can also be set. The result will be printed in the Integration Result field as well as the command log in the main GUI.

Other suggestions?

I have been able to perform the integration of the boundaries to get the current in/out of the cube (face 5 and 3).

And by selecting the faces of the small cylinders I can get the current into and out-of them at the boundary. (13/14 and 23/24)

Here is 13, for example:

 


But I still have not figured out how to do the integration over the slice intersection.

Thanks for your help,
-Randal

cylinders-in-box4.fes

Boundary integration is only available on defined (external and internal) boundaries (not general cut planes). So in your case you would have to split the cylinders in half (or at the plane you want to perform the boundary integration). This should after meshing create internal boundaries that you now can select in the "Boundary Integration" dialog box (Switch to "Boundary" mode to see the boundary numbering, and toggle the "Interior Boundaries" check box in the lower left hand side of the "Boundary Settings" dialog box to see the numbering of internal boundaries).

The reason for this (limitation) is that boundary integration is for both practical and accuracy reasons performed on selections of grid cell faces (or edges in 2D). And the way to ensure the grid generation algorithm does indeed mesh a reasonably smooth plane/boundary is to first define it in the geometry.

randress wrote

I want to calculate two currents:
   1) the total current flowing into and out-of the cube by integrating the current density over one of the voltage boundaries

and

   2) the current flowing through each/both of the small connecting cylinders by integrating the current density over the two circular, planar intersections of the cut plane and the two small cylinders.


But I still have not figured out how to do the integration over the slice intersection.