I don't like the disparate results I'm seeing with two 1 cm spheres.
But before I say anything else, I should say that I really don't understand the boundary conditions available in CST EMStudio...a situation I blame jointly on apparent bugs in the software in combination with their lousy documentation and lack of examples.
For example, in the help file, they say this:
"A boundary potential can be assigned only if the corresponding boundary condition in the "Boundaries" tab is set to "normal" or "electric".
Xmin, Ymin, Zmin, Xmax, Ymax, Zmax
Defines the boundary potential at the specific boundary. Three different settings are possible:
Default: Zero potential is assigned to the boundary.
Fixed: A defined constant potential will be assigned to the boundary.
Floating: Similar to Fixed the boundary will also have a constant potential. However its initial value is unknown and will be calculated during the simulation."
Now, I wonder what they mean by the statement "[z]ero potential is assigned to the boundary"?
Do they mean to say a potential of zero volts?
In any case, whenever I use "electric" (perfect conductor) boundary conditions, and I try to set the boundary potential to a "fixed" zero volts, using the hex mesh solver, I get an error message:
"All PEC regions are linked to source definitions. This problem is overdetermined and leads to a singular capacitance matrix."
When I use the tet mesh solver, first it says: "Fixed or floating boundary potentials have been defined, but are not available in combination with tetrahedral meshing. Using *electric* boundary conditions with zero potential."
Then it says: "No active excitation has been defined. All fields will be zero. Electrostatic Solver stops".
So, let's see, first, it said it didn't like my electric boundary conditions with a fixed potential of zero volts, so it changed things to "electric boundary conditions with zero potential"...now if that isn't the same thing I had, isn't it at least the so-called "default" condition, with it's mysterious "zero potential" whatever that means?
But then it stopped, saying that "no active excitation has been defined" (yet the spheres had assigned potentials of 1 and -1 volts).
And when I use the "default" boundary potential, I get no error message with either solver, and neither solver stops.
How is that possible? When "it" uses the "default" boundary potential with the tet mesh solver, the solver stops due to lack of "active excitation", but when I use it, it works, everything else being the same?
Apparently CST EM Studio has some bugs.
In any case, the result with "electric" boundary, "default" boundary potential and hex mesh solver is:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.985172e-013 F -1.367237e-013 F
potential2 -1.367241e-013 F 5.985172e-013 F
----------------------------------------------------
With the tet mesh solver, I get:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.750449e-013 F -1.257179e-013 F
potential2 -1.257179e-013 F 5.746637e-013 F
----------------------------------------------------
Note the difference between the two solvers for the same conditions.
Using the tet mesh with adaptive meshing, I get this:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.994367e-013 F -1.365508e-013 F
potential2 -1.365508e-013 F 6.001875e-013 F
----------------------------------------------------
With hex adaptive meshing I get this:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.946815e-013 F -1.346052e-013 F
potential2 -1.346055e-013 F 5.946815e-013 F
----------------------------------------------------
And with tet adaptive meshing I get this:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.994367e-013 F -1.365508e-013 F
potential2 -1.365508e-013 F 6.001875e-013 F
----------------------------------------------------
With "tangential" boundary conditions, the hex mesh solver gives me the warning that:
"All PEC regions are linked to source definitions. This problem is
overdetermined and leads to a singular capacitance matrix."
It gives this result:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 3.644430e-013 F -3.644392e-013 F
potential2 -3.644385e-013 F 3.644431e-013 F
----------------------------------------------------
Unlike the hex mesh solver, the tet mesh solver, with the same "tangential" boundary conditions, gives no warnings and gives a result:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 3.500884e-013 F -3.500884e-013 F
potential2 -3.500884e-013 F 3.500884e-013 F
----------------------------------------------------
And here's the result with the tet mesh solver using adaptive meshing:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 3.679652e-013 F -3.679650e-013 F
potential2 -3.679650e-013 F 3.679652e-013 F
----------------------------------------------------
And the hex mesh solver using adaptive meshing:
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 3.633909e-013 F -3.633708e-013 F
potential2 -3.633783e-013 F 3.633908e-013 F
----------------------------------------------------
Here is the hex mesh solver with "open" boundaries (the tet mesh solver does not work with open boundaries).
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.805210e-013 F -1.465024e-013 F
potential2 -1.465005e-013 F 5.805210e-013 F
----------------------------------------------------
And here is the hex mesh solver with adaptive meshing.
Capacitance Matrix:
----------------------------------------------------
potential1 potential2
potential1 5.792628e-013 F -1.459477e-013 F
potential2 -1.459462e-013 F 5.792628e-013 F
----------------------------------------------------
It seems that with CST EM Studio, you can have any result you want. You don't like the present result? Try a different solver...