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Surface charge density Vs. Capacitance

Posted Nov 14, 2011, 11:00 a.m. EST Low-Frequency Electromagnetics Version 4.2a 3 Replies

Thomas Schlegl
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Hello!

I have a problem with the solution of a very simple problem in the AC/DC-Electrostatics-Stationary modul (2D)

2 circles in a certain distance. A square box around as far boundary.
One circle is set to 1V via the Terminal interface the other is set to ground (dirichlet boundary conditions).
The boundary of the box is set to Zero Charge (for simulating Neumann boundary conditions).

After I evaluate the capacitance ("Global Evaluation") and a "Line Integration" for the surface charge density (es.nD).

I thought it should be the very same (according to Q=C*U), but it isn't.
There is always (other mesh, geometry,...) a difference between the abs-values.

Does somebody know why?

Thank you for your help!

Thomas!
3 Replies Last Post Nov 15, 2011, 3:58 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Nov 14, 2011, 2:36 p.m. EST
Hi

what ratio of differences ? 5% 10% 100% ? a few percent difference, or a fine meshed case is quite normal, all depends on model set up. Just as integrating fluxes are not always that precise. But there might be something else too, typos are quickly done ;)

--
Good luck
Ivar
Hi what ratio of differences ? 5% 10% 100% ? a few percent difference, or a fine meshed case is quite normal, all depends on model set up. Just as integrating fluxes are not always that precise. But there might be something else too, typos are quickly done ;) -- Good luck Ivar
John H.
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Posted: 1 decade ago Nov 15, 2011, 3:19 a.m. EST
Hi Thomas,

I've come across the same stumbling block myself some time ago. For some geometries, despite a very fine mesh, I saw a difference as high as 40%...

As Ivar hints at, the problem is the lack of precision in the integration of fluxes. It's a systematic numerical error in FEM calculations. The Comsol User's Guide has more details, search for the reaction force operator "reacf" and a section called "Calculating Accurate Fluxes".

In your case, the global evaluation of the capacitance is the more accurate result. You will find that you get the same value when you sum (not: integrate) the reaction force of the electrostatic potential, reacf(V), over the boundary. This is equivalent to the integration of the surface charge density, but more precise.
Hi Thomas, I've come across the same stumbling block myself some time ago. For some geometries, despite a very fine mesh, I saw a difference as high as 40%... As Ivar hints at, the problem is the lack of precision in the integration of fluxes. It's a systematic numerical error in FEM calculations. The Comsol User's Guide has more details, search for the reaction force operator "reacf" and a section called "Calculating Accurate Fluxes". In your case, the global evaluation of the capacitance is the more accurate result. You will find that you get the same value when you sum (not: integrate) the reaction force of the electrostatic potential, reacf(V), over the boundary. This is equivalent to the integration of the surface charge density, but more precise.
Thomas Schlegl
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Posted: 1 decade ago Nov 15, 2011, 3:58 a.m. EST
Hi again!

Your solution worked. Thank you very much!
What is the reaction force. I mean in what relationship (equation) is it with the capacitance?

But why do I get a different value for the global evaluation when changing the mesh (only 0.2%,
but it should be smaller when solving only an equation -> C = 2*We / deltaV^2 ) ?

Thank you again :-)

Thomas

Hi again! Your solution worked. Thank you very much! What is the reaction force. I mean in what relationship (equation) is it with the capacitance? But why do I get a different value for the global evaluation when changing the mesh (only 0.2%, but it should be smaller when solving only an equation -> C = 2*We / deltaV^2 ) ? Thank you again :-) Thomas

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