[SI-LIST] : question electrostatic solvers

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From: Jan Vercammen (jvercamm@roam.agfa.be)
Date: Tue Aug 29 2000 - 08:12:04 PDT


hello si-list,

I have a question concerning method of moments electrostatic solvers.

Some (I think most) general-purpose electrostatic solvers replace the
dielectric-dielectric interfaces with an unknown surface charge. So these solvers
atack a free-space problem.

My question is: on what is this based? Why is one allowed to remove the dielectra
and replace them by a surface charge?

I do understand (better I think) the following: the divergence of the polarization P
equals the polarization charge in the dielectric material. A volume integral of div P
can be reduced to a surface integral over the enclosed volume (divergence theorem). So
it seems likely that the potential for a location outside the dielectric volume can
be calculated using the surface charge and a volume integration is avoided. Is this
correct or am I wrong?

I have checked Paul's book (Analysis of Multiconductor Lines) and Van Bladel's
(Electromagnetic Fields, page 73+). Paul discusses the matter briefly but gives no
details. Van Bladel is, as usual, thourough, but I am missing some points in his
derivation. It will take somewhile to digest this matter.

It would be great if someone could, in plain simple words, explain the physics behind
this matter or direct me to some detailed exposition or reference(s).

regards,

Jan Vercammen
Agfa-Gevaert NV

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