[Getdp] Electrostatic charge

[pvsantos at gmail.com]

Dear GetDP developers,

I am using getdp for calculations of wave propagation in piezoelectric 
media. One of the problems I am finding is how to calculate charge 
densities. Following the procedure used in the demo Capacitor2D, this 
can be done by defining GlobalTerms. I have two questions about that:

1. How is  the GlobalCharge (Q) associated with the GlobalPotential (V)  
and the dielectric constant of the surrounding medium? In a previous 
post (see http://www.geuz.org/pipermail/getdp/2006/000890.html, I could 
not find a reply to this post), it has been mentioned that formulations:
     Formulation 1:
     - Galerkin { [ epsr[]*Dof{d v} , {d v} ] ; In Vol; Jacobian Vol ; 
Integration Int ; }
     - GlobalTerm { [ -Dof{Q}/eps0 , {V} ] ; In Grouped ; }

     Formulation 2:
     - Galerkin { [ eps0*epsr[]*Dof{d v} , {d v} ] ; In Vol; Jacobian 
Vol ; Integration Int ; }
     - GlobalTerm { [ -Dof{Q} , {V} ] ; In Grouped ; }

both work (I have also checked that), but

     Formulation 3:
     - Galerkin { [ eps0*epsr[]*Dof{d v} , {d v} ] ; In Vol; Jacobian 
Vol ; Integration Int ; }
     - GlobalTerm { [ -Dof{Q}/eps0 , {V} ] ; In Grouped ; }

gives wrong results.

2. In the 2D piezoelectric calculations, I need to determine the 
piezoelectric charge density near a conductor. For that, I need to 
perform an integral of the surface charge density (equal to the 
component  q_s of the vector (- epz_m[] * {D1 u}) perpendicular to the 
surface line. This can be done using a term of the type

     - Galerkin { [ CompY[ (epz_m[] * {D1 u}) , {d v} ]; ; In Sur; 
Jacobian Sur ; Integration Int ; }

Here, v is the potential, epz_m the piezoelectric tensor, and u the 
displacement field (determined in another formulation). The previous 
expression should work for a surface line along x. How can I get this 
normal component for a surface of arbitrary shape? The getdp manual 
mentions two functions Normal[] and NormalSource[] tha may eventually be 
appropriate for that. Can they be used for that purpose (there is no 
information on how to use them in the manual)? If so, can you please 
provide a short example?


Many thanks,

Paulo Santos

!___________________________________________________________________

             _/_/  | Dr. Paulo V. Santos
            _/_/   | Paul-Drude-Institut fuer Festkoerperelektronik
           _/      | Hausvogteiplatz 5-7
      _/_/_/_/     | D-10117 Berlin, Germany
     _/_/_/_/      | phone:   +49-30-20377-221
    _/_/_/_/       | fax:        +49-30-20377-515
   _/              | e-mail:santos at pdi-berlin.de
  _/               |
_/                |
___________________________________________________________________