{ PLATES.PDE }
{
This problem computes the field around a plate capacitor.
(adapted from "Fields of Physics on the PC" by Gunnar Backstrom)
}
title 'Plate capacitor'
Variables
u
definitions
Lx=1 Ly=1 delx=0.5 d=0.2 ddy=0.2*d
Ex=-dx(u) Ey=-dy(u)
Eabs=sqrt(Ex**2+Ey**2)
eps0=8.854e-12
eps
DEx=eps*Ex DEy=eps*Ey
Dabs=sqrt(DEx**2+DEy**2)
zero=1.e-15
equations
div(-eps*grad(u)) = 0
boundaries
Region 1
eps=eps0
start(-Lx,-Ly) Load(u)=0
line to (Lx,-Ly) to (Lx,Ly) to (-LX,Ly) to close
start(-delx/2,-d/2) value(u)=0
line to (delx/2,-d/2) to (delx/2,-d/2-ddy) to(-delx/2,-d/2-ddy)
to close
start(-delx/2,d/2+ddy) value(u)=1
line to (delx/2,d/2+ddy) to (delx/2,d/2) to(-delx/2,d/2)
to close
Region 2
eps = 7.0*eps0
start(-delx/2,-d/2)
line to (delx/2,-d/2) to (delx/2,d/2) to(-delx/2,d/2)
to close
monitors
contour(u)
plots
contour(u)
surface(u)
vector(dx(u),dy(u))
end