title
 'Electrostatic Potential and Field Lines'
COORDINATES
 cartesian2
 
VARIABLES
 V {volts}
 D

SELECT
!contourgrid=2
!overshoot
Ngrid =5
ERRLIM=1e-3
!stages=2
quadratic {Quadratic FEM basis => default = order 2}

INITIAL VALUES
V = 0
D = 0
DEFINITIONS

cm = 0.01
Lx=800*cm
Ly=1300*cm

eps0=8.854e-12 
 epr
 eps=epr*eps0
 {Equations for Electric Field}

E0= 1e-5 {Far Field}
 Ex = -dx(V) Ey = -dy(V) {components of the gradient} 
 E = -E0*grad(V) {definition of the gradient}

D0 = eps*E0
!!!!!!!!!!!!!!!!!!!!!! Dx = dx(D) Dy = dy(D)
 D_ = D0*grad(D) {D_ = eps*E0*grad(D)} 
 {components of the gradient (x,y)}
 Em = magnitude(E) 
 Dm = magnitude(D_) 
 !P = (eps - eps0)*E 
 !Pm = magnitude(P)

!trunc=.05*errlim
 !Tenergy = VOL_INTEGRAL ( V, '2' )

EQUATIONS
 V: div(grad(V)) = 0 { Potential equation }
! D: div(grad(D_)) = 0
 D: div(D_) = 0
 { adjoint equations }

CONSTRAINTS
 !bintegral(V,"inner") = bintegral(1,"inner")
BOUNDARIES

REGION 1
! eps0=8.854e-12
 epr=1
! eps=eps0*epr

start (-0.75,-1.3) 
 point value(V)=-12
 value(V)=-12

line to (0.75, -1.3)
 point value(V)=-12
 value(V)=-12
 
 line to (0.75,1.3)
 point value(V)=-12
 value(V)=-12
 
 line to (-0.75,1.3)
 point value(V)=-12
 value(V)=-12

line to (-0.75, 1.3) 
 point value(V)=-12
 value(V)=-12 
 line to close

region 2
! eps0 =8.854e-12
 epr=80
! eps=eps0*epr

start (-0.25,0)

line to (0.25,0) 
 point value(V)=12 !natural(Q)= -normal(grad(v))
 value(V) = 12 natural(V)= tangential(grad(D))

line to (0,0.5)
 point value(V)=12 !natural(Q)= -normal(grad(V))
 value(V)=12 natural(D)= tangential(grad(D))

line to (-0.25,0)
 point value(V)=12 !natural(Q)= -normal(grad(V))
 value(V)=12 natural(D)= tangential(grad(D))

line to (0,0)
 point value(V)=12
 value(V)=12 natural(D)= tangential(grad(D))
 line to close

MONITORS
 contour(V) as 'Potential'
 contour(D) as 'Field'

PLOTS
 grid(x,y)
 contour(V) as 'Potential'
 surface(V) as 'Potential and Field Lines'
 vector(-dx(V),-dy(V)) as 'Electric Field'
 vector(dx(D), dy(D))
!!!!!!!!!!!!!! contour(E) zoom(0.3, 0.3, 0.65,0.5)
vector(E) zoom(0.3, 0.3, 0.65,0.5)
 contour(V) zoom(0.3, 0.3, 0.65,0.5)
 contour(Dm) zoom(0.3, 0.3, 0.65,0.5)
!!!!!!!!!!!!!!!!!!!!!!! contour(D_)
vector(D_)
 !contour(Dex)
 !contour(Dey)
 contour(Ex)
 contour(Ey)
 contour(Em)
 !contour(P) zoom(0.3, 0.3, 0.65,0.3)
!!!!!!!!!!!!!!!!!!!!!!! contour(E) zoom(0.3, 0.4, 0.72, 0.4)
vector(E) zoom(0.3, 0.4, 0.72, 0.4)
 !contour(P) zoom(0.3, 0.4, 0.72, 0.4)
 elevation(V) from(0.707, 0.3) to (0.707,0.4)
 !vector(Dex, Dey)
 vector(Ex, Ey) as 'V/cm'
 surface(Ex)
 surface(Ey)
 !surface(Dex)
 !surface(Dey)
end