{Epot_2D_2el.PDE  - Electric POTential  D.Bakewell 17:00 We/15/8/2000  }
title 'time-dependent 2D electric potential'
SELECT
!  regrid=off  { use fixed grid for 2D problems }
  regrid=on  {enable adaptive grid - warning can take too long}
COORDINATES 
  cartesian(x,y)
VARIABLES
  Phi   	{Electric potential}  Ex   {Flux in X direction}  Ey	{Flux in X direction}
  dxE2   {dy(E^2)}	d1yE2  dyE2   {dy(E^2)}  mgrdE2 {magnitude grad(E^2)}
DEFINITIONS
  om=10^(0)
  W=10*om   {electrode boundary Width}  He=0.1*om {electrode boundary Height}
  Gap=10*om    {boundary - gap between electrodes} Hx=30*om {External height}
  a=0*om    b=0*om   	{External rectangular boundary horizontal & vertical origin}
  c=a+Gap/2. d=b+He e=c+W  f=e+Gap g=f+W h=g+Gap/2 j=b+2*He 
  V=1
EQUATIONS
 div[grad(Phi)]=0  		 {2D Laplace's equation }
 dx(Phi)=-Ex		 {for monitoring Electric field in X direction}
 dy(Phi)=-Ey		 {for monitoring Electric field in Y direction}
 dx(Ex*Ex + Ey*Ey)=dxE2
 dy(Ex*Ex + Ey*Ey)=dyE2  d1yE2=-1.*USTEP(-dyE2-1.)
 {d1yE2=-1.*USTEP(-dyE2-1)+dyE2*(1-USTEP(-dyE2-1))}
 sqrt(dxE2^2 + dyE2^2)=mgrdE2
BOUNDARIES
 Region 1            { define region 2 RECTANGLE boundary on horizontal plane }
      start (a,b) Neumann(Phi)=0
      line to (c,b) Value(Phi)=V line to (c,d) to (e,d) to (e,b)
      Neumann(Phi)=0 line to (f,b) Value(Phi)=-V line to (f,d) to (g,d) to (g,b)
       natural(Phi)=0 line to (h,b)
      Value(Phi)=0 line to (h,Hx) to (a,Hx) to finish
       time 0 to 0.05 by 0.01	{ establish time range and initial timestep }
MONITORS 
   for cycle=10  contour(Phi)  contour(Ex)  contour(Ey)
   {contour(mgrdE2)}   {  contour(grdEy2)} elevation(Phi) from (a,j) to (h,j)
     elevation(Ex) from (a,j) to (h,j) elevation(Ey) from (a,j) to (h,j)
  elevation(dxE2) from (a,j) to (h,j)   elevation(dyE2) from (a,j) to (h,j)
 elevation(d1yE2) from (a,j) to (h,j)
HISTORIES
    {history(Phi) at (20*om,20*om)}
PLOTS
 contour(Phi)
 {table(Phi)} export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\Phi.dat"
END  8745