{Epot_2D_3el.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 width/gap} He=0.1*om {electrode boundary Height}
  x0=-W*om    y0=0*om   { horizontal & vertical origin} Hx=30*om {External height}   
 {a=arbitrary}  b=y0+He 
  c=x0+W/2. d=c+W  e=c+2*W  f=c+3*W  g=c+4*W h=c+5*W j=5*W  
  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 (x0,y0) Neumann(Phi)=0 line to (c,y0)
 Value(Phi)=V line to (c,b) to (d,b) to (d,y0)
 Neumann(Phi)=0 line to (e,y0)
 Value(Phi)=-V line to (e,b) to (f,b) to (f,y0)
 Neumann(Phi)=0 line to (g,y0) 
 Value(Phi)=V line to (g,b) to (h,b) to (h,y0) 
 Neumann(Phi) = 0 line to (j,y0)
 Value(Phi)=0 line to (j,Hx)
 Neumann(Phi)=0 line to (x0,Hx)
 Value(Phi)=0 line to finish
       time 0 to 0.05 by 0.01	{ establish time range and initial timestep }
MONITORS 
   for cycle=1  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)}
END  8745