{Epot_PL_0.5el.PDE  - Electric POTential assuming PLanar surface
 D.Bakewell 16:45 9/10/2000 }
SELECT
  regrid=on  {enable adaptive grid - warning can take too long} { regrid=off }
 !errlim=8e-5
COORDINATES 
  cartesian(x,y)
VARIABLES
  Phi   	{Electric potential}
  Ex   {Flux in X direction}  Ey	{Flux in X direction} E2 {mgde}
  grdE2x   {grad E^2 in X dirn}	 grdE2y   {grad E^2 inY dirn} !LgrdE2x
! logE2 {PhiAbs PhiLog}
DEFINITIONS
  om=1*10^(-6)
  W=10*om   {electrode boundary Width}  He=0.1*om {electrode boundary Height}
  Gap=W    {boundary - gap between electrodes} Hx=10*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/2 f=b+Hx 
  V=1E1 Vo=V Mxgrde2x=GLOBALMAX(grdE2x)
  xh=pi*x/(2*W)+(pi/4)  yh=pi*y/(2*W) { h = 'hat' } 
Exi=(2.*Vo/(pi*W))*(ARCTAN(sin(xh)/sinh(yh))-ARCTAN(cos(xh)/sinh(yh)))
Eyi=(Vo/(pi*W))*(LN(cosh(yh)+cos(xh))-LN(cosh(yh)-cos(xh))+
  LN(cosh(yh)+sin(xh))-LN(cosh(yh)-sin(xh)))
Dpos=cosh(2*yh)+cos(2*xh)  Dneg=cosh(2*yh)-cos(2*xh)
Exyi=2.*Vo*cosh(yh)/(W^2)*(cos(xh)/Dpos-sin(xh)/Dneg)  Eyxi=Exyi
Exxi=2.*Vo*sinh(yh)/(W^2)*(cos(xh)/Dneg+sin(xh)/Dpos)  Eyyi=-Exxi  E2i=Exi*Exi+Eyi*Eyi
  grdE2xi=2*(Exi*Exxi+Eyi*Eyxi)  grdE2yi=2*(Exi*Exyi+Eyi*Eyyi)
{logE2i=LOG10(E2i+10^(-20))}
EQUATIONS
 div[grad(Phi)]=0  		 {2D Laplace's equation }
!PhiAbs=ABS(Phi)		 {doesn't work very well!!}
!PhiLog=LOG10(PhiAbs)
 dx(Phi)=-Ex		 {for monitoring Electric field in X direction}
 dy(Phi)=-Ey		 {for monitoring Electric field in Y direction}
E2=Ex*Ex+Ey*Ey   {logE2=LOG10(E2)}
 2*(Ex*dx(Ex)+Ey*dx(Ey))=grdE2x  {grad E^2 in X dirctn}
! Mxgrde2x=GLOBALMAX(grdE2x)
 Ex*dy(Ex)+Ey*dy(Ey)=grdE2y  {grad E^2 in Y dirctn}
{ LgrdE2x=SIGN(grdE2x)*LOG10(ABS(grdE2x))}
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)
      Neumann(Phi)=0 line to (e,f) {Value(Phi)=0}
      Neumann(Phi)=0 line to (a,f) 
      Value(Phi)=0 line to finish
MONITORS for cycle=10
 {contour(LgrdE2x)} contour(Phi) contour(Ex) contour(Ey) contour(Exi) contour(Eyi)
 {contour(grdE2x) report(MxgrdE2x)} contour(E2) contour(E2i)
  contour(grdE2xi) contour(grdE2yi)
 elevation(Phi) from (a,d) to (c,d)
  elevation(Ex) from (a,d) to (e,d) elevation(Ey) from (a,d) to (e,d)
PLOTS 
 elevation(Phi) from (a,b) to (c,b)  elevation(Phi) from (e,d) to (e,f)
 contour(Ex)  contour(Exi) contour(Ey) Contour(Eyi)
 contour(grdE2x) report(MxgrdE2x) contour(grdE2xi)
 contour(grdE2y) contour(grdE2yi)
  elevation(Ex) from (a,d) to (e,d) elevation(Ey) from (a,d) to (e,d)
   { plot prints a tag-delimited data list to the file "filename.TXT":}
 contour(Phi)
 {table(Phi)} export format {"#t#b#"} "#x#b#y#b#" file="c:\windows\desktop\Phi.dat"
  transfer(Phi) file="c:\windows\desktop\PhiTrans.dat"
END 63577