<< Click to Display Table of Contents >> Navigation:  Sample Problems > Usage > Variable_Types > complex_emw21

{ COMPLEX_EMW21.PDE

 

 This problem is an image of "Backstrom_Books|Waves|Electrodynamics|emw21.pde"  

 rewritten in terms of complex variables.

 

}  

TITLE                           { emw21.pde }  

  'Plane Wave in a Conductor'        

SELECT                                

  errlim= 1e-3                 { Limit of relative error }  

 

VARIABLES  

  Ez = complex(Ezr,Ezi)       { Real and imaginary parts }  

 

DEFINITIONS                     { SI units throughout }  

  Lx= 1.0             Ly= 0.2 { Domain size }  

  eps0= 8.85e-12      eps     { Permittivity }  

  mu0= 4*pi*1e-7      mu       { Permeability }  

  sigma                       { Electric conductivity }  

  omega= 5e9                   { Angular frequency }  

  Ez_in= 1.0                   { Input field Ez }  

  Ep= magnitude(Ez)           { Modulus of Ez }  

  phase= carg(Ez)/pi*180       { Angle }  

 

EQUATIONS  

  Ez:  del2( Ez)+ mu*omega*complex(eps*omega, -sigma)*Ez= 0  

 

BOUNDARIES  

region 'conductor'      eps= eps0       mu= mu0     sigma= 1e-1  

  start 'outer' (0,0)  

  natural(Ez)= complex(0,0)   line to (Lx,0)  

  value(Ez)= complex(0,0)     line to (Lx,Ly)     { Conducting }  

  natural(Ez)= complex(0,0)   line to (0,Ly)  

  value(Ez)= complex(Ez_in,0) line to close       { Input field }  

 

PLOTS  

  elevation( Ez, Ep) from (0,Ly/2) to (Lx,Ly/2)  

  elevation( phase) from (0,Ly/2) to (Lx,Ly/2)  

  elevation( Ez, Ep) on 'outer'  

  contour( Ezr)     contour( Ezi)            

END