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{ 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