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{ COMPLEX_VARIABLES.PDE

 

 This example demonstrates the use of complex variables in FlexPDE.

 

 Declaring a variable COMPLEX causes the definition of two subsidiary variables,

 either named by default or by use choice.  These variables represent the

 real and imaginary parts of the complex variable.

 

}

title 'Complex variables test'

variables

   U = complex (Ur,Ui)   { creates variables (Ur,Ui) }

definitions

   u0 = 1-x^2-y^2

   s = complex(4,x)

equations

  { create two coupled scalar equations, one for Ur and one for Ui }

   U: del2(U) + conj(U) + s = 0

boundaries

  Region 1

    start(-1,-1)

      value(Ur)=u0       { apply BC to Ur.  Ui defaults to natural(Ui)=0 }

      line to (1,-1) to (1,1) to (-1,1) to close

plots

  contour(Ur,Ui)         { plot both Ur and Ui overlaid }

  contour(Real(U),Imag(U))       { an equivalent representation }

  contour(U)             { another equivalent representation }

  vector(U)               { plot vectors with Ur as X component and Ui as Y component }

  elevation(U,s) from(-1,0) to (1,0)   { plot three traces: Ur, Ui and S }

  vtk(U,s)               { test various export forms }

  transfer(U,s)

end