shiftguide

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{  SHIFTGUIDE.PDE

 

  This problem demonstrates the technique of eigenvalue shifting to select

  an eigenvalue band for analysis.  Compare these results to the problem

  Waveguide20, and you will see that the negative modes here correspond to

  the modes below the shift value, while the positive modes here correspond

  to the modes above the shift value.   The result modes  in the shifted calculation

  comprise a complete range of the unshifted modes. (The correspondence is

  1:9, 2:8, 3:10, 4:11, 5:12, 6:13, 7:7, 8:6).

 

  The solution algorithm used in FlexPDE finds the eigenvalues of lowest

  magnitude, so you will always see a band of positive and negative values

  centered on the shift value.

}  

 

title "TE Waveguide - eigenvalue shifting"  

 

 

select  

 modes = 8  

 ngrid=20  

 

variables  

 hz  

 

definitions  

 L = 2  

 h = 0.5       ! half box height

 g = 0.01     ! half-guage of wall

 s = 0.3*L     ! septum depth

 tang = 0.1   ! half-width of tang

 Hx = -dx(Hz)  

 Hy = -dy(Hz)  

 Ex = Hy  

 Ey = -Hx  

 

 shift = 40   ! PERFORM AN EIGENVALUE SHIFT

 

equations  

 Hz:  del2(Hz) + lambda*Hz + shift*Hz = 0  

 

constraints  

 integral(Hz) = 0 { since Hz has only natural boundary conditions,

                       we need an additional constraint to make

                       the solution unique }  

 

boundaries  

region 1  

  start(0,0)  

  natural(Hz) = 0     line to (L,0) to (L,1) to (0,1) to (0,h+g)  

  natural(Hz) = 0  

      line to (s-g,h+g) to (s-g,h+g+tang) to (s+g,h+g+tang)  

            to (s+g,h-g-tang) to (s-g,h-g-tang) to (s-g,h-g) to (0,h-g)  

  line to close  

 

monitors  

  contour(Hz)  

 

plots  

  contour(Hz) painted report (lambda+shift) as "Shifted Lambda"  

 

summary ("compare Shifted Lambda to output of waveguide20.pde")

  report lambda  

  report (lambda+shift) as "Shifted Lambda"  

 

end