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# shiftguide

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# shiftguide

{  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