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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 |
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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
