{
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
del2(Hz) + lambda*Hz + shift*Hz = 0
constraints
integral(Hz) = 0 { since Hz has only natural boundary conditions,
we need to constrain the answer }
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
report lambda
report (lambda+shift) as "Shifted Lambda"
end