{ WAVEGUIDE.PDE
This problem solves for the Transverse-Electric modes of a T-septate
rectangular waveguide.
----- From J. Jin, "The Finite Element Method in Electromagnetics", p. 197
}
title "TE Waveguide"
select
modes = 4 { This is the number of Eigenvalues desired. }
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
equations
del2(Hz) + lambda*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
vector(Hx,Hy) as "Transverse H" norm
vector(Ex,Ey) as "Transverse E" norm
end