hi
i am solving Helmholtz equation for a rectangular waveguide using
Finite Element Method with a Fortran code.
Governing equation is
del ^ 2 (p) + k^2 (p) = 0
Left (vertical ) boundary of the domain carries the source. Right
( vertical ) boundary is the absorbing boundary with
Sommerfield Radiation Condition. Top boundary is the pressure release.
Bottom is rigid
I have verified the computer code by imposing a sine function at the
left boundary. This becomes an oscillating cylinder problem. I could
recover the mode shape in the near as well as far field. The numerical
error associated with this exercise was < 2 % (quadratic element).
Now I want to use a harmonic point source. How do I incorporate a
point source ( Hankel function H (k,0 ) becomes singular at r = 0 )
in the finite element mesh. Scooping out a small area (fraction of
wavelength )around the source, and then imposing unbounded pressure
values at nodes surrounding the source would lead to a problem same as
stress concentration. What can I do to avoid such a thing? The
pressure thus obtained differ from the theory badly. Has anybody come
across such a problem ?
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