hi all
this might look like an irrelevant topic in a group like sci.math but
i couldn't find any suitable group to
post this.
I am solving Helmholtz equation using Finite Element Method . The
finite element equations ( and expressions for element matrices) are
obtained by usual method of variational calculus. I have a rectangular
domain whose left boundary ( i.e. vertical line) has the acoustic
source, top and bottom boundaries are treated with pressure release
boundary condition. The right side ( other vertical line) is the
radiation boundary, where Neumann boundary condition is imposed.
When there are more than one normal modes of vibration, how do I treat
these normal modes at the radiation boundary? The Neumann boundary
condition must be satisfied by each of the normal modes which is
obvious.
As is well known that these normal modes are orthogonal to each other.
So the normal modes should also satisfy condition of orthogonality at
the radiation boundary. Is orthogonality of normal modes just an
abstract mathematical idea or does it have any physical meaning? Can I
simply write this condition as a1*a2, where a1 and a2 are orthogonal
vectors? Or (a1)' * a2 ( ' is derivative ) is more correct as it
alleviates nonlinear effects?
thank you.