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How to apply boundary condition in generalized eigenvalue problem?

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mdn
#1
Apr14-14, 12:45 AM
P: 34
Hi all,
Generally boundary condition (Dirichlet and Neumann) are applied on the Load Vector, in FEM formulation.
The equation i solved, is Generalized eigenvalue equation for Scalar Helmholtz equation in homogeneous wave guide with perfectly conducting wall ( Kψ =λMψ ), and found, doesn't need to apply boundary condition as here, i encounter natural boundary condition.
I want to apply this equation for anisotropic, inhomogeneous medium, and read that, i have to use vector fem with edge element and not nodal element that i used in my procedure,
to avoid non physical solution (spurious mode).
and here boundary condition are necessary, now i confused, how to apply boundary condition if there is no Load vector in formulation? and as per my reading, there is no way to apply BC on Stiffness and Mass matrix.
thanks in advance.
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Greg Bernhardt
#2
May4-14, 10:17 PM
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P: 9,467
I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
Barron
#3
May6-14, 05:46 AM
P: 7
In eigenvalue problems you can apply a zero Dirichlet boundary condition by removing the DOF from the system of equations. That means forming smaller matrices without the row and column of that DOF.

Alternatively, you can put a large stiffness on the diagonal. This connects the DOF to ground by a stiff spring. The disadvantage is that you have to choose a stiffness high enough that it won't cause spurious modes in the frequency range you're interested in.


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