How to apply boundary condition in generalized eigenvalue problem?

In summary, the conversation discusses the application of boundary conditions in FEM formulation, particularly in the context of eigenvalue equations for the Scalar Helmholtz equation. The speaker has encountered a natural boundary condition and is now unsure how to apply it in their equation. They also mention the use of vector FEM with edge elements instead of nodal elements to avoid non-physical solutions. There are suggestions for applying boundary conditions, either by removing DOF or using a large stiffness on the diagonal, but both have their limitations.
  • #1
mdn
49
0
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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  • #2
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?
 
  • #3
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.
 

FAQ: How to apply boundary condition in generalized eigenvalue problem?

What is a boundary condition in a generalized eigenvalue problem?

A boundary condition in a generalized eigenvalue problem is a set of constraints that are applied to the solution of the problem. These constraints define the behavior of the solution at the boundaries of the system, and are used to ensure that the solution is physically meaningful.

How do I determine the appropriate boundary conditions for a generalized eigenvalue problem?

The appropriate boundary conditions for a generalized eigenvalue problem depend on the specific problem being solved. They can be determined by analyzing the physical properties of the system and considering what constraints are necessary to ensure a valid solution. Boundary conditions can also be derived from the governing equations of the problem.

Can boundary conditions affect the accuracy of the solution in a generalized eigenvalue problem?

Yes, boundary conditions can significantly affect the accuracy of the solution in a generalized eigenvalue problem. Inaccurate or inappropriate boundary conditions can lead to incorrect solutions or instability in the solution. It is important to carefully consider and apply the correct boundary conditions for a reliable and accurate solution.

Are there different types of boundary conditions that can be applied in a generalized eigenvalue problem?

Yes, there are several types of boundary conditions that can be applied in a generalized eigenvalue problem. These include Dirichlet boundary conditions, Neumann boundary conditions, and mixed boundary conditions. Each type of boundary condition has its own specific requirements and effects on the solution.

How are boundary conditions implemented in the solution of a generalized eigenvalue problem?

Boundary conditions can be implemented in the solution of a generalized eigenvalue problem through various methods, such as using finite difference or finite element methods. These methods involve discretizing the problem and applying the boundary conditions to the discrete equations. Other methods, such as spectral methods, may have different approaches to implementing boundary conditions. The specific implementation will depend on the chosen numerical method for solving the problem.

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