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Value of eigenvalue linearization point

Posted 25 juil. 2018, 11:56 UTC−4 Version 5.3 1 Reply

sarah shahraini
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Hi All,

what does the Value of eigenvalue linearization point mean in the solver configuration setting?

Thanks

1 Reply Last Post 6 août 2018, 07:47 UTC−4
Henrik Sönnerlind COMSOL Employee

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Posted: 7 years ago 6 août 2018, 07:47 UTC−4

Hi Sarah,

This is used if your eigenvalue problem is nonlinear in the eigenvalue itself. Think about a simple standared eigenvalue problem like

If the matrix A itself depends on the eigenvalue, that is

then the problem is linearized using

where is the value you supply as Value of eigenvalue linearization point.

This means that you can expect accurate eigenvalues only in the vicinity of , and may have to do several analyses with different values of the the linearization point.

Regards,
Henrik

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Henrik Sönnerlind
COMSOL
Hi Sarah, This is used if your eigenvalue problem is nonlinear in the eigenvalue itself. Think about a simple standared eigenvalue problem like ( \mathbf A-\lambda \mathbf I) \mathbf x = 0 If the matrix **A** itself depends on the eigenvalue, that is ( \mathbf A(\lambda)-\lambda \mathbf I) \mathbf x = 0 then the problem is linearized using ( \mathbf A(\lambda_0)-\lambda \mathbf I) \mathbf x = 0 where \lambda_0 is the value you supply as _Value of eigenvalue linearization point_. This means that you can expect accurate eigenvalues only in the vicinity of \lambda_0, and may have to do several analyses with different values of the the linearization point. Regards, Henrik

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