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Value of eigenvalue linearization point

Posted 2018年7月25日 GMT+2 17:56Version 5.31 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 2018年8月6日 GMT+2 13:47
Henrik Sönnerlind COMSOL Employee

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Posted: 6 years ago 2018年8月6日 GMT+2 13:47

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 matrixAitself depends on the eigenvalue, that is

then the problem is linearized using

whereis the value you supply asValue 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

-------------------
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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