# [Getdp] complex eigenvalues

Christophe Geuzaine Christophe.Geuzaine at ulg.ac.be
Fri Oct 26 10:39:11 CEST 2001

```> Andri Nicolet wrote:
>
> Hello,
>
>
> Some features make the use of postprocessing with eigenvalues (using
> Lanczos algorithm) difficult.
>
> 1) Eigenvectors are stored as a time sequence as if it was the
> solution of a transient problem, real part of the 1st eigenv.,
> imaginary part of the 1st eigenv., real part of the 2nd eigenv., etc.

Not exactly. In fact, each eigenvector (real+imag part) is stored as one
solution.

> : How is it possible to access real part together with imaginary part
> in the postpro ?

with Real[] and Imag[].

> Are other time steps visible ?

In the PostProcessing, you will define a general quantity (valid for all
the "time steps", i.e. all the eigen vectors). You can then select one
particular eigenvector in the PostOperation (with the "TimeStep"
option).

> For instance, how can
> you get the complex Poynting which is the cross product of the
> electric field by the complex conjugate of the magnetic field ?

Value{ Local{ [ {e} /\ Conj[{h}] ] ; ... } }

>
> 2) The eigenvectors are known up to an arbitrary scalar factor
> (different for each eigenv.). Could it be possible to add a normation
> facility e.g. fixing L2 norm to 1 or max norm to 1 options ? This
> could be a great help in visualisation !

directly in the Lanczos algorithm, or should we implement it as an
option in a PostOperation? (It could maybe be interesting to have this
feature in other cases, e.g. to normalize time stepping results...)

>
> 3) How can you recuperate the corresponding eigenvalue in the post pro
> ?

Since the eigenvalues are stored as a pseudo time instant in the .res
file, you can use the 'TimeTable' format. At the moment, this is the
only format which outputs the value of the "time instant". In the case
of an eigenvalue problem, one line of this file can be interpreted as:

eigenvalue_index eigenvalue space_coordinates values

Christophe

--
Christophe Geuzaine

Tel: 32 (0) 4 366 37 10    http://geuz.org
Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be

```