-eigenvalues

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -eigenvalues                                                       #
 ##############################################################################
 # solutions    = 15                                                          #
 # estimation   = undefined                                                   #
 # storeallmodes= no                                                          #
 #    flowsave  = 0.0                                                         #
 #    fhighsave = 1.0e+30                                                     #
 # passes       =  2                                                          #
 # pfac2        = 1.0e-3                                                      #
 # lossy          = no                  -- lossy or dispersive computation    #
 #    flowsearch  = undefined           -- edges of the search area...        #
 #    fhighsearch = undefined           -- ...when "lossy= yes"               #
 #                                                                            #
 #                                                                            #
 # compressed   = yes                   -- minimal RAM, more CPU and IO time  #
 ##############################################################################
 # return, doit, help, ?                                                      #
 ##############################################################################

• solutions= NSOL:
  The number of basis vectors to use for solving the eigenvalue problem. This number should better not be smaller than, say, 10. The more basis vectors you allow, the more accurate will the solutions be. But: the memory requirement and CPU time is proportional to this number. If compressed= yes is specified, the memory requirement is NOT proportional to the number of basisvectors, as then the basisvectors are stored to disk and retrieved from disk.
• estimation= FUP:
  Estimation of the resonant frequency of the highest mode, i. e. the NSOL.st mode.
  This parameter is mandatory.
  A common error, that even we run into, is, to specify this estimation badly wrong. To get an estimate, compute with a coarse mesh, specify the estimated highest frequency quite high, and compute. The estimate is good, if gd1 finds about 5 less good modes than you were asking for.

• storeallmodes= [yes | no]:
  Selects whether even the static modes shall be saved.
  gd1 computes normally 20 to 30 % static modes (when passes=1), but does not store them. If you do not believe that these static modes are really static, you can enforce the storing to file with this option. When the static solutions are in the file, you can view these 'solutions' with gd1.pp.
• flowsave= FLOW, fhighsave= FHIGH:
  The frequency range where resonant fields shall be stored to disk. This is really only useful when computing in parallel, and there is enough diskspace on the compute-nodes to hold the intermediate files, but not enough diskspace on the master-node to hold all the results of the computation. For such situations, you may also specify -general, dice= yes, iodice= yes, which specifies that the resultfields shall be stored on the local disks of the compute nodes. BUT: -general, dice= yes, iodice= yes can only be used for the PVM version, not the MPI version.
• passes= NPASS:
  gd1 uses an algorithm of Tückmantel^1.31.4 to solve the eigenproblem. This algorithm establishes a set of NSOL basisvectors that are mutually orthogonal and (hopefully) span only the subspace also spanned by the eigenvectors corresponding to the NSOL lowest eigenvalues.
  But since gd1 solves the eigenproblem resulting from the discretised version of $[\varepsilon]^{-1} {\rm\nabla \times }[\mu]^{-1} {\rm\nabla \times }\vec{E} = \omega^2 \vec{E}$, gd1 normally finds 20 to 30 % eigenvalues very near to zero. These eigenvalues belong to static fields, $\omega=0$.
  If you specify passes$>$1, gd1 throws away the static components in its already established basis vectors and can find more resonant modes with the same specified NSOL. Also, the accuracy of the fields becomes somewhat better.
• pfac2= PFAC2:
  gd1 uses an algorithm of Tückmantel to solve the algebraic eigenproblem resulting from the discretised MAXWELLian equations. This algorithm has an internal accuracy factor, called pfac2, that controls the relative cleaning of the basisvectors from eigenvectors outside the range 0 to FUP, in which the NSOL resonant fields are expected.
  A smaller pfac2 leads to increased cpu-time, but better accuracy for the lower modes. A good value is pfac2=1e-3.
• lossy= [yes|no]:
  When lossy= yes, eigenvalues are searched in a geometry where the lossy parameters and dispersive parameters of materials with type= normal are taken into account. This algorithm needs four times as much memory as the lossfree algorithm.
• flowsearch= F1, fhighsearch= F2:
  Only used when lossy=yes: The frequency range where the resonances of the lossy geometry are searched in.
• doit:
  If you say "doit", the settings in "-general, -mesh, -material" are checked, the mesh is re-generated, and the iteration for the resonant fields is performed.
  After the field computation, the fields are written to file and the program stops.

Example The following specifies that we want to compute with 15 basisvectors, we want to perform two passes to search for the eigenvalues, and we estimate that the highest resonant frequency of the 15 to be found will be about 1.3 GHz. The final doit starts the eigenvalue computation.

 -eigenvalues
   solutions= 15
   passes= 2
   estimation= 1.3e9
   doit

Footnotes

... T\"uckmantel^1.3

J. Tückmantel, `Urmel with a High Speed and High Precision Eigenvector Finder', CERN/EF/RF 83-5, 11 July 1983

...1.3^1.4

J. Tückmantel `An improved version of the eigenvector processor SAP applied in URMEL', CERN/EF/RF 85-4, 4 July 1985