5. Execution phase#

  • In the case where the simultaneous iteration method is used (i.e. if OPTION =” BANDE “or” CENTRE “or” PLUS_PETITE “or” PLUS_GRANDE “or” “or” TOUT “):

if the keyword DIM_SOUS_ESPACE (under the keyword factor SOLVEUR_MODAL) is not entered or is initialized to a value strictly less than the number of requested modes nf (operand NMAX_FREQ or NMAX_CHAR_CRIT), the operator automatically calculates an admissible dimension for the projection subspace via via* the empirical formulas (cf § 3.7.1.4):

METHODE =' SORENSEN '

ndim= MIN (MAX (2+nf, mse*nf), nactive) with mse=2 by default.

METHODE =' TRI_DIAG '

ndim= MIN (MAX (7+nf, mse*nf), nactive) with mse=4 by default.

METHODE =' JACOBI '

ndim= MIN (MAX (7+nf, mse*nf), nactive) with mse=2 by default.

where nactive is the number of active degrees of freedom (that is, the total number of degrees of freedom minus the number of degrees of freedom of LAGRANGE and minus the number of linear relationships that link degrees of freedom together, [R5.01.01] §3.2) and mez is the proportionality factor set by COEF_DIM_ESPACE.

If you solve a GEP, the dimension of the subspace is doubled. The values of these various parameters are printed in file MESSAGE.

  • For option “SEPARE”: having obtained an interval containing an eigenvalue, the middle of the interval is taken to calculate the mode. When calculating the mode, the eigenvalue value is further refined. It is the result of the reverse iteration itself.

  • For option “AJUSTE

“: if separation is not possible and if in a given interval there is more than one eigenvalue value, the adjustment method is not applied to this interval. On the other hand, during the calculation of the modes, reorthogonalizations with respect to the previous modes contained in the interval will be carried out (this makes it possible to calculate modes associated with a multiple eigenvalue).