5. QZ global method (METHODE =”QZ”)#

5.1. From QEP to GEP#

Unlike the methods seen previously, the QZ method is able to handle a GEP directly. So we have only one transformation to apply to the initial QEP, that is linearization. The one empirically retained and detailed in §2.4 is

(L2) * \((\underset{\mathrm{A}}{\underset{\underbrace{}}{\left[\begin{array}{cc}\mathrm{-}\mathrm{K}& {0}_{n}\\ {0}_{n}& \alpha {\mathrm{I}}_{n}\end{array}\right]}}\mathrm{-}\lambda \underset{\mathrm{B}}{\underset{\underbrace{}}{\left[\begin{array}{cc}\mathrm{C}& \mathrm{M}\\ \alpha {\mathrm{I}}_{n}& {0}_{n}\end{array}\right]}})\left[\begin{array}{c}\mathrm{u}\\ \lambda \mathrm{u}\end{array}\right]\mathrm{=}{0}_{\mathrm{2n}}\) (5.1-1)

The GEP obtained is not structurally symmetric (or Hermitian) but it is not prejudicial to the calculation because the adapted LAPACK drivers only work non-symmetrically. For more robustness and to simplify the structuring of the code, we formulate and solve GEP (L2) in the**complex plan*. As for GEP with complex modes, we use the standard LAPACK (ZGGEV) or expert (ZGGEVX) routines, depending on the parameter TYPE_QZ =” QZ_SIMPLE “/” QZ_EQUI “.

At the end of the modal calculation, QZ returns to Code_Aster the calculated modes and these will be verified, filtered and ordered according to the same recommendations as for the complex modes of GEP (cf. [Boi09] §9.4).

5.2. Scope of use#

QEP with symmetric matrices or not (and \(\mathrm{K}\) can be complex symmetric).

The user can only specify TYPE_RESU =” DYNAMIQUE “as the class to which their calculation belongs (no buckling). The vector FREQ is then optionally entered (and not CHAR_CRIT).

5.3. Impressions in the message file#

A commented extract from the sdll113a test case is included in §2.5.

5.4. Summary of the settings#

Now let’s summarize the setting of the CALC_MODES operator with OPTION among [“CENTRE”, “PLUS_PETITE”, “TOUT”] for the QZ method.

Operand	Keyword	Default Value	References
	TYPE_RESU =” DYNAMIQUE “	“ DYNAMIQUE “	§2.1

	OPTION =” PLUS_PETITE “	“ PLUS_PETITE “	[Boi09] §9.4
	“CENTRE” “TOUT”		[Boi09] §9.4

CALC_FREQ	FREQ (if CENTRE)		[Boi09] §9.4
	AMOR_REDUIT (if CENTRE)		[Boi09] §9.4
	NMAX_FREQ	10	[Boi09] §9.4
	APPROCHE =…	Not applicable

SOLVEUR_MODAL	METHODE **=”QZ”	“SORENSEN”	[Boi09] §9
	…
	Usual “QZ” settings		[Boi09] §9

Table 5.4-1. Summary of the settings of CALC_MODES with OPTION among [ » CENTRE “,” PLUS_PETITE “,” TOUT “] with METHODE =”QZ” * (QEP) .

Note:

During the first few passes, it is strongly recommended to modify only the main parameters noted in bold. The others are more about the details of the algorithm and have been initialized empirically to standard values.