Real Symmetric Lanczos Method
6.3 Solution Method Characteristics
The real eigenvalue solution methods are categorized as shown in the following table:
Table 6-2 Real Eigenvalue Methods
Method Type Identifier Application Restriction
Givens Reduction GIV All Roots M Positive
Definite
Householder Reduction HOU All Roots M Positive
Definite Modified
Reduction
Reduction All Roots
Not Singular
Lanczos Iteration LANC Small
Number of Roots
Not Singular M Positive Semidefinite
Symmetric
MHOUGIV ,AHOUGIV [ ] λK + s[ ]M
[ ] λK + s[ ]M
K
6.4 DMAP User Interface
Input Data Blocks:
READ KAA,MAA,MR,DAR,DYNAMIC,USET,CASECC,
PARTVEC,SIL,VACOMP,INVEC,LLL,EQEXIN,GAPAR/
LAMA,PHIA,MI,OEIGS,LAMMAT,OUTVEC/
FORMAT/S,N,NEIGV/NSKIP/FLUID/SETNAME/SID/METH/
F1/F2/NE/ND/MSGLVL/MAXSET/SHFSCL/NORM/PRTSUM/
MAXRATIO $
KAA Stiffness matrix.
MAA Mass matrix.
MR Rigid body mass matrix
DAR Rigid body transformation matrix.
DYNAMIC Eigenvalue Extraction Data (output by IFP module).
USET Degree-of-freedom set membership table.
CASECC Case Control Data Table (selects EIGR, EIGRL, or EIGB entries, output by IFP module).
PARTVEC Partitioning vector with values of 1.0 at the rows corresponding to degrees of freedom which were eliminated in the partition to obtain KAA and MAA. Required for maximum efficiency. See SETNAME parameter description below.
SIL Scalar index list. Required for maximum efficiency.
VACOMP Partitioning vector of size of a-set with a value of 1.0 at the rows corresponding to r-set degrees-of-freedom. The USET table may be specified here as well. If VACOMP is purged and DAR does not have the same number of rows as KAA, then the partitioning vector will be determined from the size of MR.
INVEC Starting vector(s) for Lanczos method only or EQMAP data blocks for geometry domain parallel.
LLL Lower triangular factor from decomposition of KAA. Use to enhance shift logic for buckling eigenvalue extraction or VF01: interior
boundary partitioning vector for geometry domain parallel Lanczos method.
Output Data Blocks:
Parameters:
EQEXIN Equivalence between external and internal grid identification numbers. Required for maximum efficiency.
GAPAR Local-global boundary partitioning vector for geometry domain parallel Lanczos method.
LAMA Normal modes eigenvalue summary table.
PHIA Normal modes eigenvector matrix in the a-set.
OEIGS Real eigenvalue extraction summary.
MI Modal mass matrix.
LAMMAT Diagonal matrix containing eigenvalues on the diagonal (Lanczos and QLHOU only).
OUTVEC Last vector block (Lanczos only).
FORMAT Input-Character-no default. If FORMAT≠ ’MODES’, READ will solve a buckling problem of .
NEIGV Output-integer-no default. NEIGV is the number of eigenvectors found. If none were found, NEIGV = 0. If m modes were found (but error encountered), NEIGV = –m. If m modes were found, NEIGV = m.
NSKIP Input-integer-default=1. The method used by READ is taken from the NSKIP record of CASECC.
FLUID Input-logical-default=FALSE. If FLUID = TRUE, then the EIGRL or EIGR entry is selected from METHOD(FLUID) Case Control
command.
SETNAME Input-character-default='A'. For maximum efficiency, the rows and columns KAA and MAA must correspond to or be a partition of the displacement set specified by SETNAME. If KAA and MAA are a partition then PARTVEC must also be specified.
[ ] λ KK + [ ]d
( )
SID Input-integer-default=0. Alternate set identification number.
If SID=0, the set identification number is obtained from the METHOD command in CASECC and used to select the EIGR or EIGRL entries in DYNAMIC.
If SID>0, then METHOD command is ignored and the EIGR or EIGRL is selected by this parameter value. All subsequent parameter values (METH, F1, etc.) are ignored.
If SID<0, then both the METHOD command and all EIGR or EIGRL entries are ignored and the subsequent parameter values (METH, F1, etc.) will be used to control the eigenvalue extraction.
METH Input-character-default='LAN'. If SID<0, then METH specifies the method of eigenvalue extraction.
LAN Lanczos GIV Givens
MGIV Modified Givens HOU Householder
MHOU Modified Householder
AGIV Automatic selection of GIV or MGIV AHOU Automatic selection of HOU or MHOU F1 Input-real-default=0.0. The lower frequency bound.
F2 Input-real-default=0.0. The upper frequency bound. The default value of 0.0 implies machine infinity.
NE Input-integer-default=0. The number of estimated eigenvalues for non-Lanczos methods only. For the Lanczos method, NE is the problem size (default=20) below which the QL Householder option is used if it is enabled.
ND Input-integer-default=0. The number of desired eigenvalues.
MSGLVL Input-integer-default=0. The level of diagnostic output for the Lanczos method only.
0 no output
1 warning and fatal messages
2 summary output
3 detailed output on cost and convergence 4 detailed output on orthogonalization
MAXSET Input-integer-default=0. Vector block size for Lanczos method only.
SHFSCL Input-real-default=0.0. Estimate of the first flexible natural
frequency. SHFSCL must be greater than 0.0. For Lanczos method only.
NORM Input-character-default='MASS'. Method for normalizing eigenvectors. See “Option Selection” on page 176 for details.
PRTSUM Input-logical-default=TRUE. Lanczos eigenvalue summary print flag. See “Performance Diagnostics” on page 116 for details.
MAXRATIO Input-real-default= . May be overwritten in the DMAP by: param, maxratio, value.
105
6.5 Method Selection
EIGR Entry. The method selection of any method may be performed with the EIGR Bulk Data entry using the following format:
The SID is the set ID number corresponding to a METHOD command in the Case Control Section. METHOD should be equal to any of the identifiers given in
“Solution Method Characteristics” on page 169. F1, F2 are frequency minimum and maximum values specifying the boundaries of the user’s frequency range of interest. NE and ND are the number of roots estimated and desired to be found, respectively. On the continuation entry, the user can choose some normalization options, which are detailed in “Option Selection” on page 176.
EIGRL Entry. To select the Lanczos method in detail, the user should use the EIGRL Bulk Data entry with the following format:
The MSGLVL entry (0 through 3, default = 0) controls the amount of diagnostics output. MAXSET specifies the maximum number of vectors in a block of the Lanczos iteration. It is also equivalent to or may be overridden by the value of SYSTEM cell 263. The value of SHFSCL is an estimate for the location of the first nonzero eigenvalue of the problem.
The following parameters are only used if the F1 and F2 frequency range is to be broken up into segments. ALPH is the constant defining the modal distributions function (“Frequency Segment Option” on page 178). Its default value is 1.0, which results in a uniform distribution of segments. NUMS is the number of segments in the frequency range (default = 1). f1 to f15 are segment boundaries such that F1< f1
< f2 ... < f15 < F2. f1 to f15 if not specified will be computed based on a distribution given by ALPH.
Different combinations of F1, F2, and ND specify different options in the Lanczos module (see “Frequency and Mode Options” on page 176).
EIGR SID METHOD F1 F2 NE ND
NORM G C
EIGRL SID F1 F2 ND MSGLV
L
MAXSET SHFSCL NORM
ALPH NUMS f1 f2 f3 f4 f5 f6
f7 f8 f9 f10 f11 f12 f13 f14
f15
The main purpose of the SHFSCL is to aid the automatic shift logic in finding the eigenvalues especially in crossing the (possibly big) gap between the
computationally zero (rigid body) modes and the finite (flexible) modes. Another use of SHFSCL is to create a cutoff frequency for the so-called supported modes.
The NORMalization parameter for Lanczos is described in “Normalization Options” on page 176.
6.6 Option Selection
Real symmetric eigenvalue analysis offers several normalization, frequency and mode, and performance options.