The Block Lanczos eigenvalue solver uses the Lanczos algorithm where the Lanczos recursion is performed with a block of vectors. The Block Lanczos method uses the sparse matrix solver, overriding any solver specified via EQSLV.

The Block Lanczos method is especially powerful when searching for eigenfrequencies in a given part of the eigenvalue spectrum of a given system. The convergence rate of the eigenfrequencies will be about the same when extracting modes in the midrange and higher end of the spectrum as when extracting the lowest modes. Therefore, when you use a shift frequency (FREQB on MODOPT) to extract n modes beyond the starting value of FREQB, the algorithm extracts the n modes beyond FREQB at about the same speed as it extracts the lowest n modes.

While the Block Lanczos eigensolver is typically very robust for a wide range of applications, some element types may cause the eigensolver difficulty in achieving a final solution. These include MPC184 elements that use the Lagrange multiplier method and FLUID30, FLUID220, and FLUID221 elements that use the symmetric element matrix formulation for modal analyses (KEYOPT(2) = 2).

The PCG Lanczos method internally uses the Lanczos algorithm, combined with the PCG iterative solver. This method is significantly faster than the Block Lanczos method in the following cases:

Having ill-conditioned matrices or asking for many (say, more than 100) modes can lead to a long solution time.

The PCG Lanczos method finds only the lowest eigenvalues. If a range of eigenfrequencies is requested (MODOPT), the PCG Lanczos method finds all eigenfrequencies below the lower value of the eigenfrequency range as well as the number of requested eigenfrequencies in the given eigenfrequency range. The PCG Lanczos method is therefore not recommended for problems when the lower value of the input eigenfrequency range is far from zero.

When to Use PCG Lanczos over Block Lanczos

The Block Lanczos eigensolver is the recommended eigensolver for most applications; however, the PCG Lanczos eigensolver can be more efficient than the Block Lanczos eigensolver for certain cases. Follow these guidelines when deciding whether to use the Block Lanczos or PCG Lanczos eigensolver.

Typically, the following conditions must be met for the PCG Lanczos eigensolver to be most efficient:

The PCG Lanczos eigensolver (like all iterative solvers) is most efficient when the solution converges quickly. If the model does not converge quickly in a similar static or full transient analysis, it is expected that the PCG Lanczos eigensolver will also not converge quickly and will therefore be less efficient. The PCG Lanczos eigensolver is most efficient when finding the lowest natural frequencies of the system. (For detailed information on measuring PCG Lanczos solver efficiency, see PCG Lanczos Solver Performance Output in the Performance Guide.) As the number of requested modes begins to approach one hundred, or when requesting only higher modes, the Block Lanczos eigensolver becomes a better choice.

Other factors such as the size of the problem and the hardware being used can affect the eigensolver selection strategy. For example, when solving problems where the Block Lanczos eigensolver runs in an out-of-core mode on a system with very slow hard drive speed (that is, bad I/O performance) the PCG Lanczos eigensolver may be the better choice as it does significantly less I/O, assuming a Lev_Diff value of 1 through 4 is used (PCGOPT). Another example would be solving a model with 15 million degrees of freedom. In this case, the Block Lanczos eigensolver would need approximately 300 GB of hard drive space. If computer resources are limited, the PCG Lanczos eigensolver may be the only viable choice for solving this problem since the PCG Lanczos eigensolver does much less I/O than the Block Lanczos eigensolver. The PCG Lanczos eigensolver has been successfully used on problems exceeding 100 million degrees of freedom.

The Supernode (SNODE) solver is used to solve large, symmetric eigenvalue problems for many modes (up to 10,000 and beyond) in one solution. Typically, the reason for seeking many modes is to perform a subsequent mode-superposition or PSD analysis to solve for the response in a higher frequency range.

A supernode is a group of nodes from a group of elements. The supernodes for the model are generated automatically by the program. This method first calculates eigenmodes for each supernode in the range of 0.0 to FREQE*RangeFact (where RangeFact is specified via SNOPTION and defaults to 2.0), and then uses the supernode eigenmodes to calculate the global eigenmodes of the model in the range of FREQB to FREQE (where FREQB and FREQE are specified via MODOPT).

Typically, this method offers faster solution times than Block Lanczos or PCG Lanczos if the number of modes requested is more than 200. The accuracy of the Supernode solution can be controlled by SNOPTION. For more information, see Supernode Method in the Theory Reference.

The lumped mass matrix option (LUMPM,ON) is not allowed when using the Supernode mode-extraction method. The eigensolver will automatically be switched to Block Lanczos in this case.

When to Use Supernode

Typically, the following conditions must be met for the Supernode eigensolver to be most efficient:

For models that are dominated by solid elements or have a bulkier geometry, the Supernode eigensolver can still be more efficient than other eigensolvers; however, it may require higher numbers of modes to become the best choice in terms of performance. Other factors, such as the hardware being used, can also affect the decision of which eigensolver to use. For example, on machines with slow I/O performance the Supernode eigensolver may be the faster eigensolver (compared to Block Lanczos).

The Subspace method is an iterative algorithm that is appropriate for problems having symmetric stiffness and mass matrices ( and ). It internally uses the sparse solver for the shift-invert logic. The Subspace solver performs well when the goal is to obtain a moderate to medium number of eigenvalues on large models run in distributed parallel mode.

Sturm sequence checking (off by default) is available for this method and is controlled via SUBOPT. The command can also control memory usage of the algorithm.

The unsymmetric method, which also uses the full and matrices, is meant for problems where the stiffness and mass matrices are unsymmetric (for example, acoustic fluid-structure interaction problems). Sturm sequence checking is not available for this method. Therefore, missed modes are a possibility at the higher end of the frequencies extracted.

Solutions from the unsymmetric method can be real or complex. By default, the solution type is determined automatically (Cpxmod = AUTO on MODOPT).

For details about the complex frequency definition, see Complex Eigensolutions in the Theory Reference. For details about complex solution postprocessing, see POST1 and POST26 – Complex Results Postprocessing in the Theory Reference.

The damped method (MODOPT,DAMP) is meant for problems where damping cannot be ignored, such as rotor dynamics applications. It uses the full matrices (, , and the damping matrix ).

Sturm sequence checking is not available for this method. Therefore, modes may be missing in the higher end of the range of extracted frequencies.

In a damped system, the eigensolutions are complex and the response at different nodes can be out of phase. At any given node, the amplitude will be the vector sum of the real and imaginary components of the eigenvector.

The complex frequencies are generally pairs of complex conjugates except in cases where system matrices are unsymmetric and structural damping is present.

For an example showing the use of the MODOPT and DAMPOPT commands to extract eigenvalues within a frequency range of interest, see Example: Shift Option Usage on DAMPOPT. For details about the complex frequency definition, see Complex Eigensolutions in the Theory Reference. For details about complex solution postprocessing, see POST1 and POST26 – Complex Results Postprocessing in the Theory Reference.

 

3.8.6.1. Example: Shift Option Usage on DAMPOPT

Consider an example having many complex eigenfrequencies with the real part in the range of 0 to 3000 Hz. Using the sequence of commands below, eigenvalues are reported as shown in Figure 3.2: Eigenfrequency Spectrum with the SHIFT Option, First 1000.

/solu 
antype,modal 
modopt,damp,1000,10,3000  ! Request the first 1000 eigenvalues 
                          !   in the range 10 to 3000 Hz 
dampopt,shift,on          ! Activate the shift option 

 

Figure 3.2: Eigenfrequency Spectrum with the SHIFT Option, First 1000

Using the following command input, you can ask for only the eigenfrequencies within a frequency range starting at 1500 Hz. The result is shown in Figure 3.3: Subset of Eigenfrequencies with the SHIFT Option. The black points on the graph show the resulting subset of eigenfrequencies compared to the above case of 1000 requested eigenvalues.

/solu
antype,modal
modopt,damp,20,1500   ! Only request the first 20 
                      !   eigenvalues > 1500 Hz
dampopt,shift,on      ! Activate the shift option
                      ! The DAMP algorithm uses a shift 
                      !   of 1500 Hz to initiate the search

Figure 3.3: Subset of Eigenfrequencies with the SHIFT Option

Note that when the SHIFT option is active and FREQB is specified, the damped eigensolver only produces eigenfrequencies with a real part greater than FREQB. If FREQB is not specified, the damped eigensolver finds eigenvalues closest to the 0 Hz point.

The QR damped method (MODOPT,QRDAMP) combines the advantages of a symmetric eigensolution method with the complex Hessenberg method. The key concept is to approximately represent the complex damped eigenvalues by modal transformation using a larger number of eigenvectors of the undamped system. After the undamped mode shapes are evaluated by using the real eigensolution, the equations of motion are transformed to these modal coordinates.

Using the QR algorithm, a smaller eigenvalue problem is then solved in the modal subspace. This approach gives good results for lightly damped systems and can also apply to any arbitrary damping type: proportional or non-proportional symmetric damping, nonsymmetrical gyroscopic damping matrix, or structural damping. It is recommended to use the Damp eigensolver (MODOPT,DAMP) when the complex eigenvalues are not conjugate pairs as only half of them are output by the QRDAMP eigensolver. Such cases include, but are not limited to:

The QRDAMP eigensolver applies to models having an unsymmetrical global stiffness matrix where only a few elements contribute unsymmetric element stiffness matrices. For example, in a brake-friction problem, the local part of a model with friction contacts generates a unsymmetric stiffness matrix in contact elements. When an unsymmetric stiffness matrix is encountered, the eigenfrequencies and mode shapes obtained by the QRDAMP eigensolver should be verified by rerunning the analysis with the unsymmetric eigensolver. If an unsymmetric stiffness matrix is encountered, the QRDAMP eigensolver issues a message after completing the symmetric eigensolution.

The QRDAMP eigensolver works best when there is a larger modal subspace to converge and is therefore the best option for larger models. Because the accuracy of this method is dependent on the number of modes used in the calculations, a sufficient number of fundamental modes should be present (especially for highly damped systems) to provide good results. The QR damped method is not recommended for critically damped or overdamped systems. This method outputs both the real and imaginary eigenvalues (frequencies). By default, only the real eigenvectors (mode shapes) are output, although complex mode shapes can be calculated if needed (MODOPT).

Additional QRDAMP eigensolver options can be set via QRDOPT.

In general, Ansys, Inc. recommends using the Damp eigensolver for small models. It produces more accurate eigensolutions than the QR Damped eigensolver for damped systems.

For details about the complex frequency definition, see Complex Eigensolutions in the Theory Reference. For details about complex solution postprocessing, see POST1 and POST26 – Complex Results Postprocessing in the Theory Reference.