Eigenvalue

Users may choose between two different eigensolvers, the Lanczos algorithm presented by Hughes [1987] or the Jacobi algorithm with Ritz transformation, in order to the determine the modes of vibration of a structure. When the automatic option is selected the most proper eigensolver will be used depending on the number of the degrees of freedom of the building. The input for each algorithm is described in detail hereafter:

Lanczos algorithm
The following parameters are used to control the way in which this eigensolver works:

• Number of eigenvalues. The maximum number of eigenvalue solutions required by the user. The default value for the default predefined settings scheme is 10 which normally guarantees that, at least for standard structural configurations, all modes of interest are adequately captured. Users might wish to increase this parameter when analysing 3D irregular buildings, where modes of interest might be found beyond the 10th eigensolution.
• Maximum number of steps. The maximum number of steps required for convergence to be reached. The default value is 50, for all the predefined settings schemes, sufficiently large to ensure that, for the vast majority of structural configurations, solutions will always be obtained.

Jacobi algorithm with Ritz transformation
The user may specify:

• Number of Ritz vectors (i.e. modes) to be generated in each direction (X, Y and Z). This number cannot exceed the number of degrees of freedom of the model.
• Maximum number of steps. The default value of 50 may, in general, remain unchanged.

Note: Users should make sure that the total number of Ritz vectors in the different directions does not exceed the corresponding number of degrees-of-freedom (or of structurally meaningful modes), otherwise unrealistic mode shapes and values will be generated.