Eigenvalue
The Eigenvalue () study and study step are used to compute the eigenvalues and eigenmodes of a linear or linearized model in a generic eigenvalue formulation where the eigenvalues are not necessarily frequencies. The Eigenvalue study gives you full control of the eigenvalue formulation, in contrast to the eigenfrequency study that is adapted for specific physics interfaces. The Eigenvalue study is typically used for equation-based modeling.
Selecting an Eigenvalue study gives a solver configuration with an Eigenvalue Solver.
The Physics and Variables Selection, Values of Dependent Variables, Mesh Selection, and Adaptation and Error Estimates sections and the Include geometric nonlinearity check box are described in Common Study Step Settings. There is also detailed information in the Physics and Variables Selection and Values of Dependent Variables sections.
Study Settings
From the Eigenvalue search method list, select a search method:
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 Manual (the default), to specify some search criteria manually. See Manual Eigenvalue Search Settings below.
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 Region, to define an eigenvalue search region in a complex plane. See Manual Eigenvalue Search Settings below and The Eigenvalue Solver Algorithm.
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 All (filled matrix) to find all eigenvalues for a filled matrix. This option is only applicable for small eigenvalue problems.
Manual Eigenvalue Search Settings
By default, the physics interfaces suggest a suitable number of eigenvalues to search for. To specify the number of eigenvalues, select the check box in front of the Desired number of eigenvalues field to specify the number of eigenvalues you want the solver to return (default: 6).
In a 3D model, the first six eigenvalues are typically zero and correspond to the rigid-body modes of a 3D geometry. You may therefore need to specify a larger number of eigenvalues. The largest number of eigenvalues that the solver can compute is equal to the number of unconstrained degrees of freedom minus two.
By default, the physics interfaces suggest a suitable value around which to search for eigenvalues. To specify the value to search for eigenvalues around (shift), select the check box in front of the Search for eigenvalues around field; you can then specify a value or expression around which the eigenvalue solver should look for solutions to the eigenvalue equation (default: 0).
Use the Eigenvalue search method around shift list to control how the eigenvalue solver searches for eigenvalues around the specified shift value:
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Select Closest in absolute value (the default value) to search for eigenvalues that are closest to the shift value when measuring the distance as an absolute value.
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Select Larger real part to search for eigenvalues with a larger real part than the shift value.
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Select Smaller real part to search for eigenvalues with a smaller real part than the shift value.
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Select Larger imaginary part to search for eigenvalues with a larger imaginary part than the shift value.
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Select Smaller imaginary part to search for eigenvalues with a smaller imaginary part than the shift value.
When using a search for eigenvalues, the nonsymmetric eigenvalue solver is always used, even when the problem to solve is symmetric.
Eigenvalue Search Region Settings
Use the Approximate number of eigenvalues field to specify the approximate number of eigenvalues you want the solver to return (default: 20). The value of the Approximate number of eigenvalues will affect the Dimension of Krylov space used by the algorithm; see the Advanced section of the Eigenvalue Solver. It means that increasing the value of the Approximate number of eigenvalues will increase the memory requirement and the computational time. If the solver indicates that the value of the Approximate number of eigenvalues is smaller than the actual number of eigenvalues in the given region, it will perform a search for more eigenvalues, which increases the computational time; see The Eigenvalue Region Algorithm. Within limits it is often more efficient to provide a too large value of Approximate number of eigenvalues than a too small.
In the Maximum number of eigenvalues field, you can specify a maximum number of eigenvalues to limit the eigenvalue solver’s search for additional eigenvalues (default: 200).
The Perform consistency check check box is selected by default to increase confidence that the solver finds all eigenvalues in the search region. The work required for performing the consistency check constitutes a significant part of the total work of the eigenvalue computation.
Under Search region, you define the size of the search region for eigenvalues as a rectangle in the complex plane by specifying the Smallest real part, Largest real part, Smallest imaginary part, and Largest imaginary part in the respective text fields. The search region also works as an interval method if the Smallest imaginary part and Largest imaginary part are equal; the eigenvalue solver then only considers the real axis and vice versa.
The eigenvalue solver can in some cases return more than the desired number of eigenvalues (up to twice the desired number). These are eigenvalues that the eigenvalue solver finds without additional computational effort.
Symmetry Settings
Eigenvalue computations can be performed with a nonsymmetric solver or, if applicable, a real symmetric solver. From the Use real symmetric eigenvalue solver list, choose Automatic (the default) or Off. For the Automatic option there is the option to select the Real symmetric eigenvalue consistency check check box. This check increases the computational time and memory requirements but provides a rigorous check of the applicability of the real symmetric solver.
Study Extensions
This section contains some optional extensions of the study, such as auxiliary sweeps (see Common Study Step Settings). Adding an auxiliary parametric sweep adds an Eigenvalue Parametric attribute node to the Eigenvalue Solver.
Distribute Parametric Solver
If you are running an auxiliary sweep and want to distribute it by sending one parameter value to each compute node, select the Distribute parametric solver check box. To enable this option, click the Show button () and select Advanced Study Options.