The Eigenfrequency (
) study and study step are used to compute eigenmodes and eigenfrequencies of a linear or linearized model.
From the Eigenfrequency solver list, choose
ARPACK (the default) or
FEAST.
From the Eigenfrequency search method list, select a search method:
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All (filled matrix) to find all eigenfrequencies for a filled matrix. This option is only applicable for small eigenvalue problems. You can then specify a Maximum matrix size (default: 2000).
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Use the Eigenfrequency search method around shift list to control how the eigenvalue solver searches for eigenfrequencies around the specified shift value:
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Select Closest in absolute value (the default value) to search for eigenfrequencies 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 eigenfrequencies with a larger real part than the shift value.
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Select Smaller real part to search for eigenfrequencies with a smaller real part than the shift value.
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Select Larger imaginary part to search for eigenfrequencies with a larger imaginary part than the shift value.
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Select Smaller imaginary part to search for eigenfrequencies with a smaller imaginary part than the shift value.
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Use the Approximate number of eigenfrequencies field to specify the approximate number of eigenfrequencies you want the solver to return (default: 20). The value of the
Approximate number of eigenfrequencies 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 eigenfrequencies will increase the memory requirement and the computational time. If the solver indicates that the value of the
Approximate number of eigenfrequencies is smaller than the actual number of eigenfrequencies in the given region, it will perform a search for more eigenfrequencies, 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 eigenfrequencies than a too small.
In the Maximum number of eigenfrequencies field, you can specify a maximum number of eigenfrequencies to limit the eigenvalue solver’s search for additional eigenfrequencies (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 a unit (default: rad/s) and the size of the search region for eigenfrequencies 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.
Eigenfrequency 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 solver 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.
From the Eigenfrequency search contour list, select a search contour:
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Half contour (Hermitian problem), to define an eigenfrequency search contour by half of the whole contour. See Half Search Contour Settings below.
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You define the Whole contour by specifying the
Unit (default: rad/s),
Center of the ellipse contour,
Horizontal radius of the ellipse contour,
Vertical/horizontal axis ratio of ellipse contour (%) and
Rotation angle of the ellipse contour in the respective text fields. It is important that the horizontal radius that you specify in the
Horizontal radius of the ellipse contour field is large enough to enclose the eigenvalues of interest. In the
Vertical/horizontal axis ratio of ellipse contour (%) field, specify the ratio of the vertical radius of the ellipse over its horizontal radius, assuming that the horizontal radius is 100. In the
Rotation angle of the ellipse contour field, specify the rotation angle in degree from the vertical axis in the range of
−180 degrees to 180 degrees.
From the Number of eigenfrequencies list, select the method for evaluating the number of eigenfrequencies inside the eigenfrequency search contour:
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Stochastic estimation (the default) to use stochastic estimation to evaluate the number of eigenfrequencies. After the stochastic estimation finishes, the eigenvalue solver automatically calculates the eigenfrequencies inside the eigenfrequency search contour, using the number of eigenfrequencies calculated from stochastic estimation as the Size of initial search subspace for estimation (default: 6).
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Manual to specify the number of eigenfrequencies inside the eigenvalue search contour manually in the Approximate number of eigenfrequencies field (default: 6).
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Stochastic estimation only to use only stochastic estimation to evaluate the number of eigenfrequencies.
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In the Size of initial search subspace for estimation field (default: 6), specify the initial guess of the search subspace dimension, which can be interpreted as an initial guess for the number of eigenfrequencies inside the contour. This setting is only available when using a stochastic estimation.
From the Integration type for estimation list, select the type for integration:
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Automatic (the default) to choose the integration type automatically depending on eigenvalue solver. It means the Gauss type for real symmetric or Hermitian eigenvalue solver and the Trapezoidal type for other types of solvers.
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Gauss to use Gauss integration.
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Trapezoidal to use trapezoidal integration.
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From the Number of integration points for estimation list, select the number of points for integration:
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Automatic (the default) to define the number of points for integration automatically. It is 3 for real symmetric or Hermitian eigenvalue solvers and 6 for other types of solvers.
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Manual to specify the number of integration points for estimation manually in the Number of integration points field.
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Eigenfrequency computations can be performed with a nonsymmetric solver or, if applicable, a real symmetric solver. From the Use real symmetric or Hermitian eigenvalue solver list, choose
Automatic (the default) or
Off. For the
Automatic option there is the option to select the
Real symmetric or Hermitian eigenvalue solver 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.
There is also and option to select the Store linear system factorization check box. If selected, linear system factorizations are stored from the first FEAST iteration and reused in later iterations.
If the Study>Batch and Cluster check box is selected in the
Show More Options dialog box, select the
Distribute linear system solution check box to run the FEAST eigenvalue solver in parallel. See
Running FEAST in a Parallel MPI Mode for more information.
You define the Half contour (Hermitian problem) by specifying the
Unit,
Lower bound of search interval,
Upper bound of search interval, and
Vertical/horizontal axis ratio of ellipse contour (%) in the respective text fields.
From the Number of eigenfrequencies list, select the method for evaluating the number of eigenfrequencies inside the eigenfrequency search contour:
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Stochastic estimation (the default) to use stochastic estimation to evaluate the number of eigenfrequencies. After the stochastic estimation finishes, the eigenvalue solver automatically calculates the eigenfrequencies inside the eigenfrequency search contour, using the number of eigenfrequencies calculated from stochastic estimation as the Size of initial search subspace for estimation (default: 6).
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Manual to specify the number of eigenfrequencies inside the eigenfrequency search contour manually in the Approximate number of eigenfrequencies field (default: 6).
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Stochastic estimation only to use only stochastic estimation to evaluate the number of eigenfrequencies.
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From the Integration type for estimation list, select the type for integration:
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Automatic (the default) to choose the integration type automatically depending on eigenvalue solver. It means the Gauss type for real symmetric or Hermitian eigenvalue solver and the Trapezoidal type for other types of solvers.
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Gauss to use Gauss integration.
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Trapezoidal to use trapezoidal integration.
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Zolotarev to use Zolotarev integration.
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From the Number of integration points for estimation list, select the number of points for integration:
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Automatic (the default) to define the number of points for integration automatically. It is 3 for real symmetric or Hermitian eigenvalues.
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Manual to specify the number of integration points for estimation manually in the Number of integration points field.
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In the Size of initial search subspace for estimation field (default: 6), specify the initial guess of the search subspace dimension, which can be interpreted as an initial guess for the number of eigenvalues inside the half contour. This setting is only available when using a stochastic estimation.
If required, there is an option to select the Real symmetric or Hermitian eigenvalue solver consistency check check box. There is also an option to select the
Store linear system factorization check box. If selected, linear system factorizations are stored from the first FEAST iteration and reused in later iterations.
If the Study>Batch and Cluster check box is selected in the
Show More Options dialog box, select the
Distribute linear system solution check box to run the FEAST eigenvalue solver in parallel. See
Running FEAST in a Parallel MPI Mode for more information.
Use the settings under Values of linearization point to specify a linearization point.
From the Settings list, choose
Physics controlled (the default) to use linearization point settings controlled by the physics interfaces. Choose
User defined to specify the linearization point using the
Method list. Select:
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Initial expression to use the expressions specified on the Initial Values nodes under a specific physics interface as a linearization point.
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Solution to use a solution as a linearization point.
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Use the Study list to specify which solution to use from the available studies. Select:
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Zero solution to use a linearization point that is identically equal to zero.
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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 More Options button (
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Batch and Cluster in the
Show More Options dialog box.