Eigenvalue Parametric
The Eigenvalue Parametric node () is an attribute node that handles settings for parameter stepping to add parametric sweeps. For each set of parameter values, an eigenvalue problem is solved.
This attribute can be used together with an Eigenvalue Solver. The functionality is then similar to when Parametric is added as a subnode to a Stationary Solver, but continuation is not supported.
EigenvalueParam in the COMSOL Multiphysics Programming Reference Manual.
General
Use the Defined by study step list to specify if the settings are synchronized with the corresponding study step. Select User defined to modify the parameter table and sweep type.
Use the Sweep type list to specify the type of sweep to perform. The Specified combinations type (the default) solves for a number of given combinations of values, while the All combinations type solves for all combinations of values. Using all combinations can lead to a very large number of solutions.
Use the table with Parameter name, Parameter value list, and (optional) Parameter unit to specify parameter names, values, and units for the parametric solver. Use the Add button () to add a row to the table. Each row has one parameter name, a corresponding parameter value list, and an optional unit. The unit becomes orange if the unit that you specify does not match the unit given for the parameter where it is defined. For the Specified combinations sweep type, the lists of values must have equal length. When you click in the Parameter value list column to define the parameter values, you can click the Range button () to define a range of parameter values. The parameter unit overrides the unit of the global parameter. If no parameter unit is given, parameter values without explicit dimensions are considered dimensionless.
If more than one parameter name has been specified, the lists of parameter values are interpreted as follows: Assume that the parameter names are p1 and p2, and that p1 has the list 1 3 and p2 has the list 2 4. For the Specified combinations sweep type, the solver first uses p1 equal to 1 and p2 equal to 2. Thereafter, it uses p1 equal to 3 and p2 equal to 4. And when the sweep type is All combinations, the solver uses the following order for the parameter combinations: 1 2, 1 4, 3 2, and 3 4.
An alternative to specifying parameter names and values directly in the table is to specify them in a text file. You can use the Load from File button () to browse to such a text file. You can also click the downward arrow beside the Load from File button and choose Load From () to open the fullscreen Select File window. The read names and values are appended to the current table. The format of the text file must be such that the parameter names appear in the first column and the values for each parameter appear row-wise with a space separating the name and values, and a space separating the values. Click the Save to File button () to save the contents of the table to a text file (or to a Microsoft Excel Workbook spreadsheet if the license includes LiveLink™ for Excel®).
When loading and saving parameter table data using Excel®, the units in the Parameter unit column are included. The unit column is ignored when saving and loading parameter data to *.txt, *.csv, and *.dat files.
With the ARPACK eigenvalue solver, you can supply a starting vector for the eigenvalue computation. Doing so can accelerate convergence if a series of closely related problems are to be solved. More precisely, the convergence and the computation time can be reduced if an approximation of the solution is given. In this case, the starting vector should be a linear combination of the given approximation of the eigenvectors, and the shift should be located close to the given approximation of the eigenvalues. The following settings are related to ARPACK (see The ARPACK Eigenvalue Solver Algorithm):
From the ARPACK starting vector list, choose Default, giving a random starting vector, or From previous eigenvectors. If you chose From previous eigenvectors, a From previous eigenvectors list appears, where you can choose Summation of all eigenvectors (the default) or Eigenvector with eigenvalue closest to the shift as the new starting vector. These options can always be used without compromising the convergence. Use Summation of all eigenvectors when more than one eigenpair is requested. Use Eigenvector with eigenvalue closest to the shift when only one eigenpair is requested.
From the ARPACK shift list, choose As specified (the default) or Based on eigenvalues for last parameter. If you chose Based on eigenvalues for last parameter, also choose an option from the From previous eigenvalues list that appears: Choose Average of converged eigenvalues (the default) or Eigenvalue closest to the previous shift. In the case where the eigenvalue shift value has not been parameterized, these options could be useful, but use them only if the eigenvalues are expected to have a small variation between two consecutive parameters. If this is not the case, ARPACK may converge to unwanted eigenpairs. Use Average of converged eigenvalues when the wanted eigenvalues are “around” the shift. More precisely, when the shift is an “internal point” of the convex hull of the wanted eigenvalues. Use Eigenvalue closest to previous shift if the shift is an “external point” of the convex hull of the wanted eigenvalues. For example, if the eigenvalues are known to have positive real part and the shift is set to zero.
The shift corresponds to the value of the Search for eigenvalues around field in the study settings. The eigenpairs, computed with respect to the previous parameter, are ordered from the closest to the shift to the one farthest from the shift.
To determine what the solver does when there is a solver error or the parameter stepping fails, select an option from the On error list. Select one of the following options:
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 Stop (the default) to stop the parametric sweep and only return solutions before the error.
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 Skip parameter step to skip the parameter when there is an error and then continue.
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 Store empty solution to continue the parametric sweep and store an empty (NaN) solution for this step.
Cluster Settings
Select the Distribute parameters checkbox to distribute the parameters on several computational nodes. If the problem is too large to run on a single node, you can enable the Maximum number of groups field to use the nodes’ memory more efficiently. In this case the same parameter is solved for by several nodes that cooperate as if running a nondistributed sweep. The number of nodes that cooperate is equal to the maximum of the total number of nodes divided by the Maximum number of groups setting and 1. So if the total number of nodes is 12 and the Maximum number of groups is 3, 3 groups with 4 nodes each cooperate.
Least-Squares Data
The section only appears if you are solving an eigenvalue least-squares optimization problem.
Least-squares data are read from least squares objectives (either a file or a table), and the solver sequence is set up accordingly: If there is a least-squares objective containing parameter columns in an eigenvalue study step, an Eigenvalue Parametric solver is set up, and the parameter names and values appear under Parameters from least-square objectives.
Parameter values corresponding to the same parameter names are merged between different objectives. If the Use parameters from least-squares objectives checkbox is selected (which is the default), user-defined parameter values are merged with corresponding merged data from objectives. For parameters that are defined only in objectives and not user defined (and vice versa), globally defined values are used. If the Use parameters from least-squares objectives checkbox is selected, the following settings are available:
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The Create bounding box from the General parameter value lists checkbox is selected by default to exclude values outside the bounding box.
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The Add solution data points from the General Parameter value lists checkbox is selected by default to control if data points should also be added to the solution process that is given in the General section that are not least-squares data. These points do not affect the solution process or the least-squares objectives but can be useful, for example, for postprocessing purposes or for model debugging.
If Use parameters from least-squares objectives is off, no least-squares parameters from files are used.
You can change the default values of the Use parameters from least-squares objectives and its associated settings only if Defined by study step is set to User defined.