Mode Analysis
The Mode Analysis () study and study step are used to compute the propagation constants or wave numbers as well as propagating mode shapes for a given frequency.
For example, in electromagnetics, it is used to compute the propagation constants and mode shapes at ports and waveguide cross sections. In acoustics, it is used to compute the propagation constants and mode shapes at inlets, outlets, and cross sections of guiding structures such as ducts.
When you add a Mode Analysis study, it adds a Mode Analysis study step under the Study node. The Mode Analysis study is available with the Acoustics Module, RF Module, or Wave Optics Module.
Study Settings
Select a method to Transform: Effective mode index, Effective mode index, 2D axisymmetry, Out-of-plane wave number, Out-of-plane wave number, 2D axisymmetry, Phase velocity, or None. The available transforms and the default transform depend on the physics interfaces in the study.
Enter a value or expression for the Mode analysis frequency. The default frequency depends on the physics interfaces in the study.
From the Mode solver list, choose ARPACK (the default), FEAST, or LAPACK (filled matrix). See Eigenvalue for more information.
Values of Linearization Point
Use the settings in this section 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.
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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Any other available solution to use it as a linearization point. It can be the current solution in the sequence, or a solution from another sequence, or a solution that was stored with the Solution Store node. You select a stored solution by changing Use to the name of the stored solution. Choose a solution using the Selection list (see Values of Dependent Variables under Common Study Step Settings).
Filtering and Sorting
Filtering
The eigenvalues can be excluded if there is a filter expression that they do not satisfy. In the table below, in the Filter expression (store if positive) column, add expressions for the filtering. Those expressions can be functions of the eigenvalue lambda or eigenfrequency freq and can be logical expressions such as lambda>10. If desired, add some descriptive text in the Description column for the expressions.
The Store solutions list is always available: Choose All converged solutions (the default) or First N for the first N solutions. Then specify that number in the Maximum number of stored solutions field (default: 1000).
Sorting
The eigenvalues can be sorted in Ascending (the default) or Descending order depending on the Ordering setting. When the Sorting method is Predefined, you can choose to Sort primarily based on the Real part, Imaginary part, Real part magnitude, Imaginary part magnitude, or Absolute value. The same settings are available for the Secondarily option, which is used to resolve conflicts. The defaults for eigenvalues are Real part for Sort primarily and Imaginary part magnitude for Secondarily. For eigenfrequencies, the defaults are Imaginary part for Sort primarily and Imaginary part magnitude for Secondarily. Also, the Sort based on transformed eigenvalues checkbox is selected by default to take and eigenvalue transformation into account when sorting.
Alternatively, if you choose User defined as the Sorting method, you can define an arbitrary number of (ordered) custom sorting priority expressions in the table that appears. In the Sorting priority expression column, add expressions for the sorting in order of priority. Those expressions can be functions of the eigenvalue lambda or eigenfrequency freq. For example, you can specify an expression such as abs(freq-1) to sort according to the distance from a given shift (1 in this case). If desired, add some descriptive text in the Description column for the expressions.
Select the Conjugate-pair consecutive sort checkbox to make sure that complex-conjugate eigenpairs appear one after the other, regardless of the sorting rules.
For parametric eigenvalue problems, select the Mode following checkbox to sort the solutions (eigenvalues and corresponding eigenvectors) for the current parameter value according to the solutions for the previous parameter value. This is useful to track the changes of the eigenmodes as functions of a parameter and to generate plots such as Campbell diagrams. The initial solutions are sorted after the settings specified above.
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 checkbox. To enable this option, click the Show More Options button () and select Batch and Cluster in the Show More Options dialog.
The Physics and Variables Selection, Values of Dependent Variables, Mesh Selection, Adaptation and Error Estimates, and Geometric Entity Selection for Adaptation sections and the Include geometric nonlinearity checkbox are described in Common Study Step Settings. There is also detailed information in the Physics and Variables Selection and Values of Dependent Variables sections.
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With the Acoustics Module: Eigenmodes in a Muffler, Application Library path Acoustics_Module/Automotive/eigenmodes_in_muffler.
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With the Wave Optics Module: Stress–Optical Effects in a Photonic Waveguide, Application Library path Wave_Optics_Module/Waveguides/stress_optical.