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 or Phase velocity, Out-of-plane wave number, 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 search method list, select a search method:
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Manual (the default), to specify some search criteria manually. See Manual Mode Search Settings below.
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Region, to define a mode search region in a complex plane. See Mode Search Region Settings below.
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All (filled matrix), to search for all modes. This option is only applicable for small mode analysis problems. See All (Filled Matrix) Settings below.
Manual Mode Search Settings
Use the Desired number of modes field to specify the number of modes you want the solver to return (default: 6).
In the Search for modes around field, you can specify a value or expression around which the eigenvalue solver should look for solutions to the eigenvalue equation (default: 1).
Use the Mode search method around shift list to control how the eigenvalue solver searches for modes around the specified shift value:
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Select Closest in absolute value (the default value) to search for modes 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 modes with a larger real part than the shift value.
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Select Smaller real part to search for modes with a smaller real part than the shift value.
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Select Larger imaginary part to search for modes with a larger imaginary part than the shift value.
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Select Smaller imaginary part to search for modes with a smaller imaginary part than the shift value.
From the Use real symmetric eigenvalue solver list, choose Automatic (the default) or Off. If you chose Automatic, you can select the Real symmetric eigenvalue consistency check check box to check for positive definiteness.
Mode Search Region Settings
Use the Approximate number of modes field to specify the approximate number of modes you want the solver to return (default: 20).
In the Maximum number of modes field, you can specify a maximum number of modes to limit the eigenvalue solver’s search for additional modes (default: 200).
The Perform consistency check check box is selected by default to increase confidence that the solver finds all modes in the search region.
Under Search region, you define the size of the search region for modes 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.
From the Use real symmetric eigenvalue solver list, choose Automatic (the default) or Off. If you chose Automatic, you can select the Real symmetric eigenvalue consistency check check box to check for positive definiteness.
All (Filled Matrix) Settings
To specify a shift to use in the modes computation, select the Shift used in the modes computation check box and then enter a shift (in rad/m) in the associated text field.
In the Maximum matrix size field, enter an upper limit on the matrix size (default: 200).
From the Unit list, choose a suitable unit (default rad/m).
Values of Linearization Point
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.
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).
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 More Options button () and select Batch and Cluster in the Show More Options dialog box.
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 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.
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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_and_Couplers/stress_optical.