Modal Solver
Use the Modal Solver () to perform either parameter stepping (also called frequency response) or time stepping (also called transient response) using a reduced model. The model reduction uses precomputed eigenvalues and eigenvectors. This solver is automatically used when a Time-Dependent Modal or Frequency-Domain Modal study is added to the model.
Also see The Modal Solver Algorithm for more information.
General
Use the Defined by study step list to specify if the settings are synchronized with the corresponding study step, or select User defined to specify all settings locally.
Use the Study type list to select the basic study type. Select:
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Frequency domain to perform parameter stepping using a reduced model. Then continue defining the settings For Frequency-Domain Modal Studies.
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Time dependent to perform time stepping using a reduced model. Then continue defining the settings For Time-Dependent Modal Studies.
For Frequency-Domain Modal Studies
For a Frequency-Domain Modal study, use the Parameter values field to enter a vector of parameter values that define the parameter value span for the frequency-domain simulation. Click the Range button () to define a range of parameter values using the Range dialog box.
Exactly how the vector of parameter values is used by the solver is determined by the option Parameter list type.
An alternative to specifying parameter values directly in the Parameters values field is to specify them in a text file. You can use the Load parameter values field and the Browse button to specify such a text file. Click the Read File button to read the specified file. The read values appear in the Parameters values field.
Reading parameter values from a file overwrites any values already present in that field. The format of the text files must be such that the parameter values appear one per row.
Use the Parameter list type list to control how to interpret the parameter values entered in the Parameter values field. Select:
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Frequency (the default setting) to use the parameter values without modification.
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Fraction to multiply the parameter values by the absolute value of the largest eigenvalue in the reduced model divided by two.
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Spread to treat the parameter values as an interval around each eigenvalue in the reduced model. That is, the absolute value of each eigenvalue is multiplied by the parameter values and the resulting parameter value vectors are concatenated into one.
Use the Linearity list to specify the type of linear behavior. Select:
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Linear to use a linear solver with the same linearization point for both residual and Jacobian computation, which corresponds to one step in Newton’s method.
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Linear perturbation (the default setting) to use a linear solver that computes the Jacobian in the same way as the Linear option but uses a zero solution when computing the residual. It is useful for small-signal analysis and similar applications where the variations around a linearization point are of interest.
For Time-Dependent Modal Studies
For a Time-Dependent Modal study, select a Time unit from the list. Then use the Times field to enter a vector of times that define the time span for the simulation. Click the Range button () to define time values. Output from a simulation includes the times given in this field and the corresponding solutions.
Tolerance
Use the Relative tolerance field to enter a positive number (default value: 0.01). Depending on the selection in the Study type list in the General section, the tolerance means one of the following:
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When a Frequency-Domain Modal study is selected, the Relative tolerance is used as a termination tolerance for iterative linear system solvers and for error checking (if enabled) for direct linear system solvers.
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When a Time-Dependent Modal study is selected, the Relative tolerance is used by the solver in each time step to control the relative error. The absolute tolerance settings below work in the same way as for the time-dependent solver, but internally the full length absolute tolerance vector is transferred to the modes by the same transformation (projection) as is used to transform the problem to reduced form (the eigenmodes).
Eigenpairs
Use the Solution list to specify a solver configuration to be used when constructing the reduced model.
The Use list is available for solution sequences with additional stored solutions. When available, select an option to specify a solution containing the modes to be used in the reduced model.
Use the Eigenpairs list to specify which of the eigenpairs present in the solution to include when constructing the reduced model. The default setting is All and the solver uses all available eigenpairs. Select Manual to enter a space-separated list of Eigenpair numbers in the field.
Use the Damping ratios field to enter either a scalar value or a space-separated list with values. The total number of entered values must be one or equal to the number of eigenpairs in the reduced model. If one number is entered, that value becomes the damping ratio for all eigenpairs. If the field is empty (the default), no damping is applied by the solver.
Values of Linearization Point
A frequency-domain problem solved by the Modal Solver is assumed to be a linearization about a solution. You can specify such a solution (a linearization point) with the Prescribed by 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. Then, when Solution is selected from the Prescribed by list, specify which solution to use. Select:
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Zero to use a linearization point that is identically equal to zero.
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Any other available solution to use it as linearization point.
Select the Store linearization point and deviation in output check box to store the used linearization point in the output.
Output
The output from the solver can either be the solution, the reduced matrices, or both. Use the Compute list to specify Solution, Solution and reduced matrices, or Reduced matrices. If Solution or Solution and reduced matrices is selected, click to select the Store solution on disk check box to store the output solution on disk instead of in the computer’s internal memory (this option is active by default).
If Solution and reduced matrices or Reduced matrices is selected, click to select the check boxes corresponding to matrices and vectors that should be stored in the output. The following matrices and vectors can be exported for all modal solvers: Stiffness matrix, Damping matrix, Damping ratio matrix, Mass matrix, Projection matrix, and Load vector. For Time-Dependent Modal studies the following can also be exported: Initial value vector, Initial derivative vector, and Stiffness matrix times ud. For Frequency-Domain Modal studies the following can also be exported: Mass matrix times particular solution, Damping matrix times particular solution, and All load vectors.
Advanced
Use the Load factor field to enter a globally available scalar-valued expression (default: 1). The solver uses this expression to multiply the residual. The purpose is to facilitate the use of simple nonconstant Dirichlet boundary conditions (for frequency response) and simple nonconstant Neumann boundary conditions (for transient response).
Constants
In this section you can define constants that can be used as temporary constants in the solver. You can use the constants in the model or to define values for internal solver parameters. These constants overrule any previous definition (for example, from Global Definitions). Some examples of when it can be useful to defined constants for a solver:
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When doing more advanced solver sequences, where constants need to be changed in between calls (for example, in for loops).
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When you do not want to change the global definition of a parameter or when you cannot or do not want to use a Parametric Solver feature.
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When you want to define auxiliary parameters that are part of the equations like CFLCMP or niterCMP and where the solver does not define these parameters.
Click the Add button () to add a constant and then define its name in the Constant name column and its value (a numerical value or parameter expression) in the Constant value column. By default, any defined parameters are first added as the constant names, but you can change the names to define other constants. Click Delete () to remove the selected constant from the list.
Log
Select the Keep warnings in stored log check box if you want the warnings to remain in the log for troubleshooting or other use.