Parametric
The Parametric node () is an attribute node that handles settings for parameter stepping using a parametric solver. This node can be used together with a Stationary Solver node.
There is also an option to run a Stationary study with an Auxiliary sweep, with or without a continuation parameter. When a continuation parameter is selected, the continuation algorithm is run, which assumes that the sought solution is continuous in these parameters. If no continuation parameter is given, a plain sweep is performed where a solution is sought for each value of the parameters. In both cases, a Stationary Solver node plus a Parametric attribute is used. The parametric solver is the algorithm that is run when a Parametric attribute node is active under a Stationary Solver. Similarly the adaptive solver is the algorithm that is run when an Adaptive Mesh Refinement (Time-Dependent Adaptation) node is active under a Stationary Solver.
In order to run a parametric continuation, select the Auxiliary sweep check box under Study Extensions for the Stationary or Frequency Domain study step. Then on the study node’s Settings window, define the parameters in the table and choose one from the Run continuation for list.
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The Adaptive and Parametric Solver Log
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The Parametric Solver Algorithm
General
Select an option from the Defined by study step list to specify if the settings are synchronized with the Stationary or Frequency Domain study step, in which case this section does not require any input. The Run continuation for list also displays the same settings made under Study Extensions.
The continuation algorithm is used if a parameter is selected. Normally the step size, damping, and predictor settings are automatic. If required, you can edit the settings in the Continuation section described next.
To edit the settings, select User defined to modify the sweep type, parameter table, reuse solution from previous step setting, and the parameter to run continuation for. These settings are the same as described in Common Study Step Settings under Study Extensions.
Exactly how the parameter values are used by the solver is determined by the Sweep type and the option Parameters to store in the Output section as described below. If more than one parameter name is 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:
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For Specified combinations, 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.
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For All combinations, the solver uses this order for the parameter combinations: 1 2, 1 4, 3 2, and 3 4.
To determine what the solver does when there is a solver error or when the continuation backtracking 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 (or for the remaining continuation).
Using Store empty solution can be useful if you need to sweep over many different combinations of parameters and it is unknown which ones that will solve. It can also be useful when doing frequency sweeps where frequencies close to resonances fail.
From the Parameter value run order list choose Automatic (the default) or As specified. When using As specified, the specified order of the parameter values is used. When you use the Automatic setting, the parametric solver performs an analysis of the cost of changing the values of involved parameters, and the run order of the parameter values is modified when it is found to be more efficient. If the parameter run order is modified, the modified order is indicated in the Log window.
Continuation
This section is disabled, if Least-squares time/parameter method is set to From least-squares objective in the Optimization study step. In this case Constant is used as Predictor.
By default, the solver selects the parameter steps automatically based on the values entered in the Parameter values field in the General section.
Click to select the
Tuning of step size check box to edit these settings:
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Initial step size field to enter a positive number that determines the magnitude of the first parameter step.
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Minimum step size field to specify a safeguard against too small parameter steps.
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Maximum step size field to specify an upper bound on the parameter step size. Use this if you suspect that the solver tries to take unnecessarily long steps.
Use the Use initial damping factor for all parameter steps list to control the initial damping factor for the nonlinear solvers for the parameter steps.
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Select On to use the given Initial damping factor for the nonlinear solvers for all parameter steps.
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Select Off to use the initial damping factor only for the first parameter step.
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Select Automatic (default) to use the initial damping factor only for the first parameter step when the Automatic (Newton) or Automatic highly nonlinear (Newton) nonlinear solver method is used in the Fully Coupled solver node and use the initial damping factor in all steps for other solver combinations.
Use the Predictor list to control how the initial value for the next parameter value is determined. Select:
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Automatic (the default) to let the parametric solver choose a constant or linear predictor based on the type of stationary solver (a constant predictor for segregated solvers and a linear predictor for fully coupled solvers).
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Constant to use the solution for the present parameter value as initial guess.
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Linear to compute the initial guess by following the tangent to the solution curve at the present parameter value.
This option is overridden, and Constant used instead if you are solving for more than one parameter (that is, when you have entered more than one parameter name in the Parameter name field).
Load Case
This section displays the settings made under Study Extensions for the Stationary study step; it is synchronized with the study settings.
Least-Squares Data
The section only appears if you are solving a least-squares optimization problem with defined parameters.
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 or experimental parameters, a 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 check box 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 check box is selected, the following settings are available:
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The Use all for Continuation check box is selected by default. It will then expand all least-squares data points into a Continuation. If the least-squares data has data for the continuation parameter, it will be merged with the list that you have provided. If the direction of the continuation is not consistent, an error will be given. If you clear the Use all for Continuation check box, the given list will only be merged with the least-squares data that matches the given tuples. However, continuation will still be done for the least-squares data. This check box has no effect when Continuation is not used.
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The Create bounding box from the General parameter value lists check box is selected by default to exclude values outside the bounding box.
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The Add solution data points from the General non-continuation Parameter value lists check box is selected by default to control if extra data points should be added to the solution process. These extra data points do not affect the solution process or the least-squares objectives but can be useful, for example, for results evaluation or for model debugging. When selected and when a continuation is not used, it adds all the user-provided points and removes the duplicates. When selected with a continuation, it adds continuation sweeps for all given parameter value lists. When it is cleared, no extra continuation sweeps are added.
If Use least-squares parameters from objectives is off, no least-squares parameters from objectives 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.
Output
Use the Parameters to store list to control at what parameter values the solver stores a solution. Select:
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Steps given to store solutions at the parameter values entered in the Parameter values field in the General section.
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Steps taken by solver to store solutions at all parameter values where the solver has computed a solution. This option can generate solutions in-between the values specified by the Parameter values field in the General section if the solver needs to take shorter steps than specified by the values in that field.
Results While Solving
See Results While Solving in the Common Study Step Settings section. Also see Getting Results While Solving.
Cluster Settings
Select the Distribute parameters check box 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, then 3 groups with 4 nodes each cooperate.
Buoyancy Flow of Free Fluids: Application Library path COMSOL_Multiphysics/Fluid_Dynamics/buoyancy_free