Segregated
The Segregated node () is an attribute that handles parameters for a segregated solution approach. This attribute makes it possible to split the solution process into substeps. Each substep uses a damped version of Newton’s method.
The attribute can be used together with the Stationary Solver and Time-Dependent Solver nodes. An alternative to the segregated approach is given by the coupled solver, which is handled with the Fully Coupled attribute node. Although several Fully Coupled and Segregated attribute nodes can be attached to an operation node, only one can be active at any given time.
To add substeps to a segregated iteration, right-click the Segregated node. One segregated iteration consists of executing each active Segregated Step in the order shown in the model tree.
The convergence properties of a model might depend on the order of the segregated steps. You can move the Segregated Step nodes to change the order in which the solver runs each step.
Using the segregated solver, you can impose lower limits and upper limits for the field variables by adding Lower Limit and Upper Limit subnodes. See Lower Limit and Upper Limit.
For more information about the settings below, see:
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The Segregated Solver
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Damped Newton Methods
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Pseudo Time Stepping
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Termination Criterion for the Fully Coupled and Segregated Attribute Nodes
General
Select a Termination technique list to control how the segregated iterations are terminated. Select:
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Tolerance (the default) to terminate the segregated iterations when the estimated relative error is smaller than a specified tolerance.
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Iterations or tolerance to terminate the segregated iterations when the estimated tolerance is smaller than a specified tolerance or after a specified number of iterations, whichever comes first.
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Iterations to terminate the segregated iterations after a fixed number of iterations.
Then, based on the selected Termination technique, use the following settings:
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If Tolerance is selected, enter a Maximum number of iterations to limit the number of segregated iterations (default: 10). When the maximum number of iterations has been performed, the segregated method is terminated even if the tolerance is not fulfilled.
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If Tolerance or Iterations or tolerance is selected, enter a Tolerance factor to modify the tolerance used for termination of the segregated iterations. The actual tolerance used is this factor times the value specified in the Relative tolerance field in the General sections of the Stationary Solver and Time-Dependent Solver nodes.
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If Tolerance or Iterations or tolerance is selected, choose a Termination criterion to control how the Newton iterations are terminated for stationary problems. Select:
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Solution to terminate the Newton iterations on a solution-based estimated relative error.
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Residual to terminate the Newton iterations on a residual-based estimated relative error.
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Solution or residual to terminate the Newton iterations on the minimum of the solution-based and residual-based estimated relative errors. Then enter a scalar Residual factor (default: 1000) that multiplies the residual error estimate.
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If Iterations or Iterations or tolerance is selected, enter a Number of iterations to specify a fixed number of iterations to perform. The default is 1.
With a Time-Dependent Solver, also select the Limit on nonlinear convergence rate check box to force the nonlinear solver to terminate as soon as the convergence is estimated to be too slow. Enter a limit on the convergence rate in the accompanying field. The nonlinear convergence rate is estimated as γ = (en/e1)(1/(n − 1)), where en is the error estimate for iteration n. This can be seen as the average convergence rate after n steps (n > 1). If γ  \ γlimit (γlimit is the limit on nonlinear convergence rate), then the nonlinear solver will terminate (as if it fails). This means that the current time step will be disqualified, and a new nonlinear solve attempt will be performed with a reduced time step. For problems where the convergence rate can be slow, this option can be used to avoid unnecessary nonlinear iterations (because the solver will in those cases not converge anyways within the allotted iterations specified in the Maximum number of iterations field).
Also, with a Time-Dependent Solver, by default, a stricter tolerance is used at each Newton iteration step when Jacobian is not updated. This approach typically leads to more robust time stepping. Therefore, more nonlinear iterations might be required in each time step, and more Jacobian updates might be needed. To use the minimal Jacobian update used in earlier versions of the COMSOL Multiphysics software, select the Use linear heuristics for adaptive tolerance check box.
You can select one of the following methods for stabilization and acceleration of the nonlinear convergence from the Stabilization and acceleration list:
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None (the default) to not use any stabilization or acceleration method.
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Pseudo time-stepping to use a pseudo time-stepping method to stabilize convergence toward steady state for a stationary solver. Pseudo time stepping is not available for time-dependent solvers. See Pseudo Time Stepping for more information. For the pseudo time-stepping method, specify the following controller parameters:
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PID Controller. Choose Simple (the default) or Interpolated. The simple controller corresponds to the PID controller in versions of the COMSOL Multiphysics software earlier than version 6.2. The interpolated controller blends different types of controllers when the error reaches the Target error estimate.
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Initial CFL number. The default is 5.
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Target CFL number. The default is 10,000. The solver does not converge unless the target CFL number is reached.
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The Limit to target CFL number check box is selected by default. This setting controls how the CFL number is changed once the Target CFL number is reached. If you clear this check box, the CFL number can continue to increase until the error tolerance is fulfilled
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PID controller - proportional. The default is 0.65.
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PID controller - integral. The default is 0.05.
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PID controller - derivative. The default is 0.05.
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Target error estimate. The default is 0.1.
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Select the Anderson acceleration check box to activate Anderson acceleration for the pseudo time-stepping method.
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Select the Override Jacobian update for steps check box to override updates of the Jacobian for the segregated steps. The CFL threshold value (default: 100), which is the value of the CFL number where overriding of the Jacobian update becomes active. That is, the overriding becomes active for larger CFL numbers than the threshold. From the Jacobian update list, choose On first iteration (the default) or Minimal, which updates the Jacobian at least once and then only when the nonlinear solver fails during parameter stepping. It reuses the Jacobian for several nonlinear systems whenever deemed possible.
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Anderson acceleration, which is a nonlinear convergence acceleration method that uses information from previous Newton iterations to accelerate convergence. The Anderson acceleration method is primarily intended for acceleration of nonlinear iterations in transport problems involving, for example, crosswind diffusion stabilization. It is useful is for solving linear or almost linear problems using the segregated solver, where convergence can be improved and the performance increased. You can control the number of iteration increments to store using the Dimension of iteration space field (default: 10) and the mixing parameter as a value between 0 and 1 using the Mixing parameter field (default: 1.0). The Iteration delay field (default 0) contains the number of iterations between pseudo time stepping becomes inactive and Anderson acceleration becomes active. Enter a threshold value in the Threshold for Anderson step field (default: 10). This threshold value controls if the Anderson step or the Newton step is used in the nonlinear step. If the norm of the new step is less than the threshold times the norm of the previous step, the Anderson step is used. Otherwise, the Newton step is used. Lowering the value for the Threshold for Anderson step can improve robustness at the price of performance.
When used for pseudo time stepping, you can enter a CFL threshold value (default: 100), which is the value of the CFL number where Anderson acceleration becomes active and pseudo time stepping becomes inactive. You can also choose Use PID controller (the default) or Lock target CFL number from the Above CFL threshold list. Select Lock target CFL number if the solver should set the target CFL number once the threshold is reached, or select Use PID controller if the PID controller should still control the CFL number based on the error estimate.
Results While Solving
See Results While Solving in the Common Study Step Settings section. Also see Getting Results While Solving.