Time-Dependent Study Step
Default Settings for Heat Transfer interfaces
The default time-stepping method for the Heat Transfer interfaces is BDF at second order. It excludes algebraic variable from the error estimate.
When a Thermal Damage subfeature is present under Biological Tissue feature, particular settings for the time-dependent solver are used to efficiently compute the damage indicators:
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The Absolute Tolerance of the scaled damage indicator variable is set to 1, meaning that these variable are neglected in the error estimate.
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The damaged tissue indicator, α, is solved with an iterative Jacobi method.
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If the Adaptive mesh refinement option is selected in the study settings, the error indicator is set to , where θd, sm is the smoothed indicator of necrotic tissue (the fraction of necrotic tissue, θd, is discontinuous in general).
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If the Temperature threshold option is used in the Biological Tissue feature, the instant necrosis indicator, alphanecr, is placed in the Previous Solution step. This setting avoids wrong detection of irreversible damage due to nonlinear iterations that may go through a state where the damage criteria is met and then converge to a solution where the damage criteria is no longer met. It uses a direct linear solver. The default nonlinear method is the Newton method with constant damping factor.
When the Irreversible Transformation feature is active, similar settings are used:
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The Absolute Tolerance of the scaled irreversible transformation indicator dependent variable is set to 1.
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The irreversible transformation indicator α is solved with an iterative Jacobi method.
Default Settings for Moisture Transport interfaces
The default time-stepping method for the Moisture Transport interfaces is BDF at second order.
Tuning the Time-Dependent Solver
The quality of the time-stepping influences the nonlinear solver convergence. Tiny time steps usually lead to mildly nonlinear problems at each time step whereas large time steps can result in (fewer) highly nonlinear problems.
The default solver settings for transient heat transfer defines the maximal number of nonlinear iterations to 5. If this is not sufficient, it is recommended to use smaller time steps and to verify if the model definition does not contain discontinuities in time. If so, consider using smooth step functions to model sharp variations in time.
There are several ways to control the time step size:
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An implicit way is to define a lower relative tolerance in the study settings. When the relative tolerance is lowered, the absolute tolerance should be reduced in the same proportion.
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The most explicit way is to define a maximum time step. This is an appropriate option when the same maximum time step is relevant for the entire simulation. Otherwise, it is possible to include times of interest in the Times field of the time-dependent study and to use the Intermediate option in the Time Stepping settings.
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Lastly you can control the time step by triggering an event when a particular condition is meet (see the documentation about The Events Interface in the COMSOL Multiphysics Reference Manual). This advanced method can be efficient when the other simpler methods are not applicable.
It is also recommended to inspect the solver log and check the default scaling of dependent variables in case of convergence failure. In case of incorrect automatic scaling, consider using Manual settings in the Dependent Variable attribute node.
Time-Dependent Solver in the COMSOL Multiphysics Reference Manual