COMSOL 6.4 - Nonlinear Solver

Nonlinear solver settings depend on the heat transfer model and on the study type.

Heat transfer models with and without surface-to-ambient radiation use a fully coupled nonlinear solver attribute by default. The Jacobian update is set to minimal. A Newton nonlinear method is set by default with

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Automatic damping factor computation for stationary studies

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Constant damping factor for time-dependent studies

Segregated Solver Attribute

The segregated solver attribute is set by default when another physics interface is solved together with heat transfer. The dependent variables of the heat transfer interface are placed in a separate segregated group. It happens as well for the modeling of radiation in participating media using the Discrete Ordinates Method, or for the computation of damage in biological tissue (options available with the Heat Transfer Module.

Tuning the Nonlinear Solver

Default solver settings are defined to handle efficiently classical configurations. For particular applications, the default settings may need modifications to improve the robustness and performance of the solver.

Optimize Nonlinear Solver for Robustness

When the nonlinear solver fails or converges erratically, different options can be considered:

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Using the option forces to start the computation with a very low damping factor and increases it carefully. Alternatively a low constant damping factor can be used. The damping factor ranges between 0 and 1. A constant damping factor equal to 0.1 is a very low value and should be robust but slow to converge. For low values of the damping factor, it is thus usually needed to increase the number of nonlinear iterations. If the nonlinear solver is unstable with such a damping factor then the automatic option should be used because it makes it possible to start with a lower damping factor and gradually increases it.

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A good initial value, as close as possible from the expected solution and consistent with the boundary conditions, helps to guide the nonlinear solver to a stable physical solution. To do that:

Try to ramp the temperature on the boundary from the initial to the desired value by using an auxiliary sweep — for stationary problems — or a time-dependent step function —for time-dependent problems.

Use results from a simplified problem, for instance with no temperature dependency, or using a one-way multiphysics coupling, as initial value.

Note that it is sometimes easier to update the boundary conditions than the initial condition to get consistent initial settings.

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When it is not possible to provide a good initial value, the segregated solver associated with low damping factors in each segregated step helps to achieve convergence.

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Forcing the Jacobian update at every iteration ensures that the nonlinear solver iterates using optimal information from the equation system. This is needed when nonlinearities are due to the temperature itself — for example, in case of strong temperature dependency of material properties — or to another variable solved in the same segregated group as the temperature — for example, in natural convection models.

Optimize Convergence Speed

Low convergence can be improved by following ways:

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Using a constant damping factor equal to 1 for linear problems. The linearity is determined at the beginning of the resolution and indicated in the section of the solver window.

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Providing a good initial value is an asset for computational speed.

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In the convergence area, the fully coupled solver has a better convergence rate than the segregated solver.

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Using minimal Jacobian update option avoid to spend time in Jacobian computation. This is suited for linear models and models with mild nonlinearities.