The Bounds node adds inequality constraints on the phase field variable, which can be useful to limit the values of the dependent variable.
Enter a Penalty factor,
K. A larger penalty factor decreases the violation of the constraint, but a too large value can lead to an ill-conditioned stiffness matrix.
By default, the constraint force associated with an active bound is computed as the penalty factor K multiplied by the violation of the constraint. For example, the constraint force for a lower bound
lb < ϕ is computed as
fc = K max
(−ϕ + lb, 0). In some cases, the discontinuous derivative of the
max() operator may cause convergence issues. It is possible to use a smooth version of the constraint force by selecting the
Use transition zone check box. When selected, enter the size of the transition zone,
ϕtr. This positive number should be set based on the constraint violation that is deemed acceptable. Both the sharp and the smooth constraint force do not add a penalty contribution as long as the inequality is satisfied. The penalty factor
K will be applied in the constraint force expression for all active bounds.