Pointwise Inequality Constraint
A Pointwise Inequality Constraint is given as a restriction to the values of a closed-form expression at all points in a set of geometric entities of the same dimension. Due to computational issues, the expression has to be a closed-form expression of only control variables. Furthermore, only those control variables that are either global or available in the domain in question are usable.
Constraint
Enter a Constraint expression for the pointwise inequality constraint.
Discretization
This section contains settings for the element used to discretize the control variable. Select a Shape function type — Lagrange (the default) or Discontinuous Lagrange. Also select an Element order — Linear, Quadratic (the default), Cubic, Quartic, Quintic, Sextic, or Septic.
The Constraint method setting controls where the constraints are evaluated:
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Choose Elemental to make the software assemble the constraint on each node in each element; that is, there are usually several constraints at the same global coordinates because elements in the computational mesh overlap at nodes.
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Choose Nodal (the default) to make the software assemble a single constraint for each global node point. The nodal constraint method provides an averaging of the constraints from adjacent elements.
The default is Nodal in order to minimize the number of constraints that must be handled by the optimization solvers.
The Constraint method setting has no effect for Discontinuous Lagrange shape functions whose nodes all lie strictly inside the mesh elements.
Bounds
By default, the Lower bound and Upper bound checkboxes are selected to activate the required bounds. To specify equality constraints, make sure that the upper and lower bounds have the same value.