def avg(q: CoefficientFunction) -> CoefficientFunction:
"""
Returns the average of a scalar field.
Args:
q (CoefficientFunction): The scalar field.
Returns:
~ (CoefficientFunction): The average of q at every facet of the mesh.
"""
return 0.5 * (q + q.Other())
def jump(q: CoefficientFunction) -> CoefficientFunction:
"""
Returns the jump of a field.
Args:
q: The field.
Returns:
~: The jump of q at every facet of the mesh.
"""
return q - q.Other()
def grad_avg(q: CoefficientFunction) -> CoefficientFunction:
"""
Returns the average of the gradient of a field.
Args:
q: The field.
Returns:
~: The average of the gradient of q at every facet of the mesh.
"""
# Grad must be called differently if q is a trial or testfunction instead of a coefficientfunction/gridfunction.
if isinstance(q, ProxyFunction):
return 0.5 * (Grad(q) + Grad(q.Other()))
else:
return 0.5 * (Grad(q) + Grad(q).Other())