def MixedSpacesRestrictionAmbiguous(mesh):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element)
W = FunctionSpace(mesh, element_0)
return (V, W)
def MixedSpacesExtensionSolveAmbiguityWithComponents(mesh):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element_0)
W = FunctionSpace(mesh, element, components=[["u", "s"], "p"])
return (V, W)
def MixedSpacesExtensionAutomatic(mesh):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 2)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element_0)
W = FunctionSpace(mesh, element)
return (V, W)
def MixedSpacesRestrictionToSubElementSolveAmbiguityWithComponents(mesh):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element_00 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element, components=[("ux", "uy"), "p"])
W = FunctionSpace(mesh, element_00)
return (V, W)
def MixedSpacesRestrictionToSubElementAmbiguous(mesh):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 2) # Note that we need to use 2nd order FE otherwise
element_00 = FiniteElement("Lagrange", mesh.ufl_cell(), 2) # the automatic detection would restrict the
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1) # pressure component
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element)
W = FunctionSpace(mesh, element_00)
return (V, W)
def MixedSpacesRestrictionSolveAmbiguityWithComponents(mesh, sub_element):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element, components=["u", "p"])
assert sub_element in (0, 1)
if sub_element == 0:
W = FunctionSpace(mesh, element_0)
elif sub_element == 1:
W = FunctionSpace(mesh, element_1)
return (V, W)
def MixedSpacesRestrictionAutomatic(mesh, sub_element):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 2)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element)
assert sub_element in (0, 1)
if sub_element == 0:
W = FunctionSpace(mesh, element_0)
elif sub_element == 1:
W = FunctionSpace(mesh, element_1)
return (V, W)
def MixedSpacesExtensionFromSubElementSolveAmbiguityWithComponents(mesh, components):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element_00 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element_00)
assert components in (tuple, str)
if components is tuple:
W = FunctionSpace(mesh, element)
else:
W = FunctionSpace(mesh, element, components=[("ux", "uy"), "p"])
return (V, W)
def MixedToMixedSpacesCopySubComponentToDifferentLocation(mesh):
element_0 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element, components=[("uxx", "uxy"), ("uyx", "uyy")])
W = V
return (V, W)
def MixedToMixedSpacesCopyComponentToDifferentLocation(mesh):
element_0 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element_1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
element = MixedElement(element_0, element_1)
V = FunctionSpace(mesh, element, components=["ux", "uy"])
W = V
return (V, W)
def CustomFunctionSpace(mesh, element):
return FunctionSpace(mesh, element, components=auxiliary_V._component_to_index)
def CustomFunctionSpace(mesh, element):
return FunctionSpace(mesh, element, components=V_component._component_to_index)
def ScalarSpaces(mesh):
V = FunctionSpace(mesh, "Lagrange", 2)
W = V
return (V, W)
