I am trying to use MINI elements to solve the DFG2D-3 benchmark from the tutorial. I made the mesh from triangular elements as MINI does not work with quadrilaterals.
First I tried this:
V1 = VectorElement("Lagrange", mesh.ufl_cell(), 1)
B = VectorElement("Bubble", mesh.ufl_cell(), 3)
P2 = V1 + B
P1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
V = FunctionSpace(mesh, P2)
Q = FunctionSpace(mesh, P1)
fdim = mesh.topology.dim - 1
# Define boundary conditions
class InletVelocity():
def __init__(self, t):
self.t = t
def __call__(self, x):
values = np.zeros((gdim, x.shape[1]),dtype=PETSc.ScalarType)
values[0] = 4 * 1.5 * np.sin(self.t * np.pi/8) * x[1] * (0.41 - x[1])/(0.41**2)
return values
# Inlet
u_inlet = Function(V)
inlet_velocity = InletVelocity(t)
u_inlet.interpolate(inlet_velocity)
bcu_inflow = dirichletbc(u_inlet, locate_dofs_topological(V, fdim, ft.find(inlet_marker)))
# Walls
#u_nonslip = np.array((0,) * mesh.geometry.dim, dtype=PETSc.ScalarType)
u_nonslip = Function(V)
u_nonslip.x.set(0.)
bcu_walls = dirichletbc(u_nonslip, locate_dofs_topological(V, fdim, ft.find(wall_marker)), V)
# Obstacle
bcu_obstacle = dirichletbc(u_nonslip, locate_dofs_topological(V, fdim, ft.find(obstacle_marker)), V)
bcu = [bcu_inflow, bcu_obstacle, bcu_walls]
# Outlet
bcp_outlet = dirichletbc(PETSc.ScalarType(0), locate_dofs_topological(Q, fdim, ft.find(outlet_marker)), Q)
bcp = [bcp_outlet]
This produces an error:
Traceback (most recent call last):
File "/Users/varunkumar/opt/anaconda3/envs/fenicsx/lib/python3.10/site-packages/dolfinx/fem/bcs.py", line 125, in __init__
super().__init__(_value, dofs, V) # type: ignore
TypeError: __init__(): incompatible constructor arguments. The following argument types are supported:
1. dolfinx.cpp.fem.DirichletBC_float64(g: numpy.ndarray[numpy.float64], dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
2. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Constant<double>, dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
3. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: numpy.ndarray[numpy.int32])
4. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: List[numpy.ndarray[numpy.int32][2]], V: dolfinx::fem::FunctionSpace)
Invoked with: <dolfinx.cpp.fem.Function_float64 object at 0x142cd8ef0>, array([ 8, 9, 20, 21, 42, 43, 52, 53, 58, 59, 84,
85, 88, 89, 112, 113, 120, 121, 146, 147, 154, 155,
180, 181, 184, 185, 214, 215, 218, 219, 240, 241, 248,
249, 278, 279, 282, 283, 308, 309, 312, 313, 344, 345,
348, 349, 378, 379, 382, 383, 416, 417, 420, 421, 462,
463, 466, 467, 518, 519, 522, 523, 574, 575, 578, 579,
632, 633, 636, 637, 702, 703, 706, 707, 782, 783, 820,
821, 876, 877, 916, 917, 970, 971, 1024, 1025, 1086, 1087,
1136, 1137, 1206, 1207, 1260, 1261, 1336, 1337, 1398, 1399, 1478,
1479, 1540, 1541, 1618, 1619, 1688, 1689, 1784, 1785, 1872, 1873,
1982, 1983, 2082, 2083, 2192, 2193, 2298, 2299, 2416, 2417, 2522,
2523, 2650, 2651, 2768, 2769, 2898, 2899, 3010, 3011, 3016, 3017,
3258, 3259, 3270, 3271, 3508, 3509, 3522, 3523, 3636, 3637, 3646,
3647, 3650, 3651, 3784, 3785, 4038, 4039, 4042, 4043, 4046, 4047,
4170, 4171, 4316, 4317], dtype=int32), FunctionSpace(Mesh(VectorElement(Basix element (P, triangle, 3, equispaced, unset, False), 2), 0), EnrichedElement(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), VectorElement(FiniteElement('Bubble', triangle, 3), dim=2)))
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "/Users/varunkumar/Downloads/FEniCSx v0.6/DFG2D-3-Crank.py", line 151, in <module>
bcu_walls = dirichletbc(u_nonslip, locate_dofs_topological(V, fdim, ft.find(wall_marker)), V)
File "/Users/varunkumar/opt/anaconda3/envs/fenicsx/lib/python3.10/site-packages/dolfinx/fem/bcs.py", line 183, in dirichletbc
return formcls(value, dofs, V)
File "/Users/varunkumar/opt/anaconda3/envs/fenicsx/lib/python3.10/site-packages/dolfinx/fem/bcs.py", line 127, in __init__
super().__init__(_value, dofs, V._cpp_object) # type: ignore
TypeError: __init__(): incompatible constructor arguments. The following argument types are supported:
1. dolfinx.cpp.fem.DirichletBC_float64(g: numpy.ndarray[numpy.float64], dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
2. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Constant<double>, dofs: numpy.ndarray[numpy.int32], V: dolfinx::fem::FunctionSpace)
3. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: numpy.ndarray[numpy.int32])
4. dolfinx.cpp.fem.DirichletBC_float64(g: dolfinx::fem::Function<double>, dofs: List[numpy.ndarray[numpy.int32][2]], V: dolfinx::fem::FunctionSpace)
Invoked with: <dolfinx.cpp.fem.Function_float64 object at 0x142cd8ef0>, array([ 8, 9, 20, 21, 42, 43, 52, 53, 58, 59, 84,
85, 88, 89, 112, 113, 120, 121, 146, 147, 154, 155,
180, 181, 184, 185, 214, 215, 218, 219, 240, 241, 248,
249, 278, 279, 282, 283, 308, 309, 312, 313, 344, 345,
348, 349, 378, 379, 382, 383, 416, 417, 420, 421, 462,
463, 466, 467, 518, 519, 522, 523, 574, 575, 578, 579,
632, 633, 636, 637, 702, 703, 706, 707, 782, 783, 820,
821, 876, 877, 916, 917, 970, 971, 1024, 1025, 1086, 1087,
1136, 1137, 1206, 1207, 1260, 1261, 1336, 1337, 1398, 1399, 1478,
1479, 1540, 1541, 1618, 1619, 1688, 1689, 1784, 1785, 1872, 1873,
1982, 1983, 2082, 2083, 2192, 2193, 2298, 2299, 2416, 2417, 2522,
2523, 2650, 2651, 2768, 2769, 2898, 2899, 3010, 3011, 3016, 3017,
3258, 3259, 3270, 3271, 3508, 3509, 3522, 3523, 3636, 3637, 3646,
3647, 3650, 3651, 3784, 3785, 4038, 4039, 4042, 4043, 4046, 4047,
4170, 4171, 4316, 4317], dtype=int32), <dolfinx.cpp.fem.FunctionSpace object at 0x142cc94f0>
Then I tried this from The FEniCS Book:
V1 = VectorFunctionSpace(mesh, ("Lagrange", 1))
B = VectorFunctionSpace(mesh, ("Bubble", 3))
V = V1 + B
P1 = FiniteElement("Lagrange", mesh.ufl_cell(), 1)
Q = FunctionSpace(mesh, P1)
This produces an error:
Traceback (most recent call last):
File "/Users/varunkumar/Downloads/FEniCSx v0.6/DFG2D-3-Crank.py", line 113, in <module>
V = V1 + B
TypeError: unsupported operand type(s) for +: 'FunctionSpace' and 'FunctionSpace'
Any suggestions on what’s wrong would be very helpful. 