DirichletBC suppress on some dofs

mesh
1

Hi,

I am trying to apply the DirichletBC on the top side of mesh except two y dofs of left-top and right-top vertices as shown in figure.

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I think I can use the pointwise method, but the definition of subdomains of points and DirichletBCs would be complex and inefficient.

import fenics as fe
mesh = fe.UnitSquareMesh(2,2)
V = fe.VectorFunctionSpace(mesh, 'P', 1)
u = fe.Function(V)
bc1 = fe.DirichletBC(V.sub(0), u, subdomain_all_points_on_top, method='pointwise')
bc1 = fe.DirichletBC(V.sub(1), u, subdomain_all_points_on_top_except_left_right_corner, method='pointwise')
bc = [bc1, bc2]

Is there a way to assign DirichletBC based on dof like the way of assigning nodal force?
Or is it possible to suppress the assigning of DirichletBC values on these dofs?

Thanks,
Ming

2

You should be able to do this by just setting different geometric criteria for the two BCs:

import fenics as fe
mesh = fe.UnitSquareMesh(8,8)
V = fe.VectorFunctionSpace(mesh, 'P', 1)
u = fe.Function(V)

# Define geometric criteria for BCs on different components:
on_top =  " && x[1] > 1.0-DOLFIN_EPS"
subdomain_all_points_on_top = "x[0]>-DOLFIN_EPS"+on_top
subdomain_all_points_on_top_except_left_right_corner \
    = "x[0] > DOLFIN_EPS && x[0] < 1.0-DOLFIN_EPS"+on_top

# Set BCs according to components of u (rather than the full vector u,
# as in the original MWE):
u0,u1 = u.split(deepcopy=False)
bc1 = fe.DirichletBC(V.sub(0), u0,
                     subdomain_all_points_on_top, method='pointwise')
bc2 = fe.DirichletBC(V.sub(1), u1,
                     subdomain_all_points_on_top_except_left_right_corner,
                     method='pointwise')
bc = [bc1, bc2]

# Demonstrate:
utest = fe.Function(V)
utest.interpolate(fe.Constant((1,1)))
u.interpolate(fe.Constant((2,3)))
for b in bc:
    b.apply(utest.vector())
from matplotlib import pyplot as plt
utest0,utest1 = utest.split()
plt.figure()
fe.plot(utest0)
fe.plot(mesh)
plt.figure()
fe.plot(utest1)
fe.plot(mesh)
plt.show()