Pure periodic boundary conditions

1

Hi,

I’m trying to implement periodic boundary conditions on a 2D square mesh.
I followed the example in the doc.

from fenics import *
import matplotlib.pyplot as plt
import numpy as np
plt.switch_backend("WebAgg")

class Left(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], 0.0)

class Right(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[0], 5.0)

class Bottom(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[1], 0.0)

class Top(SubDomain):
    def inside(self, x, on_boundary):
        return near(x[1], 5.0)

# mesh = UnitSquareMesh(20, 20)
mesh = RectangleMesh(Point(0.0, 0.0), Point(5.0, 5.0), 50, 50)

# Initialize sub-domain instances
left = Left()
top = Top()
right = Right()
bottom = Bottom()

# Initialize mesh function for boundary domains
boundaries = MeshFunction("size_t", mesh, mesh.topology().dim()-1)
boundaries.set_all(0)
left.mark(boundaries, 1)
top.mark(boundaries, 2)
right.mark(boundaries, 3)
bottom.mark(boundaries, 4)

# Define boundaries
B = "near(x[1], 0)"
T = "near(x[1], 5)"
L = "near(x[0], 0)"
R = "near(x[0], 5)"

class PeriodicBoundary(SubDomain):

    # Left boundary is "target domain" G
    def inside(self, x, on_boundary):
        return bool(x[0] < DOLFIN_EPS and x[0] > -DOLFIN_EPS and on_boundary)

    # Map right boundary (H) to left boundary (G)
    def map(self, x, y):
        y[0] = x[0] - 5.0
        y[1] = x[1]

pbc = PeriodicBoundary()

V = VectorFunctionSpace(mesh, 'P', 2, dim=2, constrained_domain=pbc)

# Boundary conditions
bc_L = DirichletBC(V, Constant((0,0)), L)
bc_R = DirichletBC(V, Constant((1,0)), R)
bc_T = DirichletBC(V, Constant((1,0)), T)
bc_B = DirichletBC(V, Constant((0,0)), B)
bcs = [ bc_T]





Psi = interpolate(Constant((1,0)), V)
w = TestFunction(V)

F = dot(grad(Psi[0]), grad(w[0]))*dx - Psi[0]*w[0]*dx + (Psi[0]**2+Psi[1]**2)*Psi[0]*w[0]*dx \
   +dot(grad(Psi[1]), grad(w[1]))*dx - Psi[1]*w[1]*dx + (Psi[0]**2+Psi[1]**2)*Psi[1]*w[1]*dx \
   + 0.4*w[0]*ds

solve(F == 0, Psi, bcs)

I want to have periodic BC on x=0 and x=5, and Dirichlet BC on y=5, Neumann BC on y=0.
The results showed the solver also applied the Neumann BC on x=0 and x=5.
How do I correct this?

Thank you.

2

I think I solved the problem.

I missed the following line

ds = Measure('ds', domain=mesh, subdomain_data=boundaries)