Moving mesh to specific points

Question

I have a unit square mesh with a Dirichlet line defined by points 'a' and 'b'. I have defined a function that returns true if an input 'x' is on this line, which I input into DirichletBC. That is, something like:

def u0_boundary(x, on_boundary):
    return on_boundary or on_line(x, line_x)
bc = DirichletBC(V, u0, u0_boundary)

However, I'm having trouble getting the mesh to overlap with this line, so that the vertex is actually defined as a boundary condition.

I imagine the easiest way to do this is to adjust the mesh using mesh.move, but I'm having trouble parsing the documentation to figure out how this would work. Can I query the boundary with BoundaryMesh and append the line somehow? Do I need to manually define the mesh with MeshEditor?

Any advice would be greatly appreciated! Thank you!

Comments

It's not really clear from your description. What does on_line() do? It is better if you provide a minimal working example.

---

Yes, of course. Here's a fully functioning snippet.

from dolfin import *
import numpy as np

mesh = UnitSquareMesh(100, 100)

V = FunctionSpace(mesh, 'Lagrange', 1)
u = TrialFunction(V)
v = TestFunction(V)
f = Constant(-1.0)
a = inner(nabla_grad(u), nabla_grad(v))*dx
L = f*v*dx
u0 = Constant(0.0)

def on_line(x):
    return abs(x[1] - 1.1*x[0]) < 1E-15
def u0_boundary(x, on_boundary):
    return on_boundary or on_line(x)

bc = DirichletBC(V, u0, u0_boundary)
u = Function(V)
solve(a == L, u, bc)

plot(u)
file = File("fenics-output.pvd")
file << u

Changing the value 1.1 in on_line to 1 aligns the values with the mesh, causing it to give the correct solution. But as is, it does not.

Answer 1

Ok, you can move points quite easily (in current dolfin)

mesh = UnitSquareMesh(10, 10)
for x in mesh.coordinates():
    x[0] += 0.1*x[1]

for example

Comments

Thank you for the response. This helps!