Issues with marking subdomains for 3D geometry

General
1

Hi all,
I am new to FEA in general and have been working on a steady state heating model for a 3D cylinder. For this case, I have created a simple cylinder mesh, with radius R and thickness H, defined the boundaries and then tried to use MeshFunction to mark the boundaries, but I cannot seem to mark the barrel of the cylinder at all.

My code is shown below.

from fenics import *
import matplotlib.pyplot as plt
from dolfin import *
import numpy as np

H = 0.06
R = 450e-3/2
cylinder = Cylinder(Point(0,0,0),Point(0,0,H),R,R)
geometry = cylinder

msh = generate_mesh(geometry,42)
V = FunctionSpace(msh,'P',2)
T = TestFunction(V)      # v
dT = TrialFunction(V)    # u

tol = 1e-14

class All(SubDomain):
    def inside(self, x, on_boundary):
        return on_boundary

class Barrel(SubDomain):
    tol = 1e-14
    def inside(self,x,on_boundary):
        return np.isclose(x[0] ** 2 + x[1] ** 2, R**2) and on_boundary

# Along HR surface (z=0)
class HR(SubDomain):
    tol = 1e-14
    def inside(self,x,on_boundary):
        return near(x[2],0,tol) and on_boundary

# Along AR surface (z=H)
class AR(SubDomain):
    tol = 1e-14
    def inside(self,x,on_boundary):
        return near(x[2],H,tol) and on_boundary

# Marking boundaries
boundary_markers = MeshFunction("size_t", msh, msh.topology().dim()-1,0) 
bAll = All()
bBar = Barrel()
bHR = HR()
bAR = AR()
bAll.mark(boundary_markers, 0)
bBar.mark(boundary_markers, 1)
bHR.mark(boundary_markers, 2)
bAR.mark(boundary_markers, 3)
File('Domain.pvd') << boundary_markers

From my understand, the first face (z=0) should be marked 2, the second 3 and the barrel 1. But my barrel stays 0 (or stays whatever the marking of all facets in the mesh are). I am not too sure what I am doing wrong here. Any help would be so great!

2

Perhaps this relates to your issue: A problem about the function near() - #2 by dokken

also Explicitly defining the subdomains and boundaries return warning Found no facets matching domain for boundary condition

3

I have tried both of the solutions to those problems. Increasing the tolerance for near does not help, and neither does further refining my mesh.

4

Using this, I can mark the barrel easily.

boundary_markers = MeshFunction("size_t", msh, msh.topology().dim()-1) 
CompiledSubDomain("near(x[2], 0.06, tol) && on_boundary", tol=1e-14).mark(boundary_markers,1)

image

5

I’m a bit confused. Seems like you are marking the end face as 1, and everything else as 0. Not the barrel only as 0.

6

Can you mark the area which is the barrel? I can’t find it.

7

The barrel is marked by the following in my code.

class Barrel(SubDomain):
    tol = 1e-14
    def inside(self,x,on_boundary):
        return np.isclose(x[0] ** 2 + x[1] ** 2, R**2) and on_boundary

The barrel is the remaining boundary of the cylinder minus the two end faces.