Boundaries/ mesh

1

Hello,

I have 3 boxes (one inside the other) and I am trying to apply boundary conditions on points on the upper side of the outside box. For example I would like to apply boundary conditions on points were -2<x<2 (with step 1) , y=0, z=2

import matplotlib.pyplot as plt
from dolfin import *
from vtkplotter.dolfin import datadir, plot
import numpy as np

mesh = Mesh(“dolfinmesh.xml”)
mesh_file_volume = MeshFunction(‘size_t’, mesh ,“dolfinmesh_volume_meshvalue.xml”)
mesh_file_boundary = MeshFunction(‘size_t’ , mesh , “dolfinmesh_bcfunc.xml”)

V = FunctionSpace(mesh, “Lagrange”, 1)

2

Please supply a minimal working example that illustrates what you would like to achieve.

Note that there are many examples on how to apply boundary conditions on the forum. See for instance: Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio

4

Please format your problem using ```, and remove all unnecessary code such that it is easy to see what your issue is. For instance consider using a built-in UnitSquareMesh, and apply a boundary condition on it, such as shown in the Poisson demo:
https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/documented/poisson/demo_poisson.py.rst

5

Sorry for my previous inaccurate posts,

Basically I have a 3D box and I want to apply boundary conditions on the specific points that I mention inside the bc1, bc2, bc3, bc4,…bc9
The points are:
(x, y, z)
2, 0, 2
1.5, 0, 2
0.5, 0, 2
0, 0, 2
-0.5, 0, 2
-1, 0, 2
-1.5, 0, 2
-2, 0, 2

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

mesh = Mesh(“dolfinmesh.xml”)
mesh_file_volume = MeshFunction(‘size_t’, mesh ,“dolfinmesh_volume_meshvalue.xml”)
mesh_file_boundary = MeshFunction(‘size_t’ , mesh , “dolfinmesh_bcfunc.xml”)

V = FunctionSpace(mesh, “Lagrange”, 1)

‘’’’
bc1 = DirichletBC(V, Constant(2.46),“near(x[0] , 2.0) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc2 = DirichletBC(V, Constant(2.43),“near(x[0] , 1.5) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc3 = DirichletBC(V, Constant(2.3),“near(x[0], 1.0) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc4 = DirichletBC(V, Constant(2.6),“near(x[0], 0.5) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc5 = DirichletBC(V, Constant(4.3),“near(x[0], 0.0) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc6 = DirichletBC(V, Constant(2.44),“near(x[0], -0.5) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc7 = DirichletBC(V, Constant(2.43),“near(x[0], -1.0) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc8 = DirichletBC(V, Constant(2.55),“near(x[0], -1.5) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)
bc9 = DirichletBC(V, Constant(2.69),“near(x[0], -2.0) && x[1] == 0.0 && x[2] == 2.0”,“pointwise”)

bcs = [bc1, bc2, bc3, bc4, bc5, bc6, bc7, bc8, bc9]

‘’’’’

Define variational problem

u = TrialFunction(V)
v = TestFunction(V)
a = inner(Cgrad(u), grad(v))dx
f = Constant(0.0)
L = fvdx
A, b = assemble_system(a, L, bcs)
u_k = Function(V)
solve(A, u_k.vector(), b, ‘lu’)

File(‘saved_u.xml’) << u_k
file = File(“final2.pvd”)
file << u_k

All the above seem not to work.

6

Are the points vertices of your mesh? Otherwise you cannot apply pointwise BCs to them. A pointwise bc will add the condition to the single dof at that location, if there is no dof there, there will be no boundary condition.

7

They are not vertices of my mesh. Is there any other way that I can apply on those points boundary conditions?

8

You can approximate a dirac delta function in that region, Implement point source in the variational formulation
Note that this will not be 100% accurate, and will work better on a finer mesh.

The optimal solution is to ensure vertices at the points you want to apply a boundary condition on.

You can Also find the Closest degree of freedom to that point, see: How can I find the closest node to an arbitrary coordinates?

9

Thank you very much for your help!