nx, ny, nz = 20, 20, 20
# Initial composition field
class StepFunction(UserExpression):
def eval_cell(self, values, x, cell):
c = Cell(mesh, cell.index)
if c.midpoint()[1] > db + 0.02*np.cos(np.pi*x[0]/float(lmbdax))*np.cos(np.pi*x[2]/float(lmbdaz)):
values[0] = 1.0
else:
values[0] = 0.0
mesh = BoxMesh.create(
comm, [Point(0.0, 0.0, 0.0), Point(float(lmbdax), 1.0, float(lmbdaz))],
[nx, ny, nz], CellType.Type.tetrahedron)
# Shift the mesh to line up with the initial step function condition
scale = db * (1.0 - db)
shift = Expression(("0.0", "x[1]*(H - x[1])/S*A*cos(pi/Lx*x[0])*cos(pi/Lz*x[2])", "0.0"),
A=0.02, Lx=lmbdax, Lz=lmbdaz, H=1.0, S=scale, degree=4)
V = VectorFunctionSpace(mesh, "CG", 1)
displacement = interpolate(shift, V)
ALE.move(mesh, displacement)
# Entrainment functional measures
de = 1
cf = MeshFunction("size_t", mesh, mesh.topology().dim(), 0)
CompiledSubDomain("x[1] > db - DOLFIN_EPS", db=db).mark(cf, de)
def box():
return BoxMesh.create(
MPI.comm_world,
[Point(0, 0, 0)._cpp_object,
Point(2, 2, 2)._cpp_object], [2, 2, 5], CellType.Type.tetrahedron,
cpp.mesh.GhostMode.none)
basis = VectorSpaceBasis(nullspace_basis)
basis.orthonormalize()
_x = [basis[i] for i in range(6)]
nsp = PETSc.NullSpace()
nsp.create(_x)
return nsp
# Load mesh from file
# mesh = Mesh(MPI.comm_world)
# XDMFFile(MPI.comm_world, "../pulley.xdmf").read(mesh)
# mesh = UnitCubeMesh(2, 2, 2)
mesh = BoxMesh.create(
MPI.comm_world, [Point(0, 0, 0)._cpp_object,
Point(2, 1, 1)._cpp_object], [12, 12, 12],
CellType.Type.tetrahedron, dolfin.cpp.mesh.GhostMode.none)
cmap = dolfin.fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
# Function to mark inner surface of pulley
# def inner_surface(x, on_boundary):
# r = 3.75 - x[2]*0.17
# return (x[0]*x[0] + x[1]*x[1]) < r*r and on_boundary
def boundary(x, on_boundary):
return np.logical_or(x[:, 0] < np.finfo(float).eps,
x[:, 0] > 1.0 - np.finfo(float).eps)
