def get_centred_cube(domain_size,
max_edge_len,
centred_element_coordinate=None):
""" Generate a cube mesh centred arount [0,0,0]
optionally translates mesh slightly such that
centred_element_coordinate is at the centre of an element.
"""
domain_subdivisions = N.array(
N.ceil(N.sqrt(2) * domain_size / max_edge_len), N.uint)
mesh = dolfin.UnitCube(*domain_subdivisions)
# Transform mesh to correct dimensions
mesh.coordinates()[:] *= domain_size
mesh.coordinates()[:] -= domain_size / 2
if centred_element_coordinate is not None:
## Translate mesh slightly so that source coordinate lies at
## centroid of an element
centred_element_point = dolfin.Point(*centred_element_coordinate)
# source_elnos = mesh.all_intersected_entities(centred_element_point)
source_elnos = mesh.intersected_cells(centred_element_point)
closest_elno = source_elnos[(N.argmin([
centred_element_point.distance(dolfin.Cell(mesh, i).midpoint())
for i in source_elnos
]))]
centre_pt = dolfin.Cell(mesh, closest_elno).midpoint()
centre_coord = N.array([centre_pt.x(), centre_pt.y(), centre_pt.z()])
# The mesh intersect operator caches certain data
# structures. We need to clear them if the mesh coordinates
# are changed after calling any mesh intersection methods.
mesh.intersection_operator().clear()
mesh.coordinates()[:] -= centre_coord
return mesh
def setUp(self):
self.mesh = dolfin.UnitCube(1,1,1)
self.V = dolfin.FunctionSpace(self.mesh, "Nedelec 1st kind H(curl)", 1)
self.DUT = FillamentSource(self.V)
self.fillament_current = 2
self.fillament_endpoints = np.array([[0,0,0.7], [0,0,0.2]])
self.source_parameters = dict(
I=self.fillament_current, endpoints=self.fillament_endpoints)
def setUp(self):
self.mesh = dolfin.UnitCube(3, 3, 3)
self.V = dolfin.FunctionSpace(self.mesh, "Nedelec 1st kind H(curl)", 3)
self.u_r = dolfin.interpolate(dolfin.Expression(('0', '0', '2*x[2]')),
self.V)
self.u_i = dolfin.interpolate(
dolfin.Expression(('0', '0', '-x[2]*x[2]')), self.V)
self.x = self.u_r.vector().array() + 1j * self.u_i.vector().array()
self.DUT = ComplexVoltageAlongLine(self.V)
self.DUT.set_dofs(self.x)
def setUp(self):
self.mesh = dolfin.UnitCube(2, 2, 2)
self.function_space = dolfin.FunctionSpace(self.mesh,
"Nedelec 1st kind H(curl)",
1)
nodofs = self.function_space.dofmap().global_dimension()
self.E_dofs = np.random.random(nodofs) + 1j * np.random.random(nodofs)
self.g_dofs = np.random.random(nodofs) + 1j * np.random.random(nodofs)
self.k0 = np.random.rand() * 10
self.DUT = CalcEMFunctional(self.function_space)
# Authors: # Evan Lezar <*****@*****.**> import sys import numpy as N import os import dolfin as dol sys.path.insert(0, '../../') from sucemfem.ProblemConfigurations.EMVectorWaveEigenproblem import EigenProblem, DefaultEigenSolver from sucemfem.BoundaryConditions import PECWallsBoundaryCondition from sucemfem.Consts import c0 del sys.path[0] script_path = os.path.dirname(__file__) # Load the mesh and the material region markers mesh = dol.UnitCube(4, 4, 4) a = 1.0 b = 1.0 d = 1.0 mesh.coordinates()[:, 0] = a * mesh.coordinates()[:, 0] mesh.coordinates()[:, 1] = b * mesh.coordinates()[:, 1] mesh.coordinates()[:, 2] = d * mesh.coordinates()[:, 2] # init the PEC walls boundary condition pec_walls = PECWallsBoundaryCondition() pec_walls.init_with_mesh(mesh) # Use 3rd order basis functions order = 3 # Set up the eigen problem ep = EigenProblem()
exit()
if not dol.has_slepc():
print "DOLFIN has not been configured with SLEPc. Exiting."
exit()
class CavityDims(object):
pass
cdims = CavityDims()
cdims.a, cdims.b, cdims.c = 29, 23, 19
# Define mesh, function space
mesh = dol.UnitCube(1, 1, 1)
mesh.coordinates()[:] *= [cdims.a, cdims.b, cdims.c]
V = dol.FunctionSpace(mesh, "Nedelec 1st kind H(curl)", 4)
# Define basis and bilinear form
u = dol.TrialFunction(V)
v = dol.TestFunction(V)
m = inner(v, u) * dx # Mass form
s = dot(curl(v), curl(u)) * dx # Stiffness form
# Assemble smass form
M = dol.PETScMatrix()
S = dol.PETScMatrix()
dol.assemble(m, tensor=M, mesh=mesh)
dol.assemble(s, tensor=S, mesh=mesh)
# Authors:
# Neilen Marais <*****@*****.**>
from __future__ import division
import numpy as np
import dolfin
def as_dolfin_vector(a):
"""Convert array to a dolfin Vector() instance"""
assert len(a.shape) == 1 # 1D vectors please
v = dolfin.Vector(len(a))
v.set_local(np.require(a, requirements=['C',]))
return v
mesh = dolfin.UnitCube(1,1,1)
V = dolfin.FunctionSpace(mesh, "Nedelec 1st kind H(curl)", 2)
no = V.dofmap().global_dimension()
x = np.ones(no)
u = dolfin.Function(V, as_dolfin_vector(x))
vec = as_dolfin_vector(x)
uu = dolfin.Function(V, vec)
def main():
# Define mesh
domain_subdivisions = N.array(
N.ceil(N.sqrt(2) * domain_size / max_edge_len), N.uint)
print 'Numer of domain subdomain_subdivisions: ', domain_subdivisions
mesh = dolfin.UnitCube(*domain_subdivisions)
# Transform mesh to correct dimensions
mesh.coordinates()[:] *= domain_size
# Centred around [0,0,0]
mesh.coordinates()[:] -= domain_size / 2
## Translate mesh slightly so that source coordinate lies at
## centroid of an element
io = mesh.intersection_operator()
source_elnos = io.all_intersected_entities(source_point)
closest_elno = source_elnos[(N.argmin([
source_point.distance(dolfin.Cell(mesh, i).midpoint())
for i in source_elnos
]))]
centre_pt = dolfin.Cell(mesh, closest_elno).midpoint()
centre_coord = N.array([centre_pt.x(), centre_pt.y(), centre_pt.z()])
# There seems to be an issue with the intersect operator if the
# mesh coordinates are changed after calling it for the first
# time. Since we called it to find the centroid, we should init a
# new mesh
mesh_coords = mesh.coordinates().copy()
mesh = dolfin.UnitCube(*domain_subdivisions)
mesh.coordinates()[:] = mesh_coords
mesh.coordinates()[:] -= centre_coord
##
# Define function space
V = dolfin.FunctionSpace(mesh, "Nedelec 1st kind H(curl)", order)
k_0 = 2 * N.pi * freq / c0 # Freespace wave number
# Definite test- and trial functions
u = dolfin.TrialFunction(V)
v = dolfin.TestFunction(V)
# Define the bilinear forms
m = eps_r * inner(v, u) * dx # Mass form
s = (1 / mu_r) * dot(curl(v), curl(u)) * dx # Stiffness form
n = V.cell().n # Get the surface normal
s_0 = inner(cross(n, v), cross(n, u)) * ds # ABC boundary condition form
# Assemble forms using uBLASS matrices so that we can easily export to scipy
print 'Assembling forms'
M = dolfin.uBLASSparseMatrix()
S = dolfin.uBLASSparseMatrix()
S_0 = dolfin.uBLASSparseMatrix()
dolfin.assemble(m, tensor=M, mesh=mesh)
dolfin.assemble(s, tensor=S, mesh=mesh)
dolfin.assemble(s_0, tensor=S_0, mesh=mesh)
print 'Number of degrees of freedom: ', M.size(0)
# Set up RHS
b = N.zeros(M.size(0), dtype=N.complex128)
dofnos, rhs_contrib = calc_pointsource_contrib(V, source_coord,
source_value)
rhs_contrib = 1j * k_0 * Z0 * rhs_contrib
b[dofnos] += rhs_contrib
Msp = dolfin_ublassparse_to_scipy_csr(M)
Ssp = dolfin_ublassparse_to_scipy_csr(S)
S_0sp = dolfin_ublassparse_to_scipy_csr(S_0)
# A is the system matrix that must be solved
A = Ssp - k_0**2 * Msp + 1j * k_0 * S_0sp
solved = False
if solver == 'iterative':
# solve using scipy bicgstab
print 'solve using scipy bicgstab'
x = solve_sparse_system(A, b)
elif solver == 'direct':
import scipy.sparse.linalg
A_lu = scipy.sparse.linalg.factorized(A.T)
x = A_lu(b)
else:
raise ValueError("solver must have value 'iterative' or 'direct'")
dolfin.set_log_active(False) # evaluation seems to make a lot of noise
u_re = dolfin.Function(V)
u_im = dolfin.Function(V)
# N.require is important, since dolfin seems to expect a contiguous array
u_re.vector()[:] = N.require(N.real(x), requirements='C')
u_im.vector()[:] = N.require(N.imag(x), requirements='C')
E_field = N.zeros((len(field_pts), 3), dtype=N.complex128)
for i, fp in enumerate(field_pts):
try:
E_field[i, :] = u_re(fp) + 1j * u_im(fp)
except (RuntimeError, StandardError):
E_field[i, :] = N.nan + 1j * N.nan
import pylab as P
r1 = field_pts[:] / lam
x1 = r1[:, 0]
E_ana = N.abs(analytical_result)
E_num = E_field
P.figure()
P.plot(x1, N.abs(E_num[:, 0]), '-g', label='x_num')
P.plot(x1, N.abs(E_num[:, 1]), '-b', label='y_num')
P.plot(x1, N.abs(E_num[:, 2]), '-r', label='z_num')
P.plot(analytical_pts, E_ana, '--r', label='z_ana')
P.ylabel('E-field Magnitude')
P.xlabel('Distance (wavelengths)')
P.legend(loc='best')
P.grid(True)
P.show()
def setUp(self):
self.mesh = dolfin.UnitCube(3, 3, 3)
self.V = dolfin.FunctionSpace(self.mesh, "Nedelec 1st kind H(curl)", 2)
self.u = dolfin.interpolate(dolfin.Expression(('0', '0', '2*x[2]')),
self.V)
self.DUT = VoltageAlongLine(self.u)
def setUp(self):
self.mesh = dolfin.UnitCube(1, 1, 1)
self.no_boundary_edges = 18 # for 1x1x1 UnitCube meshed with 2
# tris on each face
self.DUT = Geometry.BoundaryEdges(self.mesh)
