def demo_facetfunction(mesh):
try:
import dolfinplot as dfp
except:
raise IOError(
"Misssing dolfinplot. git clone https://bitbucket.org/finsberg/dolfinplot.git"
)
import dolfin as df
ffun = df.MeshFunction("size_t", mesh, 2, mesh.domains())
bmesh = df.BoundaryMesh(mesh, "exterior")
Vb = df.FunctionSpace(bmesh, "DG", 0)
fb = df.Function(Vb)
mapping = bmesh.entity_map(2)
for cell in df.cells(bmesh):
# fb.vector()[cell.index()] = ffun[mapping[cell.index()]]
if ffun[mapping[cell.index()]] == 10:
fb.vector()[cell.index()] = 1
elif ffun[mapping[cell.index()]] == 30:
fb.vector()[cell.index()] = 2
elif ffun[mapping[cell.index()]] == 40:
fb.vector()[cell.index()] = 0
vtkfun = dfp.VTK_DolfinScalar(fb)
vtkfun.SetEdgeColor((0, 0, 0))
focal = (mesh.coordinates().T[0].max()) / 2.0
vtkfun.Render(view="side", dpi=300, size=(1200, 800), focal=focal)
#vtkfun.Show()
return vtkfun
def __init__(self, name: str, spec: FieldSpec, mesh: df.Mesh):
self._boundary_mesh = df.BoundaryMesh(mesh, "exterior")
self._boundary_function_space = df.FunctionSpace(
self._boundary_mesh, "CG", 1)
self._data = df.Function(self._boundary_function_space)
super().__init__(name, spec)
def __init__(self, *inputobj, **options):
c = options.pop("c", "gold")
alpha = options.pop("alpha", 1)
exterior = options.pop("exterior", False)
fast = options.pop("fast", False)
computeNormals = options.pop("computeNormals", False)
mesh, u = _inputsort(inputobj)
if not mesh:
return
if exterior:
import dolfin
meshc = dolfin.BoundaryMesh(mesh, 'exterior')
else:
meshc = mesh
poly = utils.buildPolyData(meshc.coordinates(),
meshc.cells(),
fast=fast)
Actor.__init__(
self,
poly,
c=c,
alpha=alpha,
computeNormals=computeNormals,
)
self.mesh = mesh # holds a dolfin Mesh obj
self.u = u # holds a dolfin function_data
# holds the actual values of u on the mesh
self.u_values = _compute_uvalues(u, mesh)
def loadDolfin(filename, exterior=False):
"""Reads a `Fenics/Dolfin` file format (.xml or .xdmf).
Return an ``Actor(vtkActor)`` object."""
import sys
if sys.version_info[0] < 3:
return _loadDolfin_old(filename)
import dolfin
if filename.lower().endswith('.xdmf'):
f = dolfin.XDMFFile(filename)
m = dolfin.Mesh()
f.read(m)
else:
m = dolfin.Mesh(filename)
bm = dolfin.BoundaryMesh(m, "exterior")
if exterior:
poly = utils.buildPolyData(bm.coordinates(), bm.cells(), fast=True)
else:
polyb = utils.buildPolyData(bm.coordinates(), bm.cells(), fast=True)
polym = utils.buildPolyData(m.coordinates(), m.cells(), fast=True)
app = vtk.vtkAppendPolyData()
app.AddInputData(polym)
app.AddInputData(polyb)
app.Update()
poly = app.GetOutput()
return Actor(poly).lw(0.1)
def p1_trace(fenics_space):
"""
Return the P1 trace operator.
This function returns a pair (space, trace_matrix),
where space is a BEM++ space object and trace_matrix is the corresponding
matrix that maps the coefficients of a FEniCS function to its boundary
trace coefficients in the corresponding BEM++ space.
"""
import dolfin #pylint: disable=import-error
from bempp.api.fenics_interface.coupling import fenics_space_info
from bempp.api import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
boundary_mesh = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = boundary_mesh.entity_map(0).array().astype(np.int64)
bm_coords = boundary_mesh.coordinates()
bm_cells = boundary_mesh.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from FEniCS dofs to BEM++ dofs.
# First the BEM++ dofs from the boundary vertices
from scipy.sparse import coo_matrix
bempp_dofs_from_b_vertices = p1_dof_to_vertex_matrix(space).transpose()
# Now FEniCS vertices to boundary dofs
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype='float64').tocsc()
# Finally FEniCS dofs to vertices.
vertices_from_fenics_dofs = coo_matrix(
(np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype='float64').tocsc()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * \
b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return space, trace_matrix
def test_bem_perf(self):
mesh = df.UnitCubeMesh(15, 15, 15)
boundary_mesh = df.BoundaryMesh(mesh, 'exterior', False)
c = time_counter.counter()
while c.next():
df.BoundaryMesh(mesh, 'exterior', False)
print "Boundary mesh computation for %s: %s" % (mesh, c)
c = time_counter.counter()
while c.next():
bem, _ = compute_bem_fk(boundary_mesh)
n = bem.shape[0]
print "FK BEM computation for %dx%d (%.2f Mnodes/sec): %s" % (
n, n, c.calls_per_sec(n * n / 1e6), c)
c = time_counter.counter()
while c.next():
bem, _ = compute_bem_gcr(boundary_mesh)
print "GCR BEM computation for %dx%d (%.2f Mnodes/sec): %s" % (
n, n, c.calls_per_sec(n * n / 1e6), c)
def test_snap_nearest(self):
mesh = df.UnitCubeMesh(10, 10, 10)
mesh = df.BoundaryMesh(mesh, 'exterior')
V = df.FunctionSpace(mesh, 'CG', 2)
f = df.interpolate(df.Expression('sin(x[0]+x[1]+x[2])', degree=2), V)
# A proxy expression whose action at x eval f at closest point dof to x
f_ = snap_to_nearest(f)
self.assertTrue(abs(f_(1., 1., 1.) - f(1., 1., 1.)) < 1E-13)
self.assertTrue(abs(f_(1.1, 1.1, 1.1) - f(1., 1., 1.)) < 1E-13)
def calculate_residual(self, mesh2):
boundmesh = dolfin.BoundaryMesh(mesh2, "exterior")
d = max(
[
self.bbtree.query(dolfin.Vertex(boundmesh, v_idx).point().array())[0]
for v_idx in range(boundmesh.num_vertices())
]
)
return dolfin.MPI.max(mpi_comm_world(), d)
def p1_trace(fenics_space):
"""
Return the P1 trace operator.
This function returns a pair (space, trace_matrix),
where space is a Bempp space object and trace_matrix is the corresponding
matrix that maps the coefficients of a FEniCS function to its boundary
trace coefficients in the corresponding Bempp space.
"""
import dolfin
import bempp.api
from scipy.sparse import coo_matrix
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == "Lagrange" and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
boundary_mesh = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = boundary_mesh.entity_map(0).array().astype(np.int64)
bm_coords = boundary_mesh.coordinates()
bm_cells = boundary_mesh.cells()
bempp_boundary_grid = bempp.api.Grid(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = bempp.api.function_space(bempp_boundary_grid, "P", 1)
# Now FEniCS vertices to boundary dofs
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype="float64",
).tocsc()
# Finally FEniCS dofs to vertices.
vertices_from_fenics_dofs = coo_matrix(
(
np.ones(mesh.num_vertices()),
(dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices())),
),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype="float64",
).tocsc()
# Get trace matrix by multiplication
trace_matrix = b_vertices_from_vertices @ vertices_from_fenics_dofs
# Now return everything
return space, trace_matrix
def calculate_residual(self, mesh2):
boundmesh = df.BoundaryMesh(mesh2, "exterior")
d = max(
[
self.bbtree.compute_closest_point(df.Vertex(boundmesh, v_idx).point())[
1
]
for v_idx in range(boundmesh.num_vertices())
]
)
return df.MPI.max(df.mpi_comm_world(), d)
def boundary_grid_from_fenics_mesh(fenics_mesh):
"""
Return a boundary grid from a FEniCS Mesh.
"""
from bempp import grid_from_element_data
bm = _dolfin.BoundaryMesh(fenics_mesh, "exterior", False)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),bm_cells.transpose())
return bempp_boundary_grid
def _1d2d_mesh(n, m=None):
'''Line mesh in 2d'''
if m is None: m = n
mesh1d = df.UnitSquareMesh(n, m)
mesh1d = df.BoundaryMesh(mesh1d, 'exterior')
cell_f = df.MeshFunction('size_t', mesh1d, 1, 0)
df.CompiledSubDomain('near(x[0], 0) || near(x[1], 0)').mark(cell_f, 1)
mesh1d = df.SubMesh(mesh1d, cell_f, 1)
return mesh1d
def __init__(self, *inputobj, **options):
c = options.pop("c", "gold")
alpha = options.pop("alpha", 1)
wire = options.pop("wire", True)
bc = options.pop("bc", None)
exterior = options.pop("exterior", False)
fast = options.pop("fast", False)
computeNormals = options.pop("computeNormals", False)
mesh, u = _inputsort(inputobj)
if not mesh:
return
if exterior:
import dolfin
meshc = dolfin.BoundaryMesh(mesh, 'exterior')
else:
meshc = mesh
poly = utils.buildPolyData(meshc.coordinates(),
meshc.cells(),
fast=fast)
Actor.__init__(
self,
poly,
c=c,
alpha=alpha,
wire=wire,
bc=bc,
computeNormals=computeNormals,
)
self.mesh = mesh # holds a dolfin Mesh obj
self.u = u # holds a dolfin function_data
self.u_values = None # holds the actual values of u on the mesh
u_values = None
if u:
u_values = np.array([u(p) for p in self.mesh.coordinates()])
#print(u_values)
if u_values is not None: # colorize if a dolfin function is passed
if len(u_values.shape) == 2:
if u_values.shape[1] in [2, 3]: # u_values is 2D or 3D
self.u_values = u_values
dispsizes = utils.mag(u_values)
else: # u_values is 1D
dispsizes = u_values
self.addPointScalars(dispsizes, "u_values") #.mapPointsToCells()
def p1_trace(fenics_space):
import dolfin
from .coupling import fenics_space_info
from bempp import function_space, grid_from_element_data
import numpy as np
family, degree = fenics_space_info(fenics_space)
if not (family == 'Lagrange' and degree == 1):
raise ValueError("fenics_space must be a p1 Lagrange space")
mesh = fenics_space.mesh()
bm = dolfin.BoundaryMesh(mesh, "exterior", False)
bm_nodes = bm.entity_map(0).array().astype(np.int64)
bm_coords = bm.coordinates()
bm_cells = bm.cells()
bempp_boundary_grid = grid_from_element_data(bm_coords.transpose(),
bm_cells.transpose())
# First get trace space
space = function_space(bempp_boundary_grid, "P", 1)
# Now compute the mapping from BEM++ dofs to FEniCS dofs
# First the BEM++ dofs to the boundary vertices
from ._lagrange_coupling import p1_vertex_map
from scipy.sparse import coo_matrix
vertex_to_dof_map = p1_vertex_map(space)
vertex_indices = np.arange(space.global_dof_count)
data = np.ones(space.global_dof_count)
bempp_dofs_from_b_vertices = coo_matrix(
(data, (vertex_to_dof_map, vertex_indices)), dtype='float64').tocsr()
# Now the boundary vertices to all the vertices
b_vertices_from_vertices = coo_matrix(
(np.ones(len(bm_nodes)), (np.arange(len(bm_nodes)), bm_nodes)),
shape=(len(bm_nodes), mesh.num_vertices()),
dtype='float64').tocsr()
# Finally the vertices to FEniCS dofs
vertices_from_fenics_dofs = coo_matrix(
(np.ones(mesh.num_vertices()), (dolfin.dof_to_vertex_map(fenics_space),
np.arange(mesh.num_vertices()))),
shape=(mesh.num_vertices(), mesh.num_vertices()),
dtype='float64').tocsr()
# Get trace matrix by multiplication
trace_matrix = bempp_dofs_from_b_vertices * b_vertices_from_vertices * vertices_from_fenics_dofs
# Now return everything
return (space, trace_matrix)
def _1d3d_mesh(n):
'''Line mesh in 3d'''
mesh1d = df.UnitCubeMesh(n, n, n)
cell_f = df.MeshFunction('size_t', mesh1d, 3, 0)
df.CompiledSubDomain('x[0] > x[1] - DOLFIN_EPS').mark(cell_f, 1)#
mesh1d = df.BoundaryMesh(df.SubMesh(mesh1d, cell_f, 1), 'exterior')
cell_f = df.MeshFunction('size_t', mesh1d, 2, 0)
df.CompiledSubDomain('near(x[0], x[1])').mark(cell_f, 1)
mesh1d = df.SubMesh(mesh1d, cell_f, 1)
cell_f = df.MeshFunction('size_t', mesh1d, 2, 0)
df.CompiledSubDomain('x[2] < x[1] + DOLFIN_EPS').mark(cell_f, 1)
mesh1d = df.BoundaryMesh(df.SubMesh(mesh1d, cell_f, 1), 'exterior')
cell_f = df.MeshFunction('size_t', mesh1d, 1, 0)
df.CompiledSubDomain('near(x[2], x[1])').mark(cell_f, 1)
mesh1d = df.SubMesh(mesh1d, cell_f, 1)
return mesh1d
def test_cell_ordering(self):
mesh = df.UnitCubeMesh(1, 1, 1)
centre = np.array([0.5, 0.5, 0.5])
boundary_mesh = df.BoundaryMesh(mesh, 'exterior', False)
coordinates = boundary_mesh.coordinates()
for i in xrange(boundary_mesh.num_cells()):
cell = df.Cell(boundary_mesh, i)
p1 = coordinates[cell.entities(0)[0]]
p2 = coordinates[cell.entities(0)[1]]
p3 = coordinates[cell.entities(0)[2]]
n = np.cross(p2 - p1, p3 - p1)
print "Boundary face %d, normal orientation %g" % (
i, np.sign(np.dot(n, p1 - centre)))
def check_boundaries_are_marked(
mesh: df.Mesh,
ffun: df.MeshFunction,
markers: Dict[str, int],
boundaries: List[str],
) -> None:
# Check that all boundary faces are marked
num_boundary_facets = df.BoundaryMesh(mesh, "exterior").num_cells()
if num_boundary_facets != sum(
[np.sum(ffun.array() == markers[boundary])
for boundary in boundaries], ):
raise RuntimeError(
("Not all boundary faces are marked correctly. Make sure all "
"boundary facets are marked as: {}"
"").format(", ".join(
["{} = {}".format(k, v) for k, v in markers.items()])), )
def boundary_grid_from_fenics_mesh(fenics_mesh):
"""
Create a Bempp boundary grid from a FEniCS Mesh.
Return the Bempp grid and a map from the node numberings of the FEniCS
mesh to the node numbers of the boundary grid.
"""
import bempp.api
import numpy as np
boundary_mesh = _dolfin.BoundaryMesh(fenics_mesh, "exterior", False)
bm_coords = boundary_mesh.coordinates()
bm_cells = boundary_mesh.cells()
bm_nodes = boundary_mesh.entity_map(0).array().astype(np.int64)
bempp_boundary_grid = bempp.api.Grid(bm_coords.transpose(),
bm_cells.transpose())
return bempp_boundary_grid, bm_nodes
def __init__(self,mesh,m, parameters=sb.default_parameters , degree=1, element="CG",
project_method='magpar', unit_length=1,Ms = 1.0,bench = False,
mac=0.3,p=3,num_limit=100):
sb.FemBemDeMagSolver.__init__(self,mesh,m, parameters, degree, element=element,
project_method = project_method,
unit_length = unit_length,Ms = Ms,bench = bench)
self.__name__ = "Treecode Demag Solver"
#Linear Solver parameters
method = parameters["poisson_solver"]["method"]
pc = parameters["poisson_solver"]["preconditioner"]
self.poisson_solver = df.KrylovSolver(self.poisson_matrix, method, pc)
self.phi1 = df.Function(self.V)
self.phi2 = df.Function(self.V)
# Eq (1) and code-block 2 - two first lines.
b = self.Ms*df.inner(self.w, df.grad(self.v))*df.dx
self.D = df.assemble(b)
self.p=p
self.mac=mac
self.num_limit=num_limit
self.mesh=mesh
self.bmesh = df.BoundaryMesh(mesh,False)
self.b2g_map = self.bmesh.vertex_map().array()
self.compute_triangle_normal()
self.__compute_bsa()
fast_sum=FastSum(p=self.p,mac=self.mac,num_limit=self.num_limit)
coords=self.bmesh.coordinates()
face_nodes=np.array(self.bmesh.cells(),dtype=np.int32)
fast_sum.init_mesh(coords,self.t_normals,face_nodes,self.vert_bsa)
self.fast_sum=fast_sum
self.phi2_b = np.zeros(self.bmesh.num_vertices())
def run_measurements(m, mesh, unit_length, tol, repetitions=10, H_expected=None, name="", skip=[]):
S3 = df.VectorFunctionSpace(mesh, "CG", 1)
m = vector_valued_function(m, S3)
Ms = 1
bem, boundary_to_global = compute_bem_fk(df.BoundaryMesh(mesh, 'exterior', False))
if H_expected is not None:
H = vector_valued_function(H_expected, S3)
H_expected = H.vector().array()
else:
# use default/default as reference then.
demag = fk.FKDemag()
demag.precomputed_bem(bem, boundary_to_global)
demag.setup(S3, m, Ms, unit_length)
H_expected = demag.compute_field()
del(demag)
if name == "":
pass
else:
name = name + "_"
runner = create_measurement_runner(S3, m, Ms, unit_length,
H_expected, tol, repetitions,
bem, boundary_to_global)
solvers = [s[0] for s in df.krylov_solver_methods()]
preconditioners = [p[0] for p in df.krylov_solver_preconditioners()]
results_1, failed_1 = runner("first linear solve",
"phi_1_solver", solvers,
"phi_1_preconditioner", preconditioners,
skip,
"{}timings_log_1.txt".format(name),
"{}results_1.pickled".format(name))
results_2, failed_2 = runner("second linear solve",
"phi_2_solver", solvers,
"phi_2_preconditioner", preconditioners,
skip,
"{}timings_log_2.txt".format(name),
"{}results_2.pickled".format(name))
return solvers, preconditioners, results_1, failed_1, results_2, failed_2
def run_demag_benchmark(m,
mesh,
unit_length,
tol,
repetitions=10,
name="bench",
H_expected=None):
S3 = df.VectorFunctionSpace(mesh, "CG", 1)
m = vector_valued_function(m, S3)
Ms = 1
# pre-compute BEM to save time
bem, boundary_to_global = compute_bem_fk(
df.BoundaryMesh(mesh, 'exterior', False))
if H_expected is not None:
H = vector_valued_function(H_expected, S3)
H_expected = H.vector().array()
else: # if no H_expected was passed, use default/default as reference
demag = fk.FKDemag()
demag.precomputed_bem(bem, boundary_to_global)
demag.setup(S3, m, Ms, unit_length)
H_expected = demag.compute_field()
del (demag)
# gather all solvers and preconditioners
solvers = [s[0] for s in df.krylov_solver_methods()]
preconditioners = [p[0] for p in df.krylov_solver_preconditioners()]
benchmark = prepare_benchmark(S3, m, Ms, unit_length, H_expected, tol,
repetitions, bem, boundary_to_global)
results_1 = benchmark("first linear solve",
"phi_1_solver",
solvers,
"phi_1_preconditioner",
preconditioners,
name=name + "_1")
results_2 = benchmark("second linear solve",
"phi_2_solver",
solvers,
"phi_2_preconditioner",
preconditioners,
name=name + "_2")
return solvers, preconditioners, results_1, results_2
def __init__(self, mesh, bnd, bnd_id, tol=df.DOLFIN_EPS):
df.SubDomain.__init__(self)
self.mesh = mesh
self.bnd = bnd
self.bnd_id = bnd_id
self.tol = tol
# Pick a random vertex on the bnd (assuming this vertex is a node)
facet_id = bnd.where_equal(bnd_id)[0]
facet = list(facets(mesh))[facet_id]
vertex_id = facet.entities(0)[0]
self.vertex = mesh.coordinates()[vertex_id]
self.bnd_facets = bnd.where_equal(bnd_id)
self.bmesh = df.BoundaryMesh(mesh, 'exterior')
facet_dim = self.bmesh.topology().dim()
self.cell_map = self.bmesh.entity_map(facet_dim)
def run_bem_computation_test(self, mesh):
S3 = df.VectorFunctionSpace(mesh, "Lagrange", 1, dim=3)
m = df.interpolate(df.Constant((1, 0, 0)), S3)
Ms = 1.0
bem_magpar, g2finmag = belement.BEM_matrix(mesh)
bem_finmag = np.zeros(bem_magpar.shape)
bem, b2g = compute_bem_fk(df.BoundaryMesh(mesh, 'exterior', False))
for i_dolfin in xrange(bem.shape[0]):
i_finmag = g2finmag[b2g[i_dolfin]]
for j_dolfin in xrange(bem.shape[0]):
j_finmag = g2finmag[b2g[j_dolfin]]
bem_finmag[i_finmag, j_finmag] = bem[i_dolfin, j_dolfin]
if np.max(np.abs(bem_finmag - bem_magpar)) > 1e-12:
print "Finmag:", np.round(bem_finmag, 4)
print "Magpar:", np.round(bem_magpar, 4)
print "Difference:", np.round(bem_magpar - bem_finmag, 4)
self.fail("Finmag and magpar computation of BEM differ, mesh: " +
str(mesh))
def method(L=3., H=1., R=0.3, n_segments=40, res=60, show=False, **kwargs):
"""
Generates mesh of Snausen/Snoevsen.
"""
info("Generating mesh of Snoevsen.")
# Define points:
pt_A = df.Point(0., 0.)
pt_B = df.Point(L, H)
pt_C = df.Point(L / 2 - 2 * R, 0.)
pt_D = df.Point(L / 2 + 2 * R, 0.)
pt_E = df.Point(L / 2 - 2 * R, -R)
pt_F = df.Point(L / 2 + 2 * R, -R)
pt_G = df.Point(L / 2, -R)
tube = mshr.Rectangle(pt_A, pt_B)
add_rect = mshr.Rectangle(pt_E, pt_D)
neg_circ_L = mshr.Circle(pt_E, R, segments=n_segments)
neg_circ_R = mshr.Circle(pt_F, R, segments=n_segments)
pos_circ = mshr.Circle(pt_G, R, segments=n_segments)
domain = tube + add_rect - neg_circ_L - neg_circ_R + pos_circ
mesh = mshr.generate_mesh(domain, res)
# check that mesh is periodic along x
boun = df.BoundaryMesh(mesh, "exterior")
y = boun.coordinates()[:, 1]
y = y[y < 1.]
y = y[y > 0.]
n_y = len(y)
n_y_unique = len(np.unique(y))
assert (n_y == 2 * n_y_unique)
mesh_path = os.path.join(MESHES_DIR, "snoevsen_res" + str(res))
store_mesh_HDF5(mesh, mesh_path)
if show:
df.plot(mesh, "Mesh")
plt.show()
def main():
resolution = 32 # 32 * 3
# filename = 'data/mesh_res_%d_boundary.xml' % resolution
filename = 'data/mesh_res_%d_boundary.xml' % resolution
if os.path.exists(filename):
print '=' * 60
print 'Mesh file exists, loading from file'
print '=' * 60
mesh_3d = dolfin.Mesh(filename)
else:
geometry_3d = get_geometry()
dolfin.info(geometry_3d, True)
print '=' * 60
print 'Creating mesh'
print '=' * 60
mesh_3d = dolfin.Mesh(geometry_3d, resolution)
print '=' * 60
print 'Converting to a boundary mesh'
print '=' * 60
mesh_3d = dolfin.BoundaryMesh(mesh_3d, 'exterior')
# Since much smaller, it's much easier to refine the boundary mesh
# as well. It may be worth doing this via:
# mesh_3d = dolfin.mesh.refine(mesh_3d)
print '=' * 60
print 'Saving to file:', filename
print '=' * 60
data_file = dolfin.File(filename)
data_file << mesh_3d
# Plot in either case.
print '=' * 60
print 'Plotting in interactive mode'
print '=' * 60
fh = dolfin.plot(mesh_3d,
'3D mesh',
interactive=True,
window_width=900,
window_height=700)
def mplot_mesh(ax, mesh, **kwargs):
tdim = mesh.topology().dim()
gdim = mesh.geometry().dim()
if gdim == 2 and tdim == 2:
return ax.triplot(mesh2triang(mesh), color='#808080')
elif gdim == 3 and tdim == 3:
bmesh = dolfin.BoundaryMesh(mesh, "exterior", order=False)
mplot_mesh(ax, bmesh, **kwargs)
elif gdim == 3 and tdim == 2:
xy = mesh.coordinates()
return ax.plot_trisurf(*[xy[:, i] for i in range(gdim)],
triangles=mesh.cells())
elif tdim == 1 and gdim == 1:
x = mesh.coordinates()[:, 0]
return ax.plot(x, 0 * x, 'o')
elif tdim == 1:
x = [mesh.coordinates()[:, i] for i in range(gdim)]
return ax.plot(*x)
else:
raise AttributeError(
'Matplotlib plotting backend only supports 2D mesh.')
def __init__(self, *inputobj, **options):
c = options.pop("c", None)
alpha = options.pop("alpha", 1)
exterior = options.pop("exterior", False)
fast = options.pop("fast", False)
computeNormals = options.pop("computeNormals", False)
mesh, u = _inputsort(inputobj)
if not mesh:
return
if exterior:
import dolfin
meshc = dolfin.BoundaryMesh(mesh, 'exterior')
else:
meshc = mesh
if hasattr(mesh, "coordinates"):
coords = mesh.coordinates()
else:
coords = mesh.geometry.points
poly = utils.buildPolyData(coords,
meshc.cells(),
fast=fast,
tetras=True)
Mesh.__init__(
self,
poly,
c=c,
alpha=alpha,
computeNormals=computeNormals,
)
self.mesh = mesh # holds a dolfin Mesh obj
self.u = u # holds a dolfin function_data
# holds the actual values of u on the mesh
self.u_values = _compute_uvalues(u, mesh)
def mplot_mesh(ax, mesh, **kwargs):
tdim = mesh.topology().dim()
gdim = mesh.geometry().dim()
if gdim == 2 and tdim == 2:
color = kwargs.pop("color", '#808080')
return ax.triplot(mesh2triang(mesh), color=color, **kwargs)
elif gdim == 3 and tdim == 3:
bmesh = dolfin.BoundaryMesh(mesh, "exterior", order=False)
mplot_mesh(ax, bmesh, **kwargs)
elif gdim == 3 and tdim == 2:
xy = mesh.coordinates()
return ax.plot_trisurf(*[xy[:,i] for i in range(gdim)],
triangles=mesh.cells(), **kwargs)
elif tdim == 1:
x = [mesh.coordinates()[:,i] for i in range(gdim)]
if gdim == 1:
x.append(np.zeros_like(x[0]))
ax.set_yticks([])
marker = kwargs.pop('marker', 'o')
return ax.plot(*x, marker=marker, **kwargs)
else:
assert False, "this code should not be reached"
def selfsimilarprofiles(u, nu_t, x_coord, u_cl, y_half, mesh):
"""
This routine computes
- the adimensional y-coord y_hat = y / y_1/2
- the adimensional velocity u_hat = u/u_cl
- the adimensional viscosity nu_t_hat = nu_t / (u_hat * y_hat)
INPUTS:
- the velocity field u
- the turbulent viscosity field nu_t
- the list of x coordinates x_coord
- the centerline velocities u_cl
- the jet thickness y_1/2
- the mesh
"""
boundary_mesh = dl.BoundaryMesh(mesh, "exterior")
x = boundary_mesh.coordinates()
y_coord = x[np.abs(x[:, 0] - x_coord[0]) < 1e-9, 1]
u1, u2 = u.split(deepcopy=True)
u_hat = np.zeros((y_coord.shape[0], x_coord.shape[0]))
y_hat = np.zeros((y_coord.shape[0], x_coord.shape[0]))
nu_t_hat = np.zeros((y_coord.shape[0], x_coord.shape[0]))
j = 0
for xj in x_coord:
u_clj = u_cl[j]
y_halfj = y_half[j]
i = 0
for yi in y_coord:
y_hat[i, j] = yi / y_halfj
u_hat[i, j] = u1((xj, yi)) / u_clj
nu_t_hat[i, j] = nu_t((xj, yi)) / (u_clj * y_halfj)
i += 1
j += 1
return y_hat, u_hat, nu_t_hat
def spreadFunction(u, mesh, x_max=None):
"""
This routine computes the following quantities as a function of the distance x from the inflow:
- The centerline velocity: u_cl
- The integral jet thickness: L
- The spread function (derivative of jet thickness): S
- The jet thickness: y_1/2
INPUTS:
- the velocity u
- the mesh mesh
"""
boundary_mesh = dl.BoundaryMesh(mesh, "exterior")
x = boundary_mesh.coordinates()
x_coord = x[np.abs(x[:, 1]) < 1e-9, 0]
if x_max is not None:
x_coord = x_coord[x_coord <= x_max]
e1 = dl.Expression(("1.", "0."))
u1, u2 = u.split(deepcopy=True)
Vh_grad = dl.FunctionSpace(mesh, 'RT', 1)
grad_u1 = dl.Function(Vh_grad)
test = dl.TestFunction(Vh_grad)
n = dl.FacetNormal(mesh)
dl.solve(
dl.inner(grad_u1, test) * dl.dx + u1 * dl.div(test) * dl.dx -
u1 * dl.dot(test, n) * dl.ds == 0, grad_u1)
axis = dl.AutoSubDomain(lambda x: dl.near(x[1], 0.))
axis_mesh = dl.SubMesh(boundary_mesh, axis)
Vh_axis = dl.FunctionSpace(axis_mesh, "CG", 2)
u1_axis = dl.interpolate(u1, Vh_axis)
Vh_axis_grad = dl.FunctionSpace(axis_mesh, 'CG', 1)
du1_dx = dl.Function(Vh_axis_grad)
test_axis = dl.TestFunction(Vh_axis_grad)
left_point = dl.AutoSubDomain(
lambda x, on_boundary: dl.near(x[0], x_coord[0]) and on_boundary)
right_point = dl.AutoSubDomain(
lambda x, on_boundary: dl.near(x[0], x_coord[-1]) and on_boundary)
bb_marker = dl.FacetFunction("size_t", axis_mesh)
bb_marker.set_all(0)
left_point.mark(bb_marker, 1)
right_point.mark(bb_marker, 2)
dss = dl.Measure("ds")[bb_marker]
dl.solve(
du1_dx * test_axis * dl.dx + u1_axis * test_axis.dx(0) * dl.dx +
u1_axis * test_axis * dss(1) - u1_axis * test_axis * dss(2) == 0,
du1_dx)
u_cl = np.zeros(x_coord.shape)
L = np.zeros(x_coord.shape)
S = np.zeros(x_coord.shape)
y_half = np.zeros(x_coord.shape)
i = 0
for xi in x_coord:
line_segment = dl.AutoSubDomain(lambda x: dl.near(x[0], xi))
markers = dl.FacetFunction("size_t", mesh)
markers.set_all(0)
line_segment.mark(markers, 1)
if i == 0 or (i == (x_coord.shape[0] - 1) and x_max is None):
ds = dl.ds[markers]
int_u1 = dl.assemble(u1 * ds(1))
int_du1_dx = dl.assemble(dl.dot(grad_u1, e1) * ds(1))
else:
dS = dl.dS[markers]
int_u1 = dl.assemble(dl.avg(u1) * dS(1))
int_du1_dx = dl.assemble(dl.avg(dl.dot(grad_u1, e1)) * dS(1))
u_cl[i] = u1((xi, 0.))
du_cl_dx = du1_dx((xi, 0.))
L[i] = int_u1 / u_cl[i]
S[i] = (int_du1_dx * u_cl[i] - int_u1 * du_cl_dx) / (u_cl[i] * u_cl[i])
y_half[i] = _bisection(u1, 9., 0., .5 * u_cl[i], xi)
i += 1
out = np.zeros((x_coord.shape[0], 5), dtype=x_coord.dtype)
out[:, 0] = x_coord
out[:, 1] = u_cl
out[:, 2] = L
out[:, 3] = S
out[:, 4] = y_half
return out