def create_mesh(self, extra_nodes=True):
"""
Create a mesh from the field region, optionally including the field
extra nodes.
"""
mesh = self.domain.mesh
if self.approx_order != 0:
if extra_nodes:
conn = self.econn
else:
conn = self.econn[:, :self.gel.n_vertex]
conns = [conn]
mat_ids = [mesh.cmesh.cell_groups]
descs = mesh.descs[:1]
if extra_nodes:
coors = self.coors
else:
coors = self.coors[:self.n_vertex_dof]
mesh = Mesh.from_data(self.name, coors, None, conns, mat_ids,
descs)
return mesh
def create_mesh(self, extra_nodes=True):
"""
Create a mesh from the field region, optionally including the field
extra nodes.
"""
mesh = self.domain.mesh
if self.approx_order != 0:
conns, mat_ids, descs = [], [], []
for ig, ap in self.aps.iteritems():
group = self.domain.groups[ig]
if extra_nodes:
conn = ap.econn
else:
offset = group.shape.n_ep
conn = ap.econn[:,:offset]
conns.append(conn)
mat_ids.append(mesh.mat_ids[ig])
descs.append(mesh.descs[ig])
if extra_nodes:
coors = self.coors
else:
coors = self.coors[:self.n_vertex_dof]
mesh = Mesh.from_data(self.name, coors, None, conns,
mat_ids, descs)
return mesh
def create_mesh(self, extra_nodes=True):
"""
Create a mesh from the field region, optionally including the field
extra nodes.
"""
mesh = self.domain.mesh
if self.approx_order != 0:
if extra_nodes:
conn = self.econn
else:
conn = self.econn[:, :self.gel.n_vertex]
conns = [conn]
mat_ids = [mesh.cmesh.cell_groups]
descs = mesh.descs[:1]
if extra_nodes:
coors = self.coors
else:
coors = self.coors[:self.n_vertex_dof]
mesh = Mesh.from_data(self.name, coors, None, conns,
mat_ids, descs)
return mesh
def create_mesh(self, extra_nodes=True):
"""
Create a mesh from the field region, optionally including the field
extra nodes.
"""
mesh = self.domain.mesh
if self.approx_order != 0:
conns, mat_ids, descs = [], [], []
for ig, ap in self.aps.iteritems():
group = self.domain.groups[ig]
if extra_nodes:
conn = ap.econn
else:
offset = group.shape.n_ep
conn = ap.econn[:,:offset]
conns.append(conn)
mat_ids.append(mesh.mat_ids[ig])
descs.append(mesh.descs[ig])
if extra_nodes:
coors = self.coors
else:
coors = self.coors[:self.n_vertex_dof]
mesh = Mesh.from_data(self.name, coors, None, conns,
mat_ids, descs)
return mesh
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_block_mesh(dims, shape, centre, mat_id=0, name='block',
coors=None, verbose=True):
"""
Generate a 2D or 3D block mesh. The dimension is determined by the
lenght of the shape argument.
Parameters
----------
dims : array of 2 or 3 floats
Dimensions of the block.
shape : array of 2 or 3 ints
Shape (counts of nodes in x, y, z) of the block mesh.
centre : array of 2 or 3 floats
Centre of the block.
mat_id : int, optional
The material id of all elements.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
dim = shape.shape[0]
centre = centre[:dim]
dims = dims[:dim]
n_nod = nm.prod(shape)
output('generating %d vertices...' % n_nod, verbose=verbose)
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
ngrid.shape = (dim, n_nod)
coors = x0 + ngrid.T * dd
output('...done', verbose=verbose)
n_el = nm.prod(shape - 1)
output('generating %d cells...' % n_el, verbose=verbose)
mat_ids = nm.empty((n_el,), dtype=nm.int32)
mat_ids.fill(mat_id)
conn, desc = get_tensor_product_conn(shape)
output('...done', verbose=verbose)
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def linearize(self, dofs, min_level=0, max_level=1, eps=1e-4):
"""
Linearize the solution for post-processing.
Parameters
----------
dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
mesh : Mesh instance
The adapted, nonconforming, mesh.
vdofs : array
The DOFs defined in vertices of `mesh`.
levels : array of ints
The refinement level used for each element group.
"""
assert_(dofs.ndim == 2)
n_nod, dpn = dofs.shape
assert_(n_nod == self.n_nod)
assert_(dpn == self.shape[0])
vertex_coors = self.coors[:self.n_vertex_dof, :]
ap = self.ap
ps = ap.interp.poly_spaces['v']
gps = ap.interp.gel.interp.poly_spaces['v']
vertex_conn = ap.econn[:, :self.gel.n_vertex]
eval_dofs = get_eval_dofs(dofs, ap.econn, ps, ori=ap.ori)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, coors, conn, vdofs,
mat_ids) = create_output(eval_dofs,
eval_coors,
vertex_conn.shape[0],
ps,
min_level=min_level,
max_level=max_level,
eps=eps)
mesh = Mesh.from_data('linearized_mesh', coors, None, [conn],
[mat_ids], self.domain.mesh.descs)
return mesh, vdofs, level
def linearize(self, dofs, min_level=0, max_level=1, eps=1e-4):
"""
Linearize the solution for post-processing.
Parameters
----------
dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
mesh : Mesh instance
The adapted, nonconforming, mesh.
vdofs : array
The DOFs defined in vertices of `mesh`.
levels : array of ints
The refinement level used for each element group.
"""
assert_(dofs.ndim == 2)
n_nod, dpn = dofs.shape
assert_(n_nod == self.n_nod)
assert_(dpn == self.shape[0])
vertex_coors = self.coors[:self.n_vertex_dof, :]
ap = self.ap
ps = ap.interp.poly_spaces['v']
gps = ap.interp.gel.interp.poly_spaces['v']
vertex_conn = ap.econn[:, :self.gel.n_vertex]
eval_dofs = get_eval_dofs(dofs, ap.econn, ps, ori=ap.ori)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors,
vertex_conn.shape[0], ps,
min_level=min_level,
max_level=max_level, eps=eps)
mesh = Mesh.from_data('linearized_mesh', coors, None, [conn], [mat_ids],
self.domain.mesh.descs)
return mesh, vdofs, level
def create_mesh_from_control_points(self):
offset = 0
dim = self.spbs[0].cxyz.shape[1]
coors = nm.empty((0, dim), dtype=nm.float64)
conns = []
mat_ids = []
descs = []
for ib, spb in enumerate(self.spbs):
n_nod = spb.cxyz.shape[0]
coors = nm.concatenate((coors, spb.cxyz), 0)
descs.append('3_2')
conn = []
for ij in xrange(spb.cpi.shape[1]):
for ik in xrange(spb.cpi.shape[2]):
inx = spb.cpi[:, ij, ik]
row = [[p1, p2] for p1, p2 in zip(inx[:-1], inx[1:])]
conn.extend(row)
for ij in xrange(spb.cpi.shape[0]):
for ik in xrange(spb.cpi.shape[2]):
inx = spb.cpi[ij, :, ik]
row = [[p1, p2] for p1, p2 in zip(inx[:-1], inx[1:])]
conn.extend(row)
for ij in xrange(spb.cpi.shape[0]):
for ik in xrange(spb.cpi.shape[1]):
inx = spb.cpi[ij, ik, :]
row = [[p1, p2] for p1, p2 in zip(inx[:-1], inx[1:])]
conn.extend(row)
aux = nm.empty(len(conn), dtype=nm.int32)
aux.fill(ib)
mat_ids.append(aux)
conns.append(offset + nm.array(conn, dtype=nm.int32))
offset += n_nod
mesh = Mesh.from_data('control_points', coors, None, conns, mat_ids,
descs)
return mesh
def create_mesh_from_control_points( self ):
offset = 0
dim = self.spbs[0].cxyz.shape[1]
coors = nm.empty((0, dim), dtype=nm.float64)
conns = []
mat_ids = []
descs = []
for ib, spb in enumerate( self.spbs ):
n_nod = spb.cxyz.shape[0]
coors = nm.concatenate( (coors, spb.cxyz), 0 )
descs.append( '3_2' )
conn = []
for ij in range( spb.cpi.shape[1] ):
for ik in range( spb.cpi.shape[2] ):
inx = spb.cpi[:,ij,ik]
row = [[p1, p2] for p1, p2 in zip( inx[:-1], inx[1:] )]
conn.extend( row )
for ij in range( spb.cpi.shape[0] ):
for ik in range( spb.cpi.shape[2] ):
inx = spb.cpi[ij,:,ik]
row = [[p1, p2] for p1, p2 in zip( inx[:-1], inx[1:] )]
conn.extend( row )
for ij in range( spb.cpi.shape[0] ):
for ik in range( spb.cpi.shape[1] ):
inx = spb.cpi[ij,ik,:]
row = [[p1, p2] for p1, p2 in zip( inx[:-1], inx[1:] )]
conn.extend( row )
aux = nm.empty(len(conn), dtype=nm.int32)
aux.fill(ib)
mat_ids.append(aux)
conns.append( offset + nm.array( conn, dtype = nm.int32 ) )
offset += n_nod
mesh = Mesh.from_data('control_points', coors, None, conns,
mat_ids, descs)
return mesh
def linearize(self, dofs, min_level=0, max_level=1, eps=1e-4):
"""
Linearize the solution for post-processing.
Parameters
----------
dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
mesh : Mesh instance
The adapted, nonconforming, mesh.
vdofs : array
The DOFs defined in vertices of `mesh`.
levels : array of ints
The refinement level used for each element group.
"""
assert_(dofs.ndim == 2)
n_nod, dpn = dofs.shape
assert_(n_nod == self.n_nod)
assert_(dpn == self.shape[0])
vertex_coors = self.coors[:self.n_vertex_dof, :]
coors = []
vdofs = []
conns = []
mat_ids = []
levels = []
offset = 0
for ig, ap in self.aps.iteritems():
ps = ap.interp.poly_spaces['v']
gps = ap.interp.gel.interp.poly_spaces['v']
group = self.domain.groups[ig]
vertex_conn = ap.econn[:, :group.shape.n_ep]
eval_dofs = get_eval_dofs(dofs, ap.econn, ps, ori=ap.ori)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, _coors, conn,
_vdofs, _mat_ids) = create_output(eval_dofs, eval_coors,
group.shape.n_el, ps,
min_level=min_level,
max_level=max_level, eps=eps)
_mat_ids[:] = self.domain.mesh.mat_ids[ig][0]
coors.append(_coors)
vdofs.append(_vdofs)
conns.append(conn + offset)
mat_ids.append(_mat_ids)
levels.append(level)
offset += _coors.shape[0]
coors = nm.concatenate(coors, axis=0)
vdofs = nm.concatenate(vdofs, axis=0)
mesh = Mesh.from_data('linearized_mesh', coors, None, conns, mat_ids,
self.domain.mesh.descs)
return mesh, vdofs, levels
def create_expression_output(expression, name, primary_field_name,
fields, materials, variables,
functions=None, mode='eval', term_mode=None,
extra_args=None, verbose=True, kwargs=None,
min_level=0, max_level=1, eps=1e-4):
"""
Create output mesh and data for the expression using the adaptive
linearizer.
Parameters
----------
expression : str
The expression to evaluate.
name : str
The name of the data.
primary_field_name : str
The name of field that defines the element groups and polynomial
spaces.
fields : dict
The dictionary of fields used in `variables`.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
functions : Functions instance, optional
The user functions for materials etc.
mode : one of 'eval', 'el_avg', 'qp'
The evaluation mode - 'qp' requests the values in quadrature points,
'el_avg' element averages and 'eval' means integration over
each term region.
term_mode : str
The term call mode - some terms support different call modes
and depending on the call mode different values are
returned.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable
instance)) to be used in the expression.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
out : dict
The output dictionary.
"""
field = fields[primary_field_name]
vertex_coors = field.coors[:field.n_vertex_dof, :]
coors = []
vdofs = []
conns = []
mat_ids = []
levels = []
offset = 0
for ig, ap in field.aps.iteritems():
ps = ap.interp.poly_spaces['v']
gps = ap.interp.gel.interp.poly_spaces['v']
group = field.domain.groups[ig]
vertex_conn = ap.econn[:, :group.shape.n_ep]
eval_dofs = get_eval_expression(expression, ig,
fields, materials, variables,
functions=functions,
mode=mode, extra_args=extra_args,
verbose=verbose, kwargs=kwargs)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, _coors, conn,
_vdofs, _mat_ids) = create_output(eval_dofs, eval_coors,
group.shape.n_el, ps,
min_level=min_level,
max_level=max_level, eps=eps)
_mat_ids[:] = field.domain.mesh.mat_ids[ig][0]
coors.append(_coors)
vdofs.append(_vdofs)
conns.append(conn + offset)
mat_ids.append(_mat_ids)
levels.append(level)
offset += _coors.shape[0]
coors = nm.concatenate(coors, axis=0)
vdofs = nm.concatenate(vdofs, axis=0)
mesh = Mesh.from_data('linearized_mesh', coors, None, conns, mat_ids,
field.domain.mesh.descs)
out = {}
out[name] = Struct(name='output_data', mode='vertex',
data=vdofs, var_name=name, dofs=None,
mesh=mesh, levels=levels)
out = convert_complex_output(out)
return out
def gen_mesh_from_voxels(voxels, dims, etype='q'):
"""
Generate FE mesh from voxels (volumetric data).
Parameters
----------
voxels : array
Voxel matrix, 1=material.
dims : array
Size of one voxel.
etype : integer, optional
'q' - quadrilateral or hexahedral elements
't' - triangular or tetrahedral elements
Returns
-------
mesh : Mesh instance
Finite element mesh.
"""
dims = dims.squeeze()
dim = len(dims)
nddims = nm.array(voxels.shape) + 2
nodemtx = nm.zeros(nddims, dtype=nm.int32)
if dim == 2:
#iy, ix = nm.where(voxels.transpose())
iy, ix = nm.where(voxels)
nel = ix.shape[0]
if etype == 'q':
nodemtx[ix,iy] += 1
nodemtx[ix + 1,iy] += 1
nodemtx[ix + 1,iy + 1] += 1
nodemtx[ix,iy + 1] += 1
elif etype == 't':
nodemtx[ix,iy] += 2
nodemtx[ix + 1,iy] += 1
nodemtx[ix + 1,iy + 1] += 2
nodemtx[ix,iy + 1] += 1
nel *= 2
elif dim == 3:
#iy, ix, iz = nm.where(voxels.transpose(1, 0, 2))
iy, ix, iz = nm.where(voxels)
nel = ix.shape[0]
if etype == 'q':
nodemtx[ix,iy,iz] += 1
nodemtx[ix + 1,iy,iz] += 1
nodemtx[ix + 1,iy + 1,iz] += 1
nodemtx[ix,iy + 1,iz] += 1
nodemtx[ix,iy,iz + 1] += 1
nodemtx[ix + 1,iy,iz + 1] += 1
nodemtx[ix + 1,iy + 1,iz + 1] += 1
nodemtx[ix,iy + 1,iz + 1] += 1
elif etype == 't':
nodemtx[ix,iy,iz] += 6
nodemtx[ix + 1,iy,iz] += 2
nodemtx[ix + 1,iy + 1,iz] += 2
nodemtx[ix,iy + 1,iz] += 2
nodemtx[ix,iy,iz + 1] += 2
nodemtx[ix + 1,iy,iz + 1] += 2
nodemtx[ix + 1,iy + 1,iz + 1] += 6
nodemtx[ix,iy + 1,iz + 1] += 2
nel *= 6
else:
msg = 'incorrect voxel dimension! (%d)' % dim
raise ValueError(msg)
ndidx = nm.where(nodemtx)
coors = nm.array(ndidx).transpose() * dims
nnod = coors.shape[0]
nodeid = -nm.ones(nddims, dtype=nm.int32)
nodeid[ndidx] = nm.arange(nnod)
# generate elements
if dim == 2:
elems = nm.array([nodeid[ix,iy],
nodeid[ix + 1,iy],
nodeid[ix + 1,iy + 1],
nodeid[ix,iy + 1]]).transpose()
elif dim == 3:
elems = nm.array([nodeid[ix,iy,iz],
nodeid[ix + 1,iy,iz],
nodeid[ix + 1,iy + 1,iz],
nodeid[ix,iy + 1,iz],
nodeid[ix,iy,iz + 1],
nodeid[ix + 1,iy,iz + 1],
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix,iy + 1,iz + 1]]).transpose()
if etype == 't':
elems = elems_q2t(elems)
eid = etype + str(dim)
eltab = {'q2': 4, 'q3': 8, 't2': 3, 't3': 4}
mesh = Mesh.from_data('voxel_data',
coors, nm.ones((nnod,), dtype=nm.int32),
{0: nm.ascontiguousarray(elems)},
{0: nm.ones((nel,), dtype=nm.int32)},
{0: '%d_%d' % (dim, eltab[eid])})
return mesh
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conns = mesh.conns[0]
for ii in mesh.conns[1:]:
conns = nm.vstack((conns, ii))
mat_ids = mesh.mat_ids[0]
for ii in mesh.mat_ids[1:]:
mat_ids = nm.hstack((mat_ids, ii))
coors = mesh.coors
ngrps = mesh.ngroups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conns, coors,
ngrps, ndmap0) = tiled_mesh1d(conns, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conns, coors, ngrps = tiled_mesh1d(conns, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conns], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nnfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def create_expression_output(expression, name, primary_field_name,
fields, materials, variables,
functions=None, mode='eval', term_mode=None,
extra_args=None, verbose=True, kwargs=None,
min_level=0, max_level=1, eps=1e-4):
"""
Create output mesh and data for the expression using the adaptive
linearizer.
Parameters
----------
expression : str
The expression to evaluate.
name : str
The name of the data.
primary_field_name : str
The name of field that defines the element groups and polynomial
spaces.
fields : dict
The dictionary of fields used in `variables`.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
functions : Functions instance, optional
The user functions for materials etc.
mode : one of 'eval', 'el_avg', 'qp'
The evaluation mode - 'qp' requests the values in quadrature points,
'el_avg' element averages and 'eval' means integration over
each term region.
term_mode : str
The term call mode - some terms support different call modes
and depending on the call mode different values are
returned.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable
instance)) to be used in the expression.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
out : dict
The output dictionary.
"""
field = fields[primary_field_name]
vertex_coors = field.coors[:field.n_vertex_dof, :]
ps = field.poly_space
gps = field.gel.poly_space
vertex_conn = field.econn[:, :field.gel.n_vertex]
eval_dofs = get_eval_expression(expression,
fields, materials, variables,
functions=functions,
mode=mode, extra_args=extra_args,
verbose=verbose, kwargs=kwargs)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors,
vertex_conn.shape[0], ps,
min_level=min_level,
max_level=max_level, eps=eps)
mesh = Mesh.from_data('linearized_mesh', coors, None, [conn], [mat_ids],
field.domain.mesh.descs)
out = {}
out[name] = Struct(name='output_data', mode='vertex',
data=vdofs, var_name=name, dofs=None,
mesh=mesh, level=level)
out = convert_complex_output(out)
return out
def gen_mesh_from_voxels(voxels, dims, etype='q'):
"""
Generate FE mesh from voxels (volumetric data).
Parameters
----------
voxels : array
Voxel matrix, 1=material.
dims : array
Size of one voxel.
etype : integer, optional
'q' - quadrilateral or hexahedral elements
't' - triangular or tetrahedral elements
Returns
-------
mesh : Mesh instance
Finite element mesh.
"""
dims = nm.array(dims).squeeze()
dim = len(dims)
nddims = nm.array(voxels.shape) + 2
nodemtx = nm.zeros(nddims, dtype=nm.int32)
if dim == 2:
#iy, ix = nm.where(voxels.transpose())
iy, ix = nm.where(voxels)
nel = ix.shape[0]
if etype == 'q':
nodemtx[ix,iy] += 1
nodemtx[ix + 1,iy] += 1
nodemtx[ix + 1,iy + 1] += 1
nodemtx[ix,iy + 1] += 1
elif etype == 't':
nodemtx[ix,iy] += 2
nodemtx[ix + 1,iy] += 1
nodemtx[ix + 1,iy + 1] += 2
nodemtx[ix,iy + 1] += 1
nel *= 2
elif dim == 3:
#iy, ix, iz = nm.where(voxels.transpose(1, 0, 2))
iy, ix, iz = nm.where(voxels)
nel = ix.shape[0]
if etype == 'q':
nodemtx[ix,iy,iz] += 1
nodemtx[ix + 1,iy,iz] += 1
nodemtx[ix + 1,iy + 1,iz] += 1
nodemtx[ix,iy + 1,iz] += 1
nodemtx[ix,iy,iz + 1] += 1
nodemtx[ix + 1,iy,iz + 1] += 1
nodemtx[ix + 1,iy + 1,iz + 1] += 1
nodemtx[ix,iy + 1,iz + 1] += 1
elif etype == 't':
nodemtx[ix,iy,iz] += 6
nodemtx[ix + 1,iy,iz] += 2
nodemtx[ix + 1,iy + 1,iz] += 2
nodemtx[ix,iy + 1,iz] += 2
nodemtx[ix,iy,iz + 1] += 2
nodemtx[ix + 1,iy,iz + 1] += 2
nodemtx[ix + 1,iy + 1,iz + 1] += 6
nodemtx[ix,iy + 1,iz + 1] += 2
nel *= 6
else:
msg = 'incorrect voxel dimension! (%d)' % dim
raise ValueError(msg)
ndidx = nm.where(nodemtx)
coors = nm.array(ndidx).transpose() * dims
nnod = coors.shape[0]
nodeid = -nm.ones(nddims, dtype=nm.int32)
nodeid[ndidx] = nm.arange(nnod)
# generate elements
if dim == 2:
elems = nm.array([nodeid[ix,iy],
nodeid[ix + 1,iy],
nodeid[ix + 1,iy + 1],
nodeid[ix,iy + 1]]).transpose()
elif dim == 3:
elems = nm.array([nodeid[ix,iy,iz],
nodeid[ix + 1,iy,iz],
nodeid[ix + 1,iy + 1,iz],
nodeid[ix,iy + 1,iz],
nodeid[ix,iy,iz + 1],
nodeid[ix + 1,iy,iz + 1],
nodeid[ix + 1,iy + 1,iz + 1],
nodeid[ix,iy + 1,iz + 1]]).transpose()
if etype == 't':
elems = elems_q2t(elems)
eid = etype + str(dim)
eltab = {'q2': 4, 'q3': 8, 't2': 3, 't3': 4}
mesh = Mesh.from_data('voxel_data',
coors, nm.ones((nnod,), dtype=nm.int32),
[nm.ascontiguousarray(elems)],
[nm.ones((nel,), dtype=nm.int32)],
['%d_%d' % (dim, eltab[eid])])
return mesh
def gen_tiled_mesh(mesh, grid=None, scale=1.0, eps=1e-6, ret_ndmap=False):
"""
Generate a new mesh by repeating a given periodic element
along each axis.
Parameters
----------
mesh : Mesh instance
The input periodic FE mesh.
grid : array
Number of repetition along each axis.
scale : float, optional
Scaling factor.
eps : float, optional
Tolerance for boundary detection.
ret_ndmap : bool, optional
If True, return global node map.
Returns
-------
mesh_out : Mesh instance
FE mesh.
ndmap : array
Maps: actual node id --> node id in the reference cell.
"""
bbox = mesh.get_bounding_box()
if grid is None:
iscale = max(int(1.0 / scale), 1)
grid = [iscale] * mesh.dim
conn = mesh.get_conn(mesh.descs[0])
mat_ids = mesh.cmesh.cell_groups
coors = mesh.coors
ngrps = mesh.cmesh.vertex_groups
nrep = nm.prod(grid)
ndmap = None
output('repeating %s ...' % grid)
nblk = 1
for ii, gr in enumerate(grid):
if ret_ndmap:
(conn, coors,
ngrps, ndmap0) = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, ndmap=ndmap)
ndmap = ndmap0
else:
conn, coors, ngrps = tiled_mesh1d(conn, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps)
nblk *= gr
output('...done')
mat_ids = nm.tile(mat_ids, (nrep,))
mesh_out = Mesh.from_data('tiled mesh', coors * scale, ngrps,
[conn], [mat_ids], [mesh.descs[0]])
if ret_ndmap:
return mesh_out, ndmap
else:
return mesh_out
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder', verbose=True):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
dims : array of 5 floats
Dimensions of the cylinder: inner surface semi-axes a1, b1, outer
surface semi-axes a2, b2, length.
shape : array of 3 ints
Shape (counts of nodes in radial, circumferential and longitudinal
directions) of the cylinder mesh.
centre : array of 3 floats
Centre of the cylinder.
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
force_hollow : boolean
Force hollow mesh even if inner radii a1 = b1 = 0.
is_open : boolean
Generate an open cylinder segment.
open_angle : float
Opening angle in radians.
non_uniform : boolean
If True, space the mesh nodes in radial direction so that the element
volumes are (approximately) the same, making thus the elements towards
the outer surface thinner.
name : string
Mesh name.
verbose : bool
If True, show progress of the mesh generation.
Returns
-------
mesh : Mesh instance
"""
dims = nm.asarray(dims, dtype=nm.float64)
shape = nm.asarray(shape, dtype=nm.int32)
centre = nm.asarray(centre, dtype=nm.float64)
a1, b1, a2, b2, length = dims
nr, nfi, nl = shape
origin = centre - nm.array([0.5 * length, 0.0, 0.0])
dfi = 2.0 * (nm.pi - open_angle) / nfi
if is_open:
nnfi = nfi + 1
else:
nnfi = nfi
is_hollow = force_hollow or not (max(abs(a1), abs(b1)) < 1e-15)
if is_hollow:
mr = 0
else:
mr = (nnfi - 1) * nl
grid = nm.zeros((nr, nnfi, nl), dtype=nm.int32)
n_nod = nr * nnfi * nl - mr
coors = nm.zeros((n_nod, 3), dtype=nm.float64)
angles = nm.linspace(open_angle, open_angle+(nfi)*dfi, nfi+1)
xs = nm.linspace(0.0, length, nl)
if non_uniform:
ras = nm.zeros((nr,), dtype=nm.float64)
rbs = nm.zeros_like(ras)
advol = (a2**2 - a1**2) / (nr - 1)
bdvol = (b2**2 - b1**2) / (nr - 1)
ras[0], rbs[0] = a1, b1
for ii in range(1, nr):
ras[ii] = nm.sqrt(advol + ras[ii-1]**2)
rbs[ii] = nm.sqrt(bdvol + rbs[ii-1]**2)
else:
ras = nm.linspace(a1, a2, nr)
rbs = nm.linspace(b1, b2, nr)
# This is 3D only...
output('generating %d vertices...' % n_nod, verbose=verbose)
ii = 0
for ix in range(nr):
a, b = ras[ix], rbs[ix]
for iy, fi in enumerate(angles[:nnfi]):
for iz, x in enumerate(xs):
grid[ix,iy,iz] = ii
coors[ii] = origin + [x, a * nm.cos(fi), b * nm.sin(fi)]
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
assert_(ii == n_nod)
output('...done', verbose=verbose)
n_el = (nr - 1) * nfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
output('generating %d cells...' % n_el, verbose=verbose)
ii = 0
for (ix, iy, iz) in cycle([nr-1, nnfi, nl-1]):
if iy < (nnfi - 1):
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,iy+1,iz ], grid[ix ,iy+1,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,iy+1,iz+1], grid[ix ,iy+1,iz+1]]
ii += 1
elif not is_open:
conn[ii,:] = [grid[ix ,iy ,iz ], grid[ix+1,iy ,iz ],
grid[ix+1,0,iz ], grid[ix ,0,iz ],
grid[ix ,iy ,iz+1], grid[ix+1,iy ,iz+1],
grid[ix+1,0,iz+1], grid[ix ,0,iz+1]]
ii += 1
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
output('...done', verbose=verbose)
if axis == 'z':
coors = coors[:,[1,2,0]]
elif axis == 'y':
coors = coors[:,[2,0,1]]
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def create_expression_output(
expression,
name,
primary_field_name,
fields,
materials,
variables,
functions=None,
mode="eval",
term_mode=None,
extra_args=None,
verbose=True,
kwargs=None,
min_level=0,
max_level=1,
eps=1e-4,
):
"""
Create output mesh and data for the expression using the adaptive
linearizer.
Parameters
----------
expression : str
The expression to evaluate.
name : str
The name of the data.
primary_field_name : str
The name of field that defines the element groups and polynomial
spaces.
fields : dict
The dictionary of fields used in `variables`.
materials : Materials instance
The materials used in the expression.
variables : Variables instance
The variables used in the expression.
functions : Functions instance, optional
The user functions for materials etc.
mode : one of 'eval', 'el_avg', 'qp'
The evaluation mode - 'qp' requests the values in quadrature points,
'el_avg' element averages and 'eval' means integration over
each term region.
term_mode : str
The term call mode - some terms support different call modes
and depending on the call mode different values are
returned.
extra_args : dict, optional
Extra arguments to be passed to terms in the expression.
verbose : bool
If False, reduce verbosity.
kwargs : dict, optional
The variables (dictionary of (variable name) : (Variable
instance)) to be used in the expression.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
out : dict
The output dictionary.
"""
field = fields[primary_field_name]
vertex_coors = field.coors[: field.n_vertex_dof, :]
coors = []
vdofs = []
conns = []
mat_ids = []
levels = []
offset = 0
for ig, ap in field.aps.iteritems():
ps = ap.interp.poly_spaces["v"]
gps = ap.interp.gel.interp.poly_spaces["v"]
group = field.domain.groups[ig]
vertex_conn = ap.econn[:, : group.shape.n_ep]
eval_dofs = get_eval_expression(
expression,
ig,
fields,
materials,
variables,
functions=functions,
mode=mode,
extra_args=extra_args,
verbose=verbose,
kwargs=kwargs,
)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, _coors, conn, _vdofs, _mat_ids) = create_output(
eval_dofs, eval_coors, group.shape.n_el, ps, min_level=min_level, max_level=max_level, eps=eps
)
_mat_ids[:] = field.domain.mesh.mat_ids[ig][0]
coors.append(_coors)
vdofs.append(_vdofs)
conns.append(conn + offset)
mat_ids.append(_mat_ids)
levels.append(level)
offset += _coors.shape[0]
coors = nm.concatenate(coors, axis=0)
vdofs = nm.concatenate(vdofs, axis=0)
mesh = Mesh.from_data("linearized_mesh", coors, None, conns, mat_ids, field.domain.mesh.descs)
out = {}
out[name] = Struct(
name="output_data", mode="vertex", data=vdofs, var_name=name, dofs=None, mesh=mesh, levels=levels
)
out = convert_complex_output(out)
return out
def linearize(self, dofs, min_level=0, max_level=1, eps=1e-4):
"""
Linearize the solution for post-processing.
Parameters
----------
dofs : array, shape (n_nod, n_component)
The array of DOFs reshaped so that each column corresponds
to one component.
min_level : int
The minimum required level of mesh refinement.
max_level : int
The maximum level of mesh refinement.
eps : float
The relative tolerance parameter of mesh adaptivity.
Returns
-------
mesh : Mesh instance
The adapted, nonconforming, mesh.
vdofs : array
The DOFs defined in vertices of `mesh`.
levels : array of ints
The refinement level used for each element group.
"""
assert_(dofs.ndim == 2)
n_nod, dpn = dofs.shape
assert_(n_nod == self.n_nod)
assert_(dpn == self.shape[0])
vertex_coors = self.coors[:self.n_vertex_dof, :]
coors = []
vdofs = []
conns = []
mat_ids = []
levels = []
offset = 0
for ig, ap in self.aps.iteritems():
ps = ap.interp.poly_spaces['v']
gps = ap.interp.gel.interp.poly_spaces['v']
group = self.domain.groups[ig]
vertex_conn = ap.econn[:, :group.shape.n_ep]
eval_dofs = get_eval_dofs(dofs, ap.econn, ps, ori=ap.ori)
eval_coors = get_eval_coors(vertex_coors, vertex_conn, gps)
(level, _coors, conn,
_vdofs, _mat_ids) = create_output(eval_dofs, eval_coors,
group.shape.n_el, ps,
min_level=min_level,
max_level=max_level, eps=eps)
_mat_ids[:] = self.domain.mesh.mat_ids[ig][0]
coors.append(_coors)
vdofs.append(_vdofs)
conns.append(conn + offset)
mat_ids.append(_mat_ids)
levels.append(level)
offset += _coors.shape[0]
coors = nm.concatenate(coors, axis=0)
vdofs = nm.concatenate(vdofs, axis=0)
mesh = Mesh.from_data('linearized_mesh', coors, None, conns, mat_ids,
self.domain.mesh.descs)
return mesh, vdofs, levels
