def sensitivity(self, dp_var_data, state_ap, select=None):
"""
Sensitivity of objective function evaluation for given direct
and adjoint problem states.
"""
apb = self.apb
var_data = state_ap.get_parts()
var_data.update(dp_var_data)
self.ofg_equations.set_data(var_data, ignore_unknown=True)
dim = self.sp_boxes.dim
n_mesh_nod = apb.domain.shape.n_nod
if select is None:
idsgs = nm.arange(self.dsg_vars.n_dsg, dtype=nm.int32)
else:
idsgs = select
sa = []
pbar = MyBar('sensitivity:')
pbar.init(len(idsgs))
shape = (n_mesh_nod, dim)
for ii, nu in enumerate(self.generate_mesh_velocity(shape, idsgs)):
pbar.update(ii)
self.ofg_variables['Nu'].data_from_any(nu.ravel())
## from sfepy.base.ioutils import write_vtk
## cc = nla.norm( vec_nu )
## nun = nu / cc
## out = {'v' : Struct( mode = 'vertex', data = nun,
## ap_name = 'nic', dof_types = (0,1,2) )}
## fd = open( 'anim/pert_%03d.pvtk' % (ii+1), 'w' )
## write_vtk( fd, domain.mesh, out )
## fd.close()
## print ii
val = eval_equations(self.ofg_equations,
self.ofg_variables,
term_mode=1,
preserve_caches=True)
sa.append(val)
vec_sa = nm.array(sa, nm.float64)
return vec_sa
def sensitivity(self, dp_var_data, state_ap, select=None):
"""
Sensitivity of objective function evaluation for given direct
and adjoint problem states.
"""
apb = self.apb
var_data = state_ap.get_parts()
var_data.update(dp_var_data)
self.ofg_equations.set_data(var_data, ignore_unknown=True)
dim = self.sp_boxes.dim
n_mesh_nod = apb.domain.shape.n_nod
if select is None:
idsgs = nm.arange( self.dsg_vars.n_dsg, dtype = nm.int32 )
else:
idsgs = select
sa = []
pbar = MyBar('sensitivity:')
pbar.init(len(idsgs))
shape = (n_mesh_nod, dim)
for ii, nu in enumerate(self.generate_mesh_velocity(shape, idsgs)):
pbar.update(ii)
self.ofg_variables['Nu'].set_data(nu.ravel())
## from sfepy.base.ioutils import write_vtk
## cc = nla.norm( vec_nu )
## nun = nu / cc
## out = {'v' : Struct( mode = 'vertex', data = nun,
## ap_name = 'nic', dof_types = (0,1,2) )}
## fd = open( 'anim/pert_%03d.pvtk' % (ii+1), 'w' )
## write_vtk( fd, domain.mesh, out )
## fd.close()
## print ii
val = eval_equations(self.ofg_equations, self.ofg_variables,
term_mode=1, preserve_caches=True)
sa.append( val )
vec_sa = nm.array( sa, nm.float64 )
return vec_sa
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...
bar = MyBar(" nodes:", verbose=verbose)
bar.init(n_nod)
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)]
if not (ii % 100):
bar.update(ii)
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)
n_el = (nr - 1) * nnfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
bar = MyBar(" elements:", verbose=verbose)
bar.init(n_el)
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
if not (ii % 100):
bar.update(ii)
mat_id = nm.zeros((n_el, ), dtype=nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
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 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
bar = MyBar(" repeating:")
bar.init(nrep)
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,
mybar=(bar, nblk),
ndmap=ndmap)
ndmap = ndmap0
else:
conns, coors, ngrps = tiled_mesh1d(conns,
coors,
ngrps,
ii,
gr,
bbox.transpose()[ii],
eps=eps,
mybar=(bar, nblk))
nblk *= gr
bar.update(nblk)
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_block_mesh(dims, shape, centre, mat_id=0, name='block', 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]
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
grid = nm.zeros(shape, dtype=nm.int32)
n_nod = nm.prod(shape)
coors = nm.zeros((n_nod, dim), dtype=nm.float64)
bar = MyBar(" nodes:", verbose=verbose)
bar.init(n_nod)
for ii, ic in enumerate(cycle(shape)):
grid[tuple(ic)] = ii
coors[ii] = x0 + ic * dd
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
n_el = nm.prod(shape - 1)
mat_ids = nm.empty((n_el, ), dtype=nm.int32)
mat_ids.fill(mat_id)
if (dim == 2):
conn = nm.zeros((n_el, 4), dtype=nm.int32)
bar = MyBar(" elements:", verbose=verbose)
bar.init(n_el)
for ii, (ix, iy) in enumerate(cycle(shape - 1)):
conn[ii, :] = [
grid[ix, iy], grid[ix + 1, iy], grid[ix + 1, iy + 1],
grid[ix, iy + 1]
]
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype=nm.int32)
bar = MyBar(" elements:", verbose=verbose)
bar.init(n_el)
for ii, (ix, iy, iz) in enumerate(cycle(shape - 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]
]
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
desc = '3_8'
mesh = Mesh.from_data(name, coors, None, [conn], [mat_ids], [desc])
return mesh
def gen_block_mesh(dims, shape, centre, name='block'):
"""
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.
name : string
Mesh name.
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]
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
grid = nm.zeros(shape, dtype = nm.int32)
n_nod = nm.prod(shape)
coors = nm.zeros((n_nod, dim), dtype = nm.float64)
bar = MyBar(" nodes:")
bar.init(n_nod)
for ii, ic in enumerate(cycle(shape)):
grid[tuple(ic)] = ii
coors[ii] = x0 + ic * dd
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
n_el = nm.prod(shape - 1)
mat_id = nm.zeros((n_el,), dtype = nm.int32)
if (dim == 2):
conn = nm.zeros((n_el, 4), dtype = nm.int32)
bar = MyBar(" elements:")
bar.init(n_el)
for ii, (ix, iy) in enumerate(cycle(shape - 1)):
conn[ii,:] = [grid[ix ,iy], grid[ix+1,iy ],
grid[ix+1,iy+1], grid[ix ,iy+1]]
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
desc = '2_4'
else:
conn = nm.zeros((n_el, 8), dtype = nm.int32)
bar = MyBar(" elements:")
bar.init(n_el)
for ii, (ix, iy, iz) in enumerate(cycle(shape - 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]]
if not (ii % 100):
bar.update(ii)
bar.update(ii + 1)
desc = '3_8'
mesh = Mesh.from_data(name, coors, None, [conn], [mat_id], [desc])
return mesh
def gen_cylinder_mesh(dims, shape, centre, axis='x', force_hollow=False,
is_open=False, open_angle=0.0, non_uniform=False,
name='cylinder'):
"""
Generate a cylindrical mesh along an axis. Its cross-section can be
ellipsoidal.
Parameters
----------
axis: one of 'x', 'y', 'z'
The axis of the cylinder.
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.
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.
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...
bar = MyBar(" nodes:")
bar.init(n_nod)
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)]
if not (ii % 100):
bar.update(ii)
ii += 1
if not is_hollow and (ix == 0):
if iy > 0:
grid[ix,iy,iz] = grid[ix,0,iz]
ii -= 1
print
assert_(ii == n_nod)
n_el = (nr - 1) * nnfi * (nl - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
bar = MyBar(" elements:")
bar.init(n_el)
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
if not (ii % 100):
bar.update(ii)
print
mat_id = nm.zeros((n_el,), dtype = nm.int32)
desc = '3_8'
assert_(n_nod == (conn.max() + 1))
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 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
bar = MyBar(" repeating:")
bar.init(nrep)
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, mybar=(bar, nblk),
ndmap=ndmap)
ndmap = ndmap0
else:
conns, coors, ngrps = tiled_mesh1d(conns, coors, ngrps,
ii, gr, bbox.transpose()[ii],
eps=eps, mybar=(bar, nblk))
nblk *= gr
bar.update(nblk)
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 main():
parser = OptionParser(usage=usage, version="%prog")
parser.add_option(
"-o", "", metavar="filename", action="store", dest="output_filename", default="out.vtk", help=help["filename"]
)
parser.add_option(
"-d", "--dims", metavar="dims", action="store", dest="dims", default="[1.0, 1.0, 1.0]", help=help["dims"]
)
parser.add_option(
"-s", "--shape", metavar="shape", action="store", dest="shape", default="[11, 11, 11]", help=help["shape"]
)
parser.add_option(
"-c",
"--centre",
metavar="centre",
action="store",
dest="centre",
default="[0.0, 0.0, 0.0]",
help=help["centre"],
)
(options, args) = parser.parse_args()
dims = eval("nm.array( %s, dtype = nm.float64 )" % options.dims)
shape = eval("nm.array( %s, dtype = nm.int32 )" % options.shape)
centre = eval("nm.array( %s, dtype = nm.float64 )" % options.centre)
print dims
print shape
print centre
dim = shape.shape[0]
x0 = centre - 0.5 * dims
dd = dims / (shape - 1)
grid = nm.zeros(shape, dtype=nm.float64)
n_nod = nm.prod(shape)
coors = nm.zeros((n_nod, dim + 1), dtype=nm.float64)
# This is 3D only...
bar = MyBar(" nodes:")
bar.init(n_nod)
for ii, ic in enumerate(cycle(shape)):
ix, iy, iz = ic
grid[ix, iy, iz] = ii
coors[ii, :-1] = x0 + ic * dd
if not (ii % 100):
bar.update(ii)
print
n_el = nm.prod(shape - 1)
conn = nm.zeros((n_el, 8), dtype=nm.int32)
bar = MyBar(" elements:")
bar.init(n_el)
for ii, (ix, iy, iz) in enumerate(cycle(shape - 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],
]
if not (ii % 100):
bar.update(ii)
print
mat_id = nm.zeros((n_el,), dtype=nm.int32)
desc = "3_8"
mesh = Mesh.from_data(options.output_filename, coors, [conn], [mat_id], [desc])
mesh.write(options.output_filename, io="auto")