def from_conf(conf, options):
from sfepy.discrete.fem.geometry_element import GeometryElement
gels = {}
for key in ['2_3', '2_4', '3_4', '3_8']:
gel = GeometryElement(key)
gel.create_surface_facet()
gels[key] = gel
return Test(conf=conf, options=options, gels=gels)
def from_conf(conf, options):
from sfepy.discrete.fem.geometry_element import GeometryElement
gels = {}
for key in ['2_3', '2_4', '3_4', '3_8']:
gel = GeometryElement(key)
gel.create_surface_facet()
gels[key] = gel
return Test(conf=conf, options=options, gels=gels)
def from_conf(conf, options):
from sfepy.discrete.fem.geometry_element import GeometryElement
gels = {}
gel_names = ["2_4", "3_8"]
for key in gel_names:
gel = GeometryElement(key)
gel.create_surface_facet()
gels[key] = gel
return Test(conf=conf, options=options, gel_names=gel_names, gels=gels)
def _get_bqp(geometry, order):
from sfepy.discrete import Integral
from sfepy.discrete.fem.geometry_element import GeometryElement
from sfepy.discrete.fem import Mesh, FEDomain, Field
gel = GeometryElement(geometry)
mesh = Mesh.from_data('aux', gel.coors, None, [gel.conn[None, :]], [[0]],
[geometry])
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
surf = domain.create_region('Surf', 'vertices of surface', 'facet')
field = Field.from_args('f',
nm.float64,
shape=1,
region=omega,
approx_order=1)
field.setup_surface_data(surf)
integral = Integral('aux', order=order)
field.create_bqp('Surf', integral)
sd = field.surface_data['Surf']
qp = field.qp_coors[(integral.order, sd.bkey)]
output('geometry:', geometry, 'order:', order, 'num. points:',
qp.vals.shape[1], 'true_order:',
integral.qps[gel.surface_facet_name].order)
output('min. weight:', qp.weights.min())
output('max. weight:', qp.weights.max())
return (gel, qp.vals.reshape(
(-1, mesh.dim)), nm.tile(qp.weights, qp.vals.shape[0]))
def plot_control_mesh(ax, control_points, label=False):
"""
Plot the control mesh of a NURBS given by its control points.
"""
dim = control_points.shape[-1]
ax = _get_axes(ax, dim)
shape = control_points.shape
conn, desc = get_tensor_product_conn(nm.array(shape[:-1]))
gel = GeometryElement(desc)
coors = control_points.reshape((-1, dim))
ax = pd.plot_mesh(ax, coors, conn, gel.edges)
pd.plot_points(ax, coors)
if label:
for ii, cc in enumerate(coors):
if dim == 3:
cx, cy, cz = cc
ax.text(cx, cy, cz, '%d' % ii,
color='g', fontsize=12, weight='bold')
else:
cx, cy = cc
ax.text(cx, cy, '%d' % ii,
color='g', fontsize=12, weight='bold')
return ax
def _get_qp(geometry, order):
from sfepy.discrete import Integral
from sfepy.discrete.fem.geometry_element import GeometryElement
aux = Integral('aux', order=order)
coors, weights = aux.get_qp(geometry)
true_order = aux.qps[geometry].order
output('geometry:', geometry, 'order:', order, 'num. points:',
coors.shape[0], 'true_order:', true_order)
output('min. weight:', weights.min())
output('max. weight:', weights.max())
return GeometryElement(geometry), coors, weights
def plot_parametric_mesh(ax, knots):
"""
Plot the parametric mesh of a NURBS given by its knots.
"""
knots = _get_knots_tuple(knots)
dim = len(knots)
ax = _get_axes(ax, dim)
uknots = [nm.unique(ii) for ii in knots]
shape = [len(ii) for ii in uknots]
ngrid = nm.mgrid[[slice(ii) for ii in shape]]
coors = nm.r_[[uknots[ii][ig].ravel() for ii, ig in enumerate(ngrid)]].T
conn, desc = get_tensor_product_conn(nm.array(shape))
gel = GeometryElement(desc)
ax = pd.plot_mesh(ax, coors, conn, gel.edges)
pd.plot_points(ax, coors)
return ax
def save_basis_on_mesh(mesh, options, output_dir, lin,
permutations=None, suffix=''):
if permutations is not None:
mesh = mesh.copy()
gel = GeometryElement(mesh.descs[0])
perms = gel.get_conn_permutations()[permutations]
conn = mesh.cmesh.get_cell_conn()
n_el, n_ep = conn.num, gel.n_vertex
offsets = nm.arange(n_el) * n_ep
conn.indices[:] = conn.indices.take((perms + offsets[:, None]).ravel())
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field = Field.from_args('f', nm.float64, shape=1, region=omega,
approx_order=options.max_order,
poly_space_base=options.basis)
var = FieldVariable('u', 'unknown', field)
if options.plot_dofs:
import sfepy.postprocess.plot_dofs as pd
import sfepy.postprocess.plot_cmesh as pc
ax = pc.plot_wireframe(None, mesh.cmesh)
ax = pd.plot_global_dofs(ax, field.get_coor(), field.econn)
ax = pd.plot_local_dofs(ax, field.get_coor(), field.econn)
if options.dofs is not None:
ax = pd.plot_nodes(ax, field.get_coor(), field.econn,
field.poly_space.nodes,
get_dofs(options.dofs, var.n_dof))
pd.plt.show()
output('dofs: %d' % var.n_dof)
vec = nm.empty(var.n_dof, dtype=var.dtype)
n_digit, _format = get_print_info(var.n_dof, fill='0')
name_template = os.path.join(output_dir,
'dof_%s%s.vtk' % (_format, suffix))
for ip in get_dofs(options.dofs, var.n_dof):
output('dof %d...' % ip)
vec.fill(0.0)
vec[ip] = 1.0
var.set_data(vec)
if options.derivative == 0:
out = var.create_output(vec, linearization=lin)
else:
out = create_expression_output('ev_grad.ie.Elements(u)',
'u', 'f', {'f' : field}, None,
Variables([var]),
mode='qp', verbose=False,
min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
name = name_template % ip
ensure_path(name)
out['u'].mesh.write(name, out=out)
output('...done (%s)' % name)
def main():
parser = OptionParser(usage=usage, version='%prog')
parser.add_option('-b', '--basis', metavar='name',
action='store', dest='basis',
default='lagrange', help=help['basis'])
parser.add_option('-d', '--derivative', metavar='d', type=int,
action='store', dest='derivative',
default=0, help=help['derivative'])
parser.add_option('-n', '--max-order', metavar='order', type=int,
action='store', dest='max_order',
default=2, help=help['max_order'])
parser.add_option('-g', '--geometry', metavar='name',
action='store', dest='geometry',
default='2_4', help=help['geometry'])
parser.add_option('-m', '--mesh', metavar='mesh',
action='store', dest='mesh',
default=None, help=help['mesh'])
parser.add_option('', '--permutations', metavar='permutations',
action='store', dest='permutations',
default=None, help=help['permutations'])
parser.add_option('', '--dofs', metavar='dofs',
action='store', dest='dofs',
default=None, help=help['dofs'])
parser.add_option('-l', '--lin-options', metavar='options',
action='store', dest='lin_options',
default='min_level=2,max_level=5,eps=1e-3',
help=help['lin_options'])
parser.add_option('', '--plot-dofs',
action='store_true', dest='plot_dofs',
default=False, help=help['plot_dofs'])
options, args = parser.parse_args()
if len(args) == 1:
output_dir = args[0]
else:
parser.print_help(),
return
output('polynomial space:', options.basis)
output('max. order:', options.max_order)
lin = Struct(kind='adaptive', min_level=2, max_level=5, eps=1e-3)
for opt in options.lin_options.split(','):
key, val = opt.split('=')
setattr(lin, key, eval(val))
if options.mesh is None:
dim, n_ep = int(options.geometry[0]), int(options.geometry[2])
output('reference element geometry:')
output(' dimension: %d, vertices: %d' % (dim, n_ep))
gel = GeometryElement(options.geometry)
gps = PolySpace.any_from_args(None, gel, 1,
base=options.basis)
ps = PolySpace.any_from_args(None, gel, options.max_order,
base=options.basis)
n_digit, _format = get_print_info(ps.n_nod, fill='0')
name_template = os.path.join(output_dir, 'bf_%s.vtk' % _format)
for ip in get_dofs(options.dofs, ps.n_nod):
output('shape function %d...' % ip)
def eval_dofs(iels, rx):
if options.derivative == 0:
bf = ps.eval_base(rx).squeeze()
rvals = bf[None, :, ip:ip+1]
else:
bfg = ps.eval_base(rx, diff=True)
rvals = bfg[None, ..., ip]
return rvals
def eval_coors(iels, rx):
bf = gps.eval_base(rx).squeeze()
coors = nm.dot(bf, gel.coors)[None, ...]
return coors
(level, coors, conn,
vdofs, mat_ids) = create_output(eval_dofs, eval_coors, 1,
ps, min_level=lin.min_level,
max_level=lin.max_level,
eps=lin.eps)
out = {
'bf' : Struct(name='output_data',
mode='vertex', data=vdofs,
var_name='bf', dofs=None)
}
mesh = Mesh.from_data('bf_mesh', coors, None, [conn], [mat_ids],
[options.geometry])
name = name_template % ip
ensure_path(name)
mesh.write(name, out=out)
output('...done (%s)' % name)
else:
mesh = Mesh.from_file(options.mesh)
output('mesh geometry:')
output(' dimension: %d, vertices: %d, elements: %d'
% (mesh.dim, mesh.n_nod, mesh.n_el))
if options.permutations:
if options.permutations == 'all':
from sfepy.linalg import cycle
gel = GeometryElement(mesh.descs[0])
n_perms = gel.get_conn_permutations().shape[0]
all_permutations = [ii for ii in cycle(mesh.n_el * [n_perms])]
else:
all_permutations = [int(ii)
for ii in options.permutations.split(',')]
all_permutations = nm.array(all_permutations)
np = len(all_permutations)
all_permutations.shape = (np / mesh.n_el, mesh.n_el)
output('using connectivity permutations:\n', all_permutations)
else:
all_permutations = [None]
for ip, permutations in enumerate(all_permutations):
if permutations is None:
suffix = ''
else:
suffix = '_' + '_'.join('%d' % ii for ii in permutations)
save_basis_on_mesh(mesh, options, output_dir, lin, permutations,
suffix)
p01 = c0 - plength * ps[0]
p10 = c0 + plength * ps[1]
p11 = c0 - plength * ps[1]
arr = plt3.art3d.Poly3DCollection([[p00, p01, c1], [p10, p11, c1]],
color=color)
ax.add_collection3d(arr)
if __name__ == '__main__':
from sfepy.discrete.fem.geometry_element import (GeometryElement,
geometry_data)
for key, gd in six.iteritems(geometry_data):
if key == '1_2': continue
gel = GeometryElement(key)
ax = plot_geometry(None, gel)
ax = plot_edges(ax, gel, length=0.2)
ax = plot_faces(ax, gel, radius=0.3, n_point=5)
dd = 0.05
ax.set_xlim([-dd, 1.0 + dd])
ax.set_ylim([-dd, 1.0 + dd])
if gel.dim == 3:
ax.set_zlim([-dd, 1.0 + dd])
plt.show()