"""
Computational domain, consisting of the mesh and regions.
"""
import time
import re
import numpy as nm
from sfepy.base.base import output, assert_, OneTypeList, Struct
from sfepy.fem.facets import Facets
from geometry_element import GeometryElement
from region import Region, get_dependency_graph, sort_by_dependency, get_parents
from sfepy.fem.parseReg import create_bnf, visit_stack, ParseException
from sfepy.fem.refine import refine_2_3, refine_2_4, refine_3_4, refine_3_8
from sfepy.fem.fe_surface import FESurface
import fea
[docs]def region_leaf(domain, regions, rdef, functions):
"""
Create/setup a region instance according to rdef.
"""
def _region_leaf(level, op):
token, details = op['token'], op['orig']
if token != 'KW_Region':
parse_def = token + '<' + ' '.join(details) + '>'
region = Region('leaf', rdef, domain, parse_def=parse_def)
if token == 'KW_Region':
details = details[1][2:]
aux = regions.find(details)
if not aux:
raise ValueError, 'region %s does not exist' % details
else:
if rdef[:4] == 'copy':
region = aux.copy()
else:
region = aux
elif token == 'KW_All':
region.set_vertices(nm.arange(domain.mesh.n_nod, dtype=nm.int32))
elif token == 'E_NIR':
where = details[2]
if where[0] == '[':
out = nm.array(eval(where), dtype=nm.int32)
assert_(nm.amin(out) >= 0)
assert_(nm.amax(out) < domain.mesh.n_nod)
else:
coors = domain.get_mesh_coors()
x = coors[:,0]
y = coors[:,1]
if domain.mesh.dim == 3:
z = coors[:,2]
else:
z = None
coor_dict = {'x' : x, 'y' : y, 'z': z}
out = nm.where(eval(where, {}, coor_dict))[0]
region.set_vertices(out)
elif token == 'E_NOS':
if domain.fa: # 3D.
fa = domain.fa
else:
fa = domain.ed
flag = fa.mark_surface_facets()
ii = nm.where(flag > 0)[0]
aux = nm.unique(fa.facets[ii])
if aux[0] == -1: # Triangular faces have -1 as 4. point.
aux = aux[1:]
region.can_cells = False
region.set_vertices(aux)
elif token == 'E_NBF':
where = details[2]
coors = domain.get_mesh_coors()
fun = functions[where]
out = fun(coors, domain=domain)
region.set_vertices(out)
elif token == 'E_EBF':
where = details[2]
coors = domain.get_mesh_coors()
fun = functions[where]
out = fun(coors, domain=domain)
region.set_cells(out)
elif token == 'E_EOG':
group = int(details[3])
ig = domain.mat_ids_to_i_gs[group]
group = domain.groups[ig]
region.set_from_group(ig, group.vertices, group.shape.n_el)
elif token == 'E_EOSET':
raise NotImplementedError('element sets not implemented!')
elif token == 'E_NOG':
group = int(details[3])
group_nodes = nm.where(domain.mesh.ngroups == group)[0]
region.set_vertices(group_nodes)
elif token == 'E_NOSET':
try:
set_nodes = domain.mesh.nodal_bcs[details[3]]
except KeyError:
msg = 'undefined nodal set! (%s)' % details[3]
raise ValueError(msg)
region.set_vertices(set_nodes)
elif token == 'E_ONIR':
aux = regions[details[3][2:]]
region.set_vertices(aux.all_vertices[0:1])
elif token == 'E_NI':
region.set_vertices(nm.array([int(ii) for ii in details[1:]],
dtype=nm.int32))
elif token == 'E_EI1':
region.set_cells({0 : nm.array([int(ii) for ii in details[1:]],
dtype=nm.int32)})
elif token == 'E_EI2':
num = len(details[1:]) / 2
cells = {}
for ii in range(num):
ig, iel = int(details[1+2*ii]), int(details[2+2*ii])
cells.setdefault(ig, []).append(iel)
region.set_cells(cells)
else:
output('token "%s" unkown - check regions!' % token)
raise NotImplementedError
return region
return _region_leaf
[docs]def region_op(level, op, item1, item2):
token = op['token']
if token == 'OA_SubN':
return item1.sub_n(item2)
elif token == 'OA_SubE':
return item1.sub_e(item2)
elif token == 'OA_AddN':
return item1.add_n(item2)
elif token == 'OA_AddE':
return item1.add_e(item2)
elif token == 'OA_IntersectN':
return item1.intersect_n(item2)
elif token == 'OA_IntersectE':
return item1.intersect_e(item2)
else:
raise NotImplementedError, token
[docs]class Domain(Struct):
"""
Domain is divided into groups, whose purpose is to have homogeneous
data shapes.
"""
def __init__(self, name, mesh, verbose=False):
"""Create a Domain.
Parameters
----------
name : str
Object name.
mesh : Mesh
A mesh defining the domain.
"""
geom_els = {}
for ig, desc in enumerate(mesh.descs):
gel = GeometryElement(desc)
# Create geometry elements of dimension - 1.
gel.create_surface_facet()
geom_els[desc] = gel
interps = {}
for gel in geom_els.itervalues():
key = gel.get_interpolation_name()
gel.interp = interps.setdefault(key, fea.Interpolant(key, gel))
gel = gel.surface_facet
if gel is not None:
key = gel.get_interpolation_name()
gel.interp = interps.setdefault(key, fea.Interpolant(key, gel))
Struct.__init__(self, name=name, mesh=mesh, geom_els=geom_els,
geom_interps=interps)
self.mat_ids_to_i_gs = {}
for ig, mat_id in enumerate(mesh.mat_ids):
self.mat_ids_to_i_gs[mat_id[0]] = ig
self.setup_groups()
self.fix_element_orientation()
self.setup_facets(verbose=verbose)
self.reset_regions()
self.clear_surface_groups()
[docs] def setup_groups(self):
n_nod, dim = self.mesh.coors.shape
self.shape = Struct(n_gr=len(self.mesh.conns), n_el=0,
n_nod=n_nod, dim=dim)
self.groups = {}
for ii in range(self.shape.n_gr):
gel = self.geom_els[self.mesh.descs[ii]] # Shortcut.
conn = self.mesh.conns[ii]
vertices = nm.unique(conn)
n_vertex = vertices.shape[0]
n_el, n_ep = conn.shape
n_edge = gel.n_edge
n_edge_total = n_edge * n_el
if gel.dim == 3:
n_face = gel.n_face
n_face_total = n_face * n_el
else:
n_face = n_face_total = 0
shape = Struct(n_vertex=n_vertex, n_el=n_el, n_ep=n_ep,
n_edge=n_edge, n_edge_total=n_edge_total,
n_face=n_face, n_face_total=n_face_total,
dim=self.mesh.dims[ii])
self.groups[ii] = Struct(ig=ii, vertices=vertices, conn=conn,
gel=gel, shape=shape)
self.shape.n_el += n_el
[docs] def iter_groups(self, igs=None):
if igs is None:
for ig in xrange(self.shape.n_gr): # sorted by ig.
yield self.groups[ig]
else:
for ig in igs:
yield ig, self.groups[ig]
[docs] def get_cell_offsets(self):
offs = {}
off = 0
for group in self.iter_groups():
ig = group.ig
offs[ig] = off
off += group.shape.n_el
return offs
[docs] def get_mesh_coors(self, actual=False):
"""
Return the coordinates of the underlying mesh vertices.
"""
if actual and hasattr(self.mesh, 'coors_act'):
return self.mesh.coors_act
else:
return self.mesh.coors
[docs] def get_mesh_bounding_box(self):
"""
Return the bounding box of the underlying mesh.
Returns
-------
bbox : ndarray (2, dim)
The bounding box with min. values in the first row and max. values
in the second row.
"""
return self.mesh.get_bounding_box()
[docs] def get_diameter(self):
"""
Return the diameter of the domain.
Notes
-----
The diameter corresponds to the Friedrichs constant.
"""
bbox = self.get_mesh_bounding_box()
return (bbox[1,:] - bbox[0,:]).max()
[docs] def get_conns(self):
"""
Return the element connectivity groups of the underlying mesh.
"""
return self.mesh.conns
[docs] def fix_element_orientation(self):
"""
Ensure element nodes ordering giving positive element volume.
The groups with elements of lower dimension than the space dimension
are skipped.
"""
from extmods.mesh import orient_elements
coors = self.mesh.coors
for ii, group in self.groups.iteritems():
if group.shape.dim < self.shape.dim: continue
ori, conn = group.gel.orientation, group.conn
itry = 0
while itry < 2:
flag = -nm.ones(conn.shape[0], dtype=nm.int32)
# Changes orientation if it is wrong according to swap*!
# Changes are indicated by positive flag.
orient_elements(flag, conn, coors,
ori.roots, ori.vecs,
ori.swap_from, ori.swap_to)
if nm.alltrue(flag == 0):
if itry > 0: output('...corrected')
itry = -1
break
output('warning: bad element orientation, trying to correct...')
itry += 1
if itry == 2 and flag[0] != -1:
raise RuntimeError('elements cannot be oriented! (%d, %s)'
% (ii, self.mesh.descs[ii]))
elif flag[0] == -1:
output('warning: element orienation not checked')
[docs] def has_faces(self):
return sum([group.shape.n_face
for group in self.iter_groups()]) > 0
[docs] def setup_facets(self, create_edges=True, create_faces=True,
verbose=False):
"""
Setup the edges and faces (in 3D) of domain elements.
"""
kinds = ['edges', 'faces']
is_face = self.has_faces()
create = [create_edges, create_faces and is_face]
for ii, kind in enumerate(kinds):
if create[ii]:
if verbose:
output('setting up domain %s...' % kind)
tt = time.clock()
obj = Facets.from_domain(self, kind)
obj.sort_and_orient()
obj.setup_unique()
obj.setup_neighbours()
# 'ed' or 'fa'
setattr(self, kind[:2], obj)
if verbose:
output('...done in %.2f s' % (time.clock() - tt))
if not is_face:
self.fa = None
[docs] def get_facets(self, force_faces=False):
"""
Return edge and face descriptions.
"""
if force_faces and not self.fa:
return self.ed, self.ed
else:
return self.ed, self.fa
[docs] def reset_regions(self):
"""
Reset the list of regions associated with the domain.
"""
self.regions = OneTypeList(Region)
self._region_stack = []
self._bnf = create_bnf(self._region_stack)
[docs] def create_region(self, name, select, flags=None, check_parents=True,
functions=None, add_to_regions=True):
"""
Region factory constructor. Append the new region to
self.regions list.
"""
if flags is None:
flags = {}
if check_parents:
parents = get_parents(select)
for p in parents:
if p not in [region.name for region in self.regions]:
msg = 'parent region %s of %s not found!' % (p, name)
raise ValueError(msg)
stack = self._region_stack
try:
self._bnf.parseString(select)
except ParseException:
print 'parsing failed:', select
raise
region = visit_stack(stack, region_op,
region_leaf(self, self.regions, select,
functions))
region.name = name
forbid = flags.get('forbid', None)
if forbid:
fb = re.compile('^group +\d+(\s+\d+)*$').match(forbid)
if fb:
groups = forbid[5:].strip().split()
forbid = [int(ii) for ii in groups]
else:
raise ValueError('bad forbid! (%s)' % forbid)
forbidden_igs = [self.mat_ids_to_i_gs[mat_id] for mat_id in forbid]
region.delete_groups(forbidden_igs)
region.switch_cells(flags.get('can_cells', True))
region.complete_description(self.ed, self.fa)
if add_to_regions:
self.regions.append(region)
return region
[docs] def create_regions(self, region_defs, functions=None):
output('creating regions...')
tt = time.clock()
self.reset_regions()
##
# Sort region definitions by dependencies.
graph, name_to_sort_name = get_dependency_graph(region_defs)
sorted_regions = sort_by_dependency(graph)
##
# Define regions.
for name in sorted_regions:
sort_name = name_to_sort_name[name]
rdef = region_defs[sort_name]
region = self.create_region(name, rdef.select,
flags=rdef,
check_parents=False,
functions=functions)
output(' ', region.name)
output('...done in %.2f s' % (time.clock() - tt))
return self.regions
[docs] def save_regions(self, filename, region_names=None):
"""
Save regions as individual meshes.
Parameters
----------
filename : str
The output filename.
region_names : list, optional
If given, only the listed regions are saved.
"""
import os
if region_names is None:
region_names = self.regions.get_names()
trunk, suffix = os.path.splitext(filename)
output('saving regions...')
for name in region_names:
region = self.regions[name]
output(name)
aux = self.mesh.from_region(region, self.mesh)
aux.write('%s_%s%s' % (trunk, region.name, suffix),
io='auto')
output('...done')
[docs] def save_regions_as_groups(self, filename, region_names=None):
"""
Save regions in a single mesh but mark them by using different
element/node group numbers.
If regions overlap, the result is undetermined, with exception of the
whole domain region, which is marked by group id 0.
Region masks are also saved as scalar point data for output formats
that support this.
Parameters
----------
filename : str
The output filename.
region_names : list, optional
If given, only the listed regions are saved.
"""
output('saving regions as groups...')
aux = self.mesh.copy()
n_ig = c_ig = 0
n_nod = self.shape.n_nod
# The whole domain region should go first.
names = (region_names if region_names is not None
else self.regions.get_names())
for name in names:
region = self.regions[name]
if region.all_vertices.shape[0] == n_nod:
names.remove(region.name)
names = [region.name] + names
break
out = {}
for name in names:
region = self.regions[name]
output(region.name)
aux.ngroups[region.all_vertices] = n_ig
n_ig += 1
mask = nm.zeros((n_nod, 1), dtype=nm.float64)
mask[region.all_vertices] = 1.0
out[name] = Struct(name='region', mode='vertex', data=mask,
var_name=name, dofs=None)
if region.has_cells():
for ig in region.igs:
if not region.true_cells[ig]: continue
ii = region.get_cells(ig)
aux.mat_ids[ig][ii] = c_ig
c_ig += 1
aux.write(filename, io='auto', out=out)
output('...done')
[docs] def get_element_diameters(self, ig, cells, vg, mode, square=True):
group = self.groups[ig]
diameters = nm.empty((len(cells), 1, 1, 1), dtype=nm.float64)
if vg is None:
diameters.fill(1.0)
else:
vg.get_element_diameters(diameters, group.gel.edges,
self.get_mesh_coors().copy(), group.conn,
cells, mode)
if square:
out = diameters.squeeze()
else:
out = nm.sqrt(diameters.squeeze())
return out
[docs] def surface_faces(self):
if not self.fa:
raise ValueError("no faces defined!")
fa = self.fa
flag = fa.mark_surface_facets()
surf_faces = []
itri = nm.where(flag == 3)[0]
if itri.size:
surf_faces.append(fa.facets[itri,:3])
itet = nm.where(flag == 4)[0]
if itet.size:
surf_faces.append(fa.facets[itet,:4])
isurf = nm.where(flag >= 1)[0]
if isurf.size:
lst = fa.indices[isurf]
return lst, surf_faces
[docs] def clear_surface_groups(self):
"""
Remove surface group data.
"""
self.surface_groups = {}
[docs] def create_surface_group(self, region):
"""
Create a new surface group corresponding to `region` if it does
not exist yet.
Notes
-----
Surface groups define surface facet connectivity that is needed
for :class:`sfepy.fem.mappings.SurfaceMapping`.
"""
for ig in region.igs:
groups = self.surface_groups.setdefault(ig, {})
if region.name not in groups:
region.select_cells_of_surface(reset=False)
group = self.groups[ig]
gel_faces = group.gel.get_surface_entities()
name = 'surface_group_%s_%d' % (region.name, ig)
surface_group = FESurface(name, region, gel_faces,
group.conn, ig)
groups[region.name] = surface_group
[docs] def refine(self):
"""
Uniformly refine the domain mesh.
Returns
-------
domain : Domain instance
The new domain with the refined mesh.
Notes
-----
Works only for meshes with single element type! Does not
preserve node groups!
"""
names = set()
for group in self.groups.itervalues():
names.add(group.gel.name)
if len(names) != 1:
msg = 'refine() works only for meshes with single element type!'
raise NotImplementedError(msg)
el_type = names.pop()
if el_type == '2_3':
mesh = refine_2_3(self.mesh, self.ed)
elif el_type == '2_4':
mesh = refine_2_4(self.mesh, self.ed)
elif el_type == '3_4':
mesh = refine_3_4(self.mesh, self.ed)
elif el_type == '3_8':
mesh = refine_3_8(self.mesh, self.ed, self.fa)
else:
msg = 'unsupported element type! (%s)' % el_type
raise NotImplementedError(msg)
domain = Domain(self.name + '_r', mesh)
return domain
