def get_coors(self, ig=None):
"""
Get the coordinates of vertices of unique facets in group `ig`.
Parameters
----------
ig : int, optional
The element group. If None, the coordinates for all groups
are returned, filled with zeros at places of missing
vertices, i.e. where facets having less then the full number
of vertices (`n_v`) are.
Returns
-------
coors : array
The coordinates in an array of shape `(n_f, n_v, dim)`.
uid : array
The unique ids of facets in the order of `coors`.
"""
cc = self.domain.get_mesh_coors()
if ig is None:
uid, ii = unique(self.uid_i, return_index=True)
facets = self.facets[ii]
aux = insert_strided_axis(facets, 2, cc.shape[1])
coors = nm.where(aux >= 0, cc[facets], 0.0)
else:
uid_i = self.uid_i[self.indx[ig]]
uid, ii = unique(uid_i, return_index=True)
coors = cc[self.facets[ii, :self.n_fps[ig]]]
return coors, uid
def get_coors(self, ig=None):
"""
Get the coordinates of vertices of unique facets in group `ig`.
Parameters
----------
ig : int, optional
The element group. If None, the coordinates for all groups
are returned, filled with zeros at places of missing
vertices, i.e. where facets having less then the full number
of vertices (`n_v`) are.
Returns
-------
coors : array
The coordinates in an array of shape `(n_f, n_v, dim)`.
uid : array
The unique ids of facets in the order of `coors`.
"""
cc = self.domain.get_mesh_coors()
if ig is None:
uid, ii = unique(self.uid_i, return_index=True)
facets = self.facets[ii]
aux = insert_strided_axis(facets, 2, cc.shape[1])
coors = nm.where(aux >= 0, cc[facets], 0.0)
else:
uid_i = self.uid_i[self.indx[ig]]
uid, ii = unique(uid_i, return_index=True)
coors = cc[self.facets[ii,:self.n_fps[ig]]]
return coors, uid
def treat_pbcs(self, master_equations):
"""
Treat dofs with periodic BC.
"""
umeq, indx = unique(master_equations, return_index=True)
indx.sort()
self.mtx = self.mtx[indx]
def treat_pbcs(self, master_equations):
"""
Treat dofs with periodic BC.
"""
umeq, indx = unique(master_equations, return_index=True)
indx.sort()
self.mtx = self.mtx[indx]
def get_coors(self, ig=0):
"""
Get the coordinates of vertices of unique facets in group `ig`.
Returns
-------
coors : array
The coordinates in an array of shape `(n_f, n_v, dim)`.
uid : array
The unique ids of facets in the order of `coors`.
"""
cc = self.domain.get_mesh_coors()
uid_i = self.uid_i[self.indx[ig]]
uid, ii = unique(uid_i, return_index=True)
coors = cc[self.facets[ii,:self.n_fps[ig]]]
return coors, uid
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:, self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1], ), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:, 0] = e_id
conn[:, 1] = ee[:, 0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:, 3] = ee[:, 1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:, [2, 1, 3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:, 1] - cc[:, 0]
v2 = cc[:, 2] - cc[:, 0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:, None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None, :]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:, 0] = gel.n_vertex
rconn[:, 1] = gel.edges[:, 0]
rconn[:, 2] = gel.edges[:, 1]
map_er_ed = VolumeMapping(cc, rconn, gel=gel)
# Prepare mapping from reference triangle e_R to a
# physical triangle e.
map_er_e = SurfaceMapping(dual_coors, tri_conn, gel=gel)
# Compute triangle basis (edge) vectors.
nn = surface.nodes[ueo]
edge_coors = mesh_coors[nn]
edge_centre_coors = 0.5 * edge_coors.sum(axis=1)
edge_normals = 0.5 * nodal_normals[ueo].sum(axis=1)
edge_normals /= la.norm_l2_along_axis(edge_normals)[:, None]
nn = surface.nodes[ueo]
edge_dirs = edge_coors[:, 1] - edge_coors[:, 0]
edge_dirs /= la.norm_l2_along_axis(edge_dirs)[:, None]
edge_ortho = nm.cross(edge_normals, edge_dirs)
edge_ortho /= la.norm_l2_along_axis(edge_ortho)[:, None]
# Primary face - dual sub-faces map.
# i-th row: indices to conn corresponding to sub-faces of i-th face.
face_map = nm.arange(n_fa * n_edge, dtype=nm.int32)
face_map.shape = (n_fa, n_edge)
# The actual connectivity for assembling (unique nodes per master
# faces).
asm_conn = e_id[face_map]
n_nod = ueo.shape[0] # One node per unique edge.
n_components = self.dim - 1
dual_surface = Struct(name='dual_surface_description',
dim=self.dim,
n_dual_fa=conn.shape[0],
n_dual_fp=self.dim,
n_fa=n_fa,
n_edge=n_edge,
n_nod=n_nod,
n_components=n_components,
n_dof=n_nod * n_components,
dual_coors=dual_coors,
coor_offset=coor_offset,
e_sort=e_sort,
conn=conn,
tri_conn=tri_conn,
map_er_e=map_er_e,
map_er_ed=map_er_ed,
face_map=face_map,
asm_conn=asm_conn,
nodal_normals=nodal_normals,
edge_centre_coors=edge_centre_coors,
edge_normals=edge_normals,
edge_dirs=edge_dirs,
edge_ortho=edge_ortho)
return dual_surface
def describe_dual_surface(self, surface):
n_fa, n_edge = surface.n_fa, self.sgel.n_edge
mesh_coors = self.mesh_coors
# Face centres.
fcoors = mesh_coors[surface.econn]
centre_coors = nm.dot(self.bf.squeeze(), fcoors)
surface_coors = mesh_coors[surface.nodes]
dual_coors = nm.r_[surface_coors, centre_coors]
coor_offset = surface.nodes.shape[0]
# Normals in primary mesh nodes.
nodal_normals = compute_nodal_normals(surface.nodes, self.region,
self.field)
ee = surface.leconn[:,self.sgel.edges].copy()
edges_per_face = ee.copy()
sh = edges_per_face.shape
ee.shape = edges_per_face.shape = (sh[0] * sh[1], sh[2])
edges_per_face.sort(axis=1)
eo = nm.empty((sh[0] * sh[1],), dtype=nm.object)
eo[:] = [tuple(ii) for ii in edges_per_face]
ueo, e_sort, e_id = unique(eo, return_index=True, return_inverse=True)
ueo = edges_per_face[e_sort]
# edge centre, edge point 1, face centre, edge point 2
conn = nm.empty((n_edge * n_fa, 4), dtype=nm.int32)
conn[:,0] = e_id
conn[:,1] = ee[:,0]
conn[:,2] = nm.repeat(nm.arange(n_fa, dtype=nm.int32), n_edge) \
+ coor_offset
conn[:,3] = ee[:,1]
# face centre, edge point 2, edge point 1
tri_conn = nm.ascontiguousarray(conn[:,[2,1,3]])
# Ensure orientation - outward normal.
cc = dual_coors[tri_conn]
v1 = cc[:,1] - cc[:,0]
v2 = cc[:,2] - cc[:,0]
normals = nm.cross(v1, v2)
nn = nodal_normals[surface.leconn].sum(axis=1).repeat(n_edge, 0)
centre_normals = (1.0 / surface.n_fp) * nn
centre_normals /= la.norm_l2_along_axis(centre_normals)[:,None]
dot = nm.sum(normals * centre_normals, axis=1)
assert_((dot > 0.0).all())
# Prepare mapping from reference triangle e_R to a
# triangle within reference face e_D.
gel = self.gel.surface_facet
ref_coors = gel.coors
ref_centre = nm.dot(self.bf.squeeze(), ref_coors)
cc = nm.r_[ref_coors, ref_centre[None,:]]
rconn = nm.empty((n_edge, 3), dtype=nm.int32)
rconn[:,0] = gel.n_vertex
rconn[:,1] = gel.edges[:,0]
rconn[:,2] = gel.edges[:,1]
map_er_ed = VolumeMapping(cc, rconn, gel=gel)
# Prepare mapping from reference triangle e_R to a
# physical triangle e.
map_er_e = SurfaceMapping(dual_coors, tri_conn, gel=gel)
# Compute triangle basis (edge) vectors.
nn = surface.nodes[ueo]
edge_coors = mesh_coors[nn]
edge_centre_coors = 0.5 * edge_coors.sum(axis=1)
edge_normals = 0.5 * nodal_normals[ueo].sum(axis=1)
edge_normals /= la.norm_l2_along_axis(edge_normals)[:,None]
nn = surface.nodes[ueo]
edge_dirs = edge_coors[:,1] - edge_coors[:,0]
edge_dirs /= la.norm_l2_along_axis(edge_dirs)[:,None]
edge_ortho = nm.cross(edge_normals, edge_dirs)
edge_ortho /= la.norm_l2_along_axis(edge_ortho)[:,None]
# Primary face - dual sub-faces map.
# i-th row: indices to conn corresponding to sub-faces of i-th face.
face_map = nm.arange(n_fa * n_edge, dtype=nm.int32)
face_map.shape = (n_fa, n_edge)
# The actual connectivity for assembling (unique nodes per master
# faces).
asm_conn = e_id[face_map]
n_nod = ueo.shape[0] # One node per unique edge.
n_components = self.dim - 1
dual_surface = Struct(name = 'dual_surface_description',
dim = self.dim,
n_dual_fa = conn.shape[0],
n_dual_fp = self.dim,
n_fa = n_fa,
n_edge = n_edge,
n_nod = n_nod,
n_components = n_components,
n_dof = n_nod * n_components,
dual_coors = dual_coors,
coor_offset = coor_offset,
e_sort = e_sort,
conn = conn,
tri_conn = tri_conn,
map_er_e = map_er_e,
map_er_ed = map_er_ed,
face_map = face_map,
asm_conn = asm_conn,
nodal_normals = nodal_normals,
edge_centre_coors = edge_centre_coors,
edge_normals = edge_normals,
edge_dirs = edge_dirs,
edge_ortho = edge_ortho)
return dual_surface