def __init__(self, ref_el, degree):
if degree < 1:
raise Exception("Trimmed serendipity face elements only valid for k >= 1")
flat_el = flatten_reference_cube(ref_el)
dim = flat_el.get_spatial_dimension()
if dim != 2:
raise Exception("Trimmed serendipity face elements only valid for dimensions 2")
verts = flat_el.get_vertices()
dx = ((verts[-1][0] - x)/(verts[-1][0] - verts[0][0]), (x - verts[0][0])/(verts[-1][0] - verts[0][0]))
dy = ((verts[-1][1] - y)/(verts[-1][1] - verts[0][1]), (y - verts[0][1])/(verts[-1][1] - verts[0][1]))
x_mid = 2*x-(verts[-1][0] + verts[0][0])
y_mid = 2*y-(verts[-1][1] + verts[0][1])
EL = e_lambda_1_2d_part_one(degree, dx, dy, x_mid, y_mid)
if degree >= 2:
FL = trimmed_f_lambda_2d(degree, dx, dy, x_mid, y_mid)
else:
FL = ()
Sminus_list = EL + FL
Sminus_list = [[-a[1], a[0]] for a in Sminus_list]
self.basis = {(0, 0): Array(Sminus_list)}
super(TrimmedSerendipityFace, self).__init__(ref_el=ref_el, degree=degree, mapping="contravariant piola")
def __init__(self, ref_el, degree):
flat_el = flatten_reference_cube(ref_el)
poly_set = ONPolynomialSet(hypercube_simplex_map[flat_el], degree)
dual = DPCDualSet(ref_el, flat_el, degree)
formdegree = flat_el.get_spatial_dimension() # n-form
super().__init__(poly_set=poly_set,
dual=dual,
order=degree,
ref_el=ref_el,
formdegree=formdegree)
def __init__(self, ref_el):
flat_el = flatten_reference_cube(ref_el)
poly_set = polynomial_set.ONPolynomialSet(
hypercube_simplex_map[flat_el], 0)
dual = P0Dual(ref_el)
degree = 0
formdegree = ref_el.get_spatial_dimension() # n-form
super(DPC0, self).__init__(poly_set=poly_set,
dual=dual,
order=degree,
ref_el=ref_el,
formdegree=formdegree)
def __init__(self, ref_el, degree):
if degree < 1:
raise Exception("Trimmed Serendipity_k edge elements only valid for k >= 1")
flat_el = flatten_reference_cube(ref_el)
dim = flat_el.get_spatial_dimension()
if dim != 2:
if dim != 3:
raise Exception("Trimmed Serendipity_k edge elements only valid for dimensions 2 and 3")
verts = flat_el.get_vertices()
dx = ((verts[-1][0] - x)/(verts[-1][0] - verts[0][0]), (x - verts[0][0])/(verts[-1][0] - verts[0][0]))
dy = ((verts[-1][1] - y)/(verts[-1][1] - verts[0][1]), (y - verts[0][1])/(verts[-1][1] - verts[0][1]))
x_mid = 2*x-(verts[-1][0] + verts[0][0])
y_mid = 2*y-(verts[-1][1] + verts[0][1])
try:
dz = ((verts[-1][2] - z)/(verts[-1][2] - verts[0][2]), (z - verts[0][2])/(verts[-1][2] - verts[0][2]))
z_mid = 2*z-(verts[-1][2] + verts[0][2])
except IndexError:
dz = None
z_mid = None
if dim == 2:
EL = e_lambda_1_2d_part_one(degree, dx, dy, x_mid, y_mid)
else:
EL = e_lambda_1_3d_trimmed(degree, dx, dy, dz, x_mid, y_mid, z_mid)
if degree >= 2:
if dim == 2:
FL = trimmed_f_lambda_2d(degree, dx, dy, x_mid, y_mid)
else:
FL = f_lambda_1_3d_trimmed(degree, dx, dy, dz, x_mid, y_mid, z_mid)
else:
FL = ()
if dim == 3:
if degree >= 4:
IL = I_lambda_1_3d(degree, dx, dy, dz, x_mid, y_mid, z_mid) + I_lambda_1_tilde_3d(degree, dx, dy,
dz, x_mid,
y_mid, z_mid)
else:
IL = ()
Sminus_list = EL + FL
if dim == 3:
Sminus_list = Sminus_list + IL
if dim == 2:
self.basis = {(0, 0): Array(Sminus_list)}
else:
self.basis = {(0, 0, 0): Array(Sminus_list)}
super(TrimmedSerendipityEdge, self).__init__(ref_el=ref_el, degree=degree, mapping="covariant piola")
def __init__(self, ref_el, degree):
if degree < 1:
raise Exception("Trimmed serendipity face elements only valid for k >= 1")
flat_el = flatten_reference_cube(ref_el)
dim = flat_el.get_spatial_dimension()
if dim != 2:
if dim != 3:
raise Exception("Trimmed serendipity face elements only valid for dimensions 2 and 3")
verts = flat_el.get_vertices()
dx = ((verts[-1][0] - x)/(verts[-1][0] - verts[0][0]), (x - verts[0][0])/(verts[-1][0] - verts[0][0]))
dy = ((verts[-1][1] - y)/(verts[-1][1] - verts[0][1]), (y - verts[0][1])/(verts[-1][1] - verts[0][1]))
x_mid = 2*x-(verts[-1][0] + verts[0][0])
y_mid = 2*y-(verts[-1][1] + verts[0][1])
try:
dz = ((verts[-1][2] - z)/(verts[-1][2] - verts[0][2]), (z - verts[0][2])/(verts[-1][2] - verts[0][2]))
z_mid = 2*z-(verts[-1][2] + verts[0][2])
except IndexError:
dz = None
z_mid = None
if dim == 3:
FL = f_lambda_2_3d(degree, dx, dy, dz, x_mid, y_mid, z_mid)
if (degree > 1):
IL = I_lambda_2_3d(degree, dx, dy, dz, x_mid, y_mid, z_mid)
else:
IL = ()
Sminus_list = FL + IL
self.basis = {(0, 0, 0): Array(Sminus_list)}
super(TrimmedSerendipityDiv, self).__init__(ref_el=ref_el, degree=degree, mapping="contravariant piola")
else:
# Put all 2 dimensional stuff here.
if degree < 1:
raise Exception("Trimmed serendipity face elements only valid for k >= 1")
EL = e_lambda_1_2d_part_one(degree, dx, dy, x_mid, y_mid)
if degree >= 2:
FL = trimmed_f_lambda_2d(degree, dx, dy, x_mid, y_mid)
else:
FL = ()
Sminus_list = EL + FL
Sminus_list = [[-a[1], a[0]] for a in Sminus_list]
self.basis = {(0, 0): Array(Sminus_list)}
super(TrimmedSerendipityDiv, self).__init__(ref_el=ref_el, degree=degree, mapping="contravariant piola")
def __init__(self, ref_el, degree):
flat_el = flatten_reference_cube(ref_el)
dim = flat_el.get_spatial_dimension()
flat_topology = flat_el.get_topology()
verts = flat_el.get_vertices()
dx = ((verts[-1][0] - x)/(verts[-1][0] - verts[0][0]), (x - verts[0][0])/(verts[-1][0] - verts[0][0]))
dy = ((verts[-1][1] - y)/(verts[-1][1] - verts[0][1]), (y - verts[0][1])/(verts[-1][1] - verts[0][1]))
x_mid = 2*x-(verts[-1][0] + verts[0][0])
y_mid = 2*y-(verts[-1][1] + verts[0][1])
try:
dz = ((verts[-1][2] - z)/(verts[-1][2] - verts[0][2]), (z - verts[0][2])/(verts[-1][2] - verts[0][2]))
z_mid = 2*z-(verts[-1][2] + verts[0][2])
except IndexError:
dz = None
z_mid = None
VL = v_lambda_0(dim, dx, dy, dz)
EL = []
FL = []
IL = []
s_list = []
entity_ids = {}
cur = 0
for top_dim, entities in flat_topology.items():
entity_ids[top_dim] = {}
for entity in entities:
entity_ids[top_dim][entity] = []
for j in sorted(flat_topology[0]):
entity_ids[0][j] = [cur]
cur = cur + 1
EL += e_lambda_0(degree, dim, dx, dy, dz, x_mid, y_mid, z_mid)
for j in sorted(flat_topology[1]):
entity_ids[1][j] = list(range(cur, cur + degree - 1))
cur = cur + degree - 1
FL += f_lambda_0(degree, dim, dx, dy, dz, x_mid, y_mid, z_mid)
for j in sorted(flat_topology[2]):
entity_ids[2][j] = list(range(cur, cur + tr(degree)))
cur = cur + tr(degree)
if dim == 3:
IL += i_lambda_0(degree, dx, dy, dz, x_mid, y_mid, z_mid)
entity_ids[3] = {}
entity_ids[3][0] = list(range(cur, cur + len(IL)))
cur = cur + len(IL)
s_list = VL + EL + FL + IL
assert len(s_list) == cur
formdegree = 0
super(Serendipity, self).__init__(ref_el=ref_el, dual=None, order=degree, formdegree=formdegree)
self.basis = {(0,)*dim: Array(s_list)}
topology = ref_el.get_topology()
unflattening_map = compute_unflattening_map(topology)
unflattened_entity_ids = {}
unflattened_entity_closure_ids = {}
entity_closure_ids = make_entity_closure_ids(flat_el, entity_ids)
for dim, entities in sorted(topology.items()):
unflattened_entity_ids[dim] = {}
unflattened_entity_closure_ids[dim] = {}
for dim, entities in sorted(flat_topology.items()):
for entity in entities:
unflat_dim, unflat_entity = unflattening_map[(dim, entity)]
unflattened_entity_ids[unflat_dim][unflat_entity] = entity_ids[dim][entity]
unflattened_entity_closure_ids[unflat_dim][unflat_entity] = entity_closure_ids[dim][entity]
self.entity_ids = unflattened_entity_ids
self.entity_closure_ids = unflattened_entity_closure_ids
self._degree = degree
self.flat_el = flat_el
def __init__(self, ref_el, degree, mapping):
if degree < 1:
raise Exception(
"Trimmed serendipity elements only valid for k >= 1")
flat_el = flatten_reference_cube(ref_el)
dim = flat_el.get_spatial_dimension()
self.fdim = dim
if dim != 3:
if dim != 2:
raise Exception(
"Trimmed serendipity elements only valid for dimensions 2 and 3"
)
flat_topology = flat_el.get_topology()
entity_ids = {}
cur = 0
for top_dim, entities in flat_topology.items():
entity_ids[top_dim] = {}
for entity in entities:
entity_ids[top_dim][entity] = []
# 3-d case.
if dim == 3:
entity_ids[3] = {}
for l in sorted(flat_topology[1]):
entity_ids[1][l] = list(range(cur, cur + degree))
cur = cur + degree
if (degree > 1):
face_ids = degree
for k in range(2, degree):
face_ids += 2 * (k - 1)
for j in sorted(flat_topology[2]):
entity_ids[2][j] = list(range(cur, cur + face_ids))
cur += face_ids
interior_ids = 0
for k in range(4, degree):
interior_ids = interior_ids + 3 * choose_ijk_total(k - 4)
if (degree > 3):
if (degree == 4):
interior_tilde_ids = 3
elif (degree == 5):
interior_tilde_ids = 8
elif (degree == 6):
interior_tilde_ids = 6 + 3 * (degree - 3)
else:
interior_tilde_ids = 6 + 3 * (degree - 4)
else:
interior_tilde_ids = 0
entity_ids[3][0] = list(
range(cur, cur + interior_ids + interior_tilde_ids))
cur = cur + interior_ids + interior_tilde_ids
else:
for j in sorted(flat_topology[1]):
entity_ids[1][j] = list(range(cur, cur + degree))
cur = cur + degree
if (degree >= 2):
entity_ids[2][0] = list(
range(cur,
cur + 2 * triangular_number(degree - 2) + degree))
cur += 2 * triangular_number(degree - 2) + degree
formdegree = 1
entity_closure_ids = make_entity_closure_ids(flat_el, entity_ids)
super(TrimmedSerendipity, self).__init__(ref_el=ref_el,
dual=None,
order=degree,
formdegree=formdegree,
mapping=mapping)
topology = ref_el.get_topology()
unflattening_map = compute_unflattening_map(topology)
unflattened_entity_ids = {}
unflattened_entity_closure_ids = {}
for dim, entities in sorted(topology.items()):
unflattened_entity_ids[dim] = {}
unflattened_entity_closure_ids[dim] = {}
for dim, entities in sorted(flat_topology.items()):
for entity in entities:
unflat_dim, unflat_entity = unflattening_map[(dim, entity)]
unflattened_entity_ids[unflat_dim][unflat_entity] = entity_ids[
dim][entity]
unflattened_entity_closure_ids[unflat_dim][
unflat_entity] = entity_closure_ids[dim][entity]
self.entity_ids = unflattened_entity_ids
self.entity_closure_ids = unflattened_entity_closure_ids
self._degree = degree
self.flat_el = flat_el