def __init__(self, name, regions, dof_names, dof_map_fun, variables,
functions=None):
Struct.__init__(self, name=name, regions=regions, dof_names=dof_names)
if dof_map_fun is not None:
self.dof_map_fun = get_condition_value(dof_map_fun, functions,
'LCBC', 'dof_map_fun')
self._setup_dof_names(variables)
def __init__(self, name, regions, dof_names, dof_map_fun, shift_fun, variables, ts, functions):
LCBCOperator.__init__(self, name, regions, dof_names, dof_map_fun, variables, functions=functions)
self.shift_fun = get_condition_value(shift_fun, functions, "LCBC", "shift")
mvar = variables[self.var_names[0]]
svar = variables[self.var_names[1]]
mfield = mvar.field
sfield = svar.field
nmaster = mfield.get_dofs_in_region(regions[0], merge=True)
nslave = sfield.get_dofs_in_region(regions[1], merge=True)
if nmaster.shape != nslave.shape:
msg = "shifted EPBC node list lengths do not match!\n(%s,\n %s)" % (nmaster, nslave)
raise ValueError(msg)
mcoor = mfield.get_coor(nmaster)
scoor = sfield.get_coor(nslave)
i1, i2 = self.dof_map_fun(mcoor, scoor)
self.mdofs = expand_nodes_to_equations(nmaster[i1], dof_names[0], self.all_dof_names[0])
self.sdofs = expand_nodes_to_equations(nslave[i2], dof_names[1], self.all_dof_names[1])
self.shift = self.shift_fun(ts, scoor[i2], regions[1])
meq = mvar.eq_map.eq[self.mdofs]
seq = svar.eq_map.eq[self.sdofs]
# Ignore DOFs with EBCs or EPBCs.
mia = nm.where(meq >= 0)[0]
sia = nm.where(seq >= 0)[0]
ia = nm.intersect1d(mia, sia)
meq = meq[ia]
seq = seq[ia]
num = len(ia)
ones = nm.ones(num, dtype=nm.float64)
n_dofs = [variables.adi.n_dof[ii] for ii in self.var_names]
mtx = sp.coo_matrix((ones, (meq, seq)), shape=n_dofs)
self.mtx = mtx.tocsr()
self.rhs = self.shift.ravel()[ia]
self.ameq = meq
self.aseq = seq
self.n_mdof = len(nm.unique(meq))
self.n_sdof = len(nm.unique(seq))
self.n_new_dof = 0
def __init__(self, name, regions, dof_names, dof_map_fun, shift_fun,
variables, ts, functions):
LCBCOperator.__init__(self, name, regions, dof_names, dof_map_fun,
variables, functions=functions)
self.shift_fun = get_condition_value(shift_fun, functions,
'LCBC', 'shift')
mvar = variables[self.var_names[0]]
svar = variables[self.var_names[1]]
mfield = mvar.field
sfield = svar.field
nmaster = mfield.get_dofs_in_region(regions[0], merge=True)
nslave = sfield.get_dofs_in_region(regions[1], merge=True)
if nmaster.shape != nslave.shape:
msg = 'shifted EPBC node list lengths do not match!\n(%s,\n %s)' %\
(nmaster, nslave)
raise ValueError(msg)
mcoor = mfield.get_coor(nmaster)
scoor = sfield.get_coor(nslave)
i1, i2 = self.dof_map_fun(mcoor, scoor)
self.mdofs = expand_nodes_to_equations(nmaster[i1], dof_names[0],
self.all_dof_names[0])
self.sdofs = expand_nodes_to_equations(nslave[i2], dof_names[1],
self.all_dof_names[1])
self.shift = self.shift_fun(ts, scoor[i2], regions[1])
meq = mvar.eq_map.eq[self.mdofs]
seq = svar.eq_map.eq[self.sdofs]
# Ignore DOFs with EBCs or EPBCs.
mia = nm.where(meq >= 0)[0]
sia = nm.where(seq >= 0)[0]
ia = nm.intersect1d(mia, sia)
meq = meq[ia]
seq = seq[ia]
num = len(ia)
ones = nm.ones(num, dtype=nm.float64)
n_dofs = [variables.adi.n_dof[ii] for ii in self.var_names]
mtx = sp.coo_matrix((ones, (meq, seq)), shape=n_dofs)
self.mtx = mtx.tocsr()
self.rhs = self.shift.ravel()[ia]
self.ameq = meq
self.aseq = seq
self.n_mdof = len(nm.unique(meq))
self.n_sdof = len(nm.unique(seq))
self.n_new_dof = 0
def __init__(self, name, regions, dof_names, dof_map_fun,
constraints, variables, ts=None, functions=None):
MRLCBCOperator.__init__(self, name, regions, dof_names, dof_map_fun,
variables, functions=functions)
import sympy as sm
n_c = self.field.n_components
dpn = len(self.dof_names)
n_nod = self.mdofs.shape[0]
assert_(dpn <= n_c)
if (isinstance(constraints, basestr)
or isinstance(constraints, Function)):
fun = get_condition_value(constraints, functions,
'nodal', 'constraints')
coors = self.field.get_coor(self.mdofs)
mtx, rhs = fun(ts, coors, self.region)
else:
mtx, rhs = constraints
mtx = nm.tile(mtx, (n_nod, 1, 1))
rhs = nm.tile(rhs, (n_nod, 1))
n_ceq = mtx.shape[1]
assert_(n_ceq == rhs.shape[1])
assert_(dpn == mtx.shape[2])
assert_(n_ceq <= dpn)
data = []
rows = []
cols = []
rhss = nm.zeros(n_nod * dpn, dtype=nm.float64)
n_new = 0
us = [sm.Symbol('u%d' % ii) for ii in range(dpn)]
for im, nmtx in enumerate(mtx):
eqs = sm.Matrix(nmtx) * sm.Matrix(us) - rhs[im][:, None]
sol = sm.solve(eqs)
assert_(len(sol) == n_ceq)
imasters = []
ifixed = []
islaves = set()
ccs = []
for key, _poly in six.iteritems(sol):
imaster = int(key.name[1:])
imasters.append(imaster)
if not isinstance(_poly, sm.Float):
poly = _poly.as_poly()
# Workaround for poly.all_coeffs() not applicable to
# multivariate polynomials.
coefs = []
for ii, uu in enumerate(us):
if poly.has(uu):
coefs.append(poly.coeff_monomial(uu))
islaves.add(ii)
coefs.append(poly.TC())
ccs.append(coefs)
else: # Degenerated constraint - fixed master.
ifixed.append(imaster)
ccs.append([float(_poly)])
islaves = sorted(islaves)
for ii, imaster in enumerate(imasters):
coefs = ccs[ii]
em = dpn * im + imaster
rhss[em] = coefs[-1]
if imaster in ifixed: continue
# Master DOF is expressed in terms of slave DOFs.
for ii, islave in enumerate(islaves):
es = ii + n_new
rows.append(em)
cols.append(es)
data.append(coefs[ii])
# Slave DOFs are copied.
for ii, islave in enumerate(islaves):
em = dpn * im + islave
es = ii + n_new
rows.append(em)
cols.append(es)
data.append(1.0)
n_new += len(islaves)
rows = nm.array(rows, dtype=nm.int32)
cols = nm.array(cols, dtype=nm.int32)
data = nm.array(data, dtype=nm.float64)
mtx = sp.coo_matrix((data, (rows, cols)), shape=(n_nod * dpn, n_new))
self.n_mdof = n_nod * dpn
self.n_new_dof = n_new
self.mtx = mtx.tocsr()
self.rhs = rhss
def map_equations(self, bcs, field, ts, functions, problem=None,
warn=False):
"""
Create the mapping of active DOFs from/to all DOFs.
Parameters
----------
bcs : Conditions instance
The Dirichlet or periodic boundary conditions (single
condition instances). The dof names in the conditions must
already be canonized.
field : Field instance
The field of the variable holding the DOFs.
ts : TimeStepper instance
The time stepper.
functions : Functions instance
The registered functions.
problem : Problem instance, optional
The problem that can be passed to user functions as a context.
warn : bool, optional
If True, warn about BC on non-existent nodes.
Returns
-------
active_bcs : set
The set of boundary conditions active in the current time.
Notes
-----
- Periodic bc: master and slave DOFs must belong to the same
field (variables can differ, though).
"""
if bcs is None:
self._init_empty(field)
return set()
eq_ebc = nm.zeros((self.var_di.n_dof,), dtype=nm.int32)
val_ebc = nm.zeros((self.var_di.n_dof,), dtype=field.dtype)
master_slave = nm.zeros((self.var_di.n_dof,), dtype=nm.int32)
chains = []
active_bcs = set()
for bc in bcs:
# Skip conditions that are not active in the current time.
if not is_active_bc(bc, ts=ts, functions=functions):
continue
active_bcs.add(bc.key)
if isinstance(bc, DGEssentialBC):
ntype = "DGEBC"
region = bc.region
elif isinstance(bc, DGPeriodicBC):
ntype = "DGEPBC"
region = bc.regions[0]
elif isinstance(bc, EssentialBC):
ntype = 'EBC'
region = bc.region
elif isinstance(bc, PeriodicBC):
ntype = 'EPBC'
region = bc.regions[0]
if warn:
clean_msg = ('warning: ignoring nonexistent %s node (%s) in '
% (ntype, self.var_di.var_name))
else:
clean_msg = None
# Get master region nodes.
master_nod_list = field.get_dofs_in_region(region)
if len(master_nod_list) == 0:
continue
if ntype == 'EBC': # EBC.
dofs, val = bc.dofs
##
# Evaluate EBC values.
fun = get_condition_value(val, functions, 'EBC', bc.name)
if isinstance(fun, Function):
aux = fun
fun = lambda coors: aux(ts, coors,
bc=bc, problem=problem)
nods, vv = field.set_dofs(fun, region, len(dofs), clean_msg)
eq = expand_nodes_to_equations(nods, dofs, self.dof_names)
# Duplicates removed here...
eq_ebc[eq] = 1
if vv is not None: val_ebc[eq] = nm.ravel(vv)
elif ntype == "DGEBC":
dofs, val = bc.dofs
##
# Evaluate EBC values.
fun = get_condition_value(val, functions, 'EBC', bc.name)
if isinstance(fun, Function):
aux = fun
fun = lambda coors: aux(ts, coors,
bc=bc, problem=problem)
values = field.get_bc_facet_values(fun, region, diff=bc.diff)
bc2bfi = field.get_bc_facet_idx(region)
self.dg_ebc_val.setdefault(bc.diff, []).append(values)
self.dg_ebc.setdefault(bc.diff, []).append(bc2bfi)
self.n_dg_ebc += 1
elif ntype == "DGEPBC":
# ensure matching boundaries?
master_bc2bfi = field.get_bc_facet_idx(region)
slave_bc2bfi = field.get_bc_facet_idx(bc.regions[1])
self.dg_epbc.append((master_bc2bfi, slave_bc2bfi))
self.n_dg_epbc += 1
else: # EPBC.
region = bc.regions[1]
slave_nod_list = field.get_dofs_in_region(region)
nmaster = nm.unique(master_nod_list)
# Treat fields not covering the whole domain.
if nmaster[0] == -1:
nmaster = nmaster[1:]
nslave = nm.unique(slave_nod_list)
# Treat fields not covering the whole domain.
if nslave[0] == -1:
nslave = nslave[1:]
## print nmaster + 1
## print nslave + 1
if nmaster.shape != nslave.shape:
msg = 'EPBC list lengths do not match!\n(%s,\n %s)' %\
(nmaster, nslave)
raise ValueError(msg)
if (nmaster.shape[0] == 0) and (nslave.shape[0] == 0):
continue
mcoor = field.get_coor(nmaster)
scoor = field.get_coor(nslave)
fun = get_condition_value(bc.match, functions, 'EPBC', bc.name)
if isinstance(fun, Function):
i1, i2 = fun(mcoor, scoor)
else:
i1, i2 = fun
## print nm.c_[mcoor[i1], scoor[i2]]
## print nm.c_[nmaster[i1], nslave[i2]] + 1
meq = expand_nodes_to_equations(nmaster[i1], bc.dofs[0],
self.dof_names)
seq = expand_nodes_to_equations(nslave[i2], bc.dofs[1],
self.dof_names)
m_assigned = nm.where(master_slave[meq] != 0)[0]
s_assigned = nm.where(master_slave[seq] != 0)[0]
if m_assigned.size or s_assigned.size: # Chain EPBC.
aux = master_slave[meq[m_assigned]]
sgn = nm.sign(aux)
om_chain = zip(meq[m_assigned], (aux - sgn) * sgn)
chains.extend(om_chain)
aux = master_slave[seq[s_assigned]]
sgn = nm.sign(aux)
os_chain = zip(seq[s_assigned], (aux - sgn) * sgn)
chains.extend(os_chain)
m_chain = zip(meq[m_assigned], seq[m_assigned])
chains.extend(m_chain)
msd = nm.setdiff1d(s_assigned, m_assigned)
s_chain = zip(meq[msd], seq[msd])
chains.extend(s_chain)
msa = nm.union1d(m_assigned, s_assigned)
ii = nm.setdiff1d(nm.arange(meq.size), msa)
master_slave[meq[ii]] = seq[ii] + 1
master_slave[seq[ii]] = - meq[ii] - 1
else:
master_slave[meq] = seq + 1
master_slave[seq] = - meq - 1
chains = group_chains(chains)
resolve_chains(master_slave, chains)
self.master = nm.nonzero(master_slave > 0)[0]
self.slave = master_slave[self.master] - 1
# Propagate EBCs via PBCs.
mask = eq_ebc[self.master] > 0
im0 = self.master[mask]
im1 = self.slave[mask]
mask = eq_ebc[self.slave] > 0
is0 = self.slave[mask]
is1 = self.master[mask]
val_ebc[im1] = val_ebc[im0]
eq_ebc[im1] = eq_ebc[im0]
val_ebc[is1] = val_ebc[is0]
eq_ebc[is1] = eq_ebc[is0]
self.eq_ebc = nm.nonzero(eq_ebc > 0)[0]
self.val_ebc = val_ebc[self.eq_ebc]
assert_((self.eq_ebc.shape == self.val_ebc.shape))
self.eq[self.eq_ebc] = -2
self.eq[self.master] = -1
self._mark_unused(field)
self.eqi = self.eq[self.eq >= 0]
self.eq[self.eqi] = nm.arange(self.eqi.shape[0], dtype=nm.int32)
self.eq[self.master] = self.eq[self.slave]
self.n_eq = self.eqi.shape[0]
self.n_ebc = self.eq_ebc.shape[0]
self.n_epbc = self.master.shape[0]
return active_bcs
def map_equations(self, bcs, field, ts, functions, problem=None,
warn=False):
"""
Create the mapping of active DOFs from/to all DOFs.
Parameters
----------
bcs : Conditions instance
The Dirichlet or periodic boundary conditions (single
condition instances). The dof names in the conditions must
already be canonized.
field : Field instance
The field of the variable holding the DOFs.
ts : TimeStepper instance
The time stepper.
functions : Functions instance
The registered functions.
problem : Problem instance, optional
The problem that can be passed to user functions as a context.
warn : bool, optional
If True, warn about BC on non-existent nodes.
Returns
-------
active_bcs : set
The set of boundary conditions active in the current time.
Notes
-----
- Periodic bc: master and slave DOFs must belong to the same
field (variables can differ, though).
"""
if bcs is None:
self._init_empty(field)
return set()
eq_ebc = nm.zeros((self.var_di.n_dof,), dtype=nm.int32)
val_ebc = nm.zeros((self.var_di.n_dof,), dtype=field.dtype)
master_slave = nm.zeros((self.var_di.n_dof,), dtype=nm.int32)
chains = []
active_bcs = set()
for bc in bcs:
# Skip conditions that are not active in the current time.
if not is_active_bc(bc, ts=ts, functions=functions):
continue
active_bcs.add(bc.key)
if isinstance(bc, EssentialBC):
ntype = 'EBC'
region = bc.region
else:
ntype = 'EPBC'
region = bc.regions[0]
if warn:
clean_msg = ('warning: ignoring nonexistent %s node (%s) in '
% (ntype, self.var_di.var_name))
else:
clean_msg = None
# Get master region nodes.
master_nod_list = field.get_dofs_in_region(region)
if len(master_nod_list) == 0:
continue
if ntype == 'EBC': # EBC.
dofs, val = bc.dofs
##
# Evaluate EBC values.
fun = get_condition_value(val, functions, 'EBC', bc.name)
if isinstance(fun, Function):
aux = fun
fun = lambda coors: aux(ts, coors,
bc=bc, problem=problem)
nods, vv = field.set_dofs(fun, region, len(dofs), clean_msg)
eq = expand_nodes_to_equations(nods, dofs, self.dof_names)
# Duplicates removed here...
eq_ebc[eq] = 1
if vv is not None: val_ebc[eq] = nm.ravel(vv)
else: # EPBC.
region = bc.regions[1]
slave_nod_list = field.get_dofs_in_region(region)
nmaster = nm.unique(nm.hstack(master_nod_list))
# Treat fields not covering the whole domain.
if nmaster[0] == -1:
nmaster = nmaster[1:]
nslave = nm.unique(nm.hstack(slave_nod_list))
# Treat fields not covering the whole domain.
if nslave[0] == -1:
nslave = nslave[1:]
## print nmaster + 1
## print nslave + 1
if nmaster.shape != nslave.shape:
msg = 'EPBC list lengths do not match!\n(%s,\n %s)' %\
(nmaster, nslave)
raise ValueError(msg)
if (nmaster.shape[0] == 0) and (nslave.shape[0] == 0):
continue
mcoor = field.get_coor(nmaster)
scoor = field.get_coor(nslave)
fun = get_condition_value(bc.match, functions, 'EPBC', bc.name)
if isinstance(fun, Function):
i1, i2 = fun(mcoor, scoor)
else:
i1, i2 = fun
## print nm.c_[mcoor[i1], scoor[i2]]
## print nm.c_[nmaster[i1], nslave[i2]] + 1
meq = expand_nodes_to_equations(nmaster[i1], bc.dofs[0],
self.dof_names)
seq = expand_nodes_to_equations(nslave[i2], bc.dofs[1],
self.dof_names)
m_assigned = nm.where(master_slave[meq] != 0)[0]
s_assigned = nm.where(master_slave[seq] != 0)[0]
if m_assigned.size or s_assigned.size: # Chain EPBC.
aux = master_slave[meq[m_assigned]]
sgn = nm.sign(aux)
om_chain = zip(meq[m_assigned], (aux - sgn) * sgn)
chains.extend(om_chain)
aux = master_slave[seq[s_assigned]]
sgn = nm.sign(aux)
os_chain = zip(seq[s_assigned], (aux - sgn) * sgn)
chains.extend(os_chain)
m_chain = zip(meq[m_assigned], seq[m_assigned])
chains.extend(m_chain)
msd = nm.setdiff1d(s_assigned, m_assigned)
s_chain = zip(meq[msd], seq[msd])
chains.extend(s_chain)
msa = nm.union1d(m_assigned, s_assigned)
ii = nm.setdiff1d(nm.arange(meq.size), msa)
master_slave[meq[ii]] = seq[ii] + 1
master_slave[seq[ii]] = - meq[ii] - 1
else:
master_slave[meq] = seq + 1
master_slave[seq] = - meq - 1
chains = group_chains(chains)
resolve_chains(master_slave, chains)
ii = nm.argwhere(eq_ebc == 1)
self.eq_ebc = nm.atleast_1d(ii.squeeze())
self.val_ebc = nm.atleast_1d(val_ebc[ii].squeeze())
self.master = nm.argwhere(master_slave > 0).squeeze()
self.slave = master_slave[self.master] - 1
assert_((self.eq_ebc.shape == self.val_ebc.shape))
self.eq[self.eq_ebc] = -2
self.eq[self.master] = -1
self._mark_unused(field)
self.eqi = nm.compress(self.eq >= 0, self.eq)
self.eq[self.eqi] = nm.arange(self.eqi.shape[0], dtype=nm.int32)
self.eq[self.master] = self.eq[self.slave]
self.n_eq = self.eqi.shape[0]
self.n_ebc = self.eq_ebc.shape[0]
self.n_epbc = self.master.shape[0]
return active_bcs
