import numpy as nm
from sfepy.linalg import dot_sequences
from sfepy.terms.terms import Term, terms
from sfepy.terms.terms_th import THTerm, ETHTerm
[docs]class DotProductTerm(Term):
r"""
Volume and surface :math:`L^2()` weighted dot product for both
scalar and vector fields. If the region is a surface and
either virtual or state variable is a vector, the orientation
of the normal vectors is outwards to the parent region of the virtual
variable. Can be evaluated. Can use derivatives.
:Definition:
.. math::
\int_{\cal{D}} q p \mbox{ , }
\int_{\cal{D}} \ul{v} \cdot \ul{u}\\
\int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , }
\int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , }\\
\int_{\cal{D}} c q p \mbox{ , }
\int_{\cal{D}} c \ul{v} \cdot \ul{u} \mbox{ , }
\int_{\cal{D}} \ul{v} \cdot \ull{c} \cdot \ul{u}
:Arguments:
- material: :math:`c` or :math:`\ull{c}` (optional)
- virtual/parameter_1: :math:`q` or :math:`\ul{v}`
- state/parameter_2: :math:`p` or :math:`\ul{u}`
"""
name = 'dw_dot'
arg_types = (('opt_material', 'virtual', 'state'),
('opt_material', 'parameter_1', 'parameter_2'))
arg_shapes_dict = {
'cell': [{'opt_material' : '1, 1', 'virtual' : (1, 'state'),
'state' : 1, 'parameter_1' : 1, 'parameter_2' : 1},
{'opt_material' : None},
{'opt_material' : '1, 1', 'virtual' : ('D', 'state'),
'state' : 'D', 'parameter_1' : 'D', 'parameter_2' : 'D'},
{'opt_material' : 'D, D'},
{'opt_material' : None}],
'facet': [{'opt_material' : '1, 1', 'virtual' : (1, 'state'),
'state' : 1, 'parameter_1' : 1, 'parameter_2' : 1},
{'opt_material' : None},
{'opt_material' : '1, 1', 'virtual' : (1, None),
'state' : 'D'},
{'opt_material' : None},
{'opt_material' : '1, 1', 'virtual' : ('D', None),
'state' : 1},
{'opt_material' : None},
{'opt_material' : '1, 1', 'virtual' : ('D', 'state'),
'state' : 'D', 'parameter_1' : 'D', 'parameter_2' : 'D'},
{'opt_material' : 'D, D'},
{'opt_material' : None}]
}
modes = ('weak', 'eval')
integration = ('cell', 'facet')
[docs] @staticmethod
def dw_dot(out, mat, val_qp, vgeo, sgeo, fun, fmode):
status = fun(out, mat, val_qp, vgeo, sgeo, fmode)
return status
[docs] @staticmethod
def d_dot(out, mat, val1_qp, val2_qp, geo):
if mat is None:
if val1_qp.shape[2] > 1:
if val2_qp.shape[2] == 1:
aux = dot_sequences(val1_qp, geo.normal, mode='ATB')
vec = dot_sequences(aux, val2_qp, mode='AB')
else:
vec = dot_sequences(val1_qp, val2_qp, mode='ATB')
else:
vec = val1_qp * val2_qp
elif mat.shape[-1] == 1:
if val1_qp.shape[2] > 1:
vec = mat * dot_sequences(val1_qp, val2_qp, mode='ATB')
else:
vec = mat * val1_qp * val2_qp
else:
aux = dot_sequences(mat, val2_qp, mode='AB')
vec = dot_sequences(val1_qp, aux, mode='ATB')
status = geo.integrate(out, vec)
return status
[docs] def get_fargs(self, mat, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
vgeo, _ = self.get_mapping(virtual)
if mode == 'weak':
if mat is None:
n_cell, n_qp, dim, n_n, n_c = self.get_data_shape(state)
mat = nm.ones((1, n_qp, 1, 1), dtype=nm.float64)
sgeo, _ = self.get_mapping(state)
if diff_var is None:
val_qp = self.get(state, 'val')
fmode = 0
else:
val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
fmode = 1
if state.n_components > 1:
if ((self.act_integration == 'cell')
or (virtual.n_components > 1)):
fun = terms.dw_volume_dot_vector
else:
fun = terms.dw_surface_s_v_dot_n
else:
if ((self.act_integration == 'cell')
or (virtual.n_components == 1)):
fun = terms.dw_volume_dot_scalar
else:
fun = terms.dw_surface_v_dot_n_s
return mat, val_qp, vgeo, sgeo, fun, fmode
elif mode == 'eval':
val1_qp = self.get(virtual, 'val')
val2_qp = self.get(state, 'val')
return mat, val1_qp, val2_qp, vgeo
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))
[docs] def get_eval_shape(self, mat, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
n_cell, n_qp, dim, n_n, n_c = self.get_data_shape(state)
return (n_cell, 1, 1, 1), state.dtype
[docs] def set_arg_types(self):
if self.mode == 'weak':
self.function = self.dw_dot
else:
self.function = self.d_dot
[docs]class BCNewtonTerm(DotProductTerm):
r"""
Newton boundary condition term.
:Definition:
.. math::
\int_{\Gamma} \alpha q (p - p_{\rm outer})
:Arguments:
- material_1 : :math:`\alpha`
- material_2 : :math:`p_{\rm outer}`
- virtual : :math:`q`
- state : :math:`p`
"""
name = 'dw_bc_newton'
arg_types = ('material_1', 'material_2', 'virtual', 'state')
arg_shapes = {'material_1' : '1, 1', 'material_2' : '1, 1',
'virtual' : (1, 'state'), 'state' : 1}
mode = 'weak'
integration = 'facet'
arg_shapes_dict = None
[docs] def get_fargs(self, alpha, p_outer, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
fargs = DotProductTerm.get_fargs(self, alpha, virtual, state,
mode, term_mode, diff_var,
**kwargs)
fargs = fargs[:1] + (fargs[1] - p_outer,) + fargs[2:]
return fargs
[docs]class DotSProductVolumeOperatorWTHTerm(THTerm):
r"""
Fading memory volume :math:`L^2(\Omega)` weighted dot product for
scalar fields. Can use derivatives.
:Definition:
.. math::
\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q
:Arguments:
- ts : :class:`TimeStepper` instance
- material : :math:`\Gcal(\tau)`
- virtual : :math:`q`
- state : :math:`p`
"""
name = 'dw_volume_dot_w_scalar_th'
arg_types = ('ts', 'material', 'virtual', 'state')
arg_shapes = {'material' : '.: N, 1, 1',
'virtual' : (1, 'state'), 'state' : 1}
function = staticmethod(terms.dw_volume_dot_scalar)
[docs] def get_fargs(self, ts, mats, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
vg, _ = self.get_mapping(state)
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(state)
if diff_var is None:
def iter_kernel():
for ii, mat in enumerate(mats):
val_qp = self.get(state, 'val', step=-ii)
mat = nm.tile(mat, (n_el, n_qp, 1, 1))
yield ii, (ts.dt * mat, val_qp, vg, vg, 0)
fargs = iter_kernel
else:
val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
mat = nm.tile(mats[0], (n_el, n_qp, 1, 1))
fargs = ts.dt * mat, val_qp, vg, vg, 1
return fargs
[docs]class DotSProductVolumeOperatorWETHTerm(ETHTerm):
r"""
Fading memory volume :math:`L^2(\Omega)` weighted dot product for
scalar fields. This term has the same definition as
dw_volume_dot_w_scalar_th, but assumes an exponential approximation of
the convolution kernel resulting in much higher efficiency. Can use
derivatives.
:Definition:
.. math::
\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q
:Arguments:
- ts : :class:`TimeStepper` instance
- material_0 : :math:`\Gcal(0)`
- material_1 : :math:`\exp(-\lambda \Delta t)` (decay at :math:`t_1`)
- virtual : :math:`q`
- state : :math:`p`
"""
name = 'dw_volume_dot_w_scalar_eth'
arg_types = ('ts', 'material_0', 'material_1', 'virtual', 'state')
arg_shapes = {'material_0' : '1, 1', 'material_1' : '1, 1',
'virtual' : (1, 'state'), 'state' : 1}
function = staticmethod(terms.dw_volume_dot_scalar)
[docs] def get_fargs(self, ts, mat0, mat1, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
vg, _, key = self.get_mapping(state, return_key=True)
if diff_var is None:
val_qp = self.get(state, 'val')
key += tuple(self.arg_names[ii] for ii in [1, 2, 4])
data = self.get_eth_data(key, state, mat1, val_qp)
fargs = (ts.dt * mat0, data.history + data.values, vg, vg, 0)
else:
aux = nm.array([0], ndmin=4, dtype=nm.float64)
fargs = ts.dt * mat0, aux, vg, vg, 1
return fargs
[docs]class VectorDotGradScalarTerm(Term):
r"""
Volume dot product of a vector and a gradient of scalar.
Can be evaluated.
:Definition:
.. math::
\int_{\Omega} \ul{v} \cdot \nabla p \mbox{ , }
\int_{\Omega} \ul{u} \cdot \nabla q \\
\int_{\Omega} c \ul{v} \cdot \nabla p \mbox{ , }
\int_{\Omega} c \ul{u} \cdot \nabla q \\
\int_{\Omega} \ul{v} \cdot (\ull{c} \nabla p) \mbox{ , }
\int_{\Omega} \ul{u} \cdot (\ull{c} \nabla q)
:Arguments 1:
- material: :math:`c` or :math:`\ull{c}` (optional)
- virtual/parameter_v: :math:`\ul{v}`
- state/parameter_s: :math:`p`
:Arguments 2:
- material : :math:`c` or :math:`\ull{c}` (optional)
- state : :math:`\ul{u}`
- virtual : :math:`q`
"""
name = 'dw_v_dot_grad_s'
arg_types = (('opt_material', 'virtual', 'state'),
('opt_material', 'state', 'virtual'),
('opt_material', 'parameter_v', 'parameter_s'))
arg_shapes = [{'opt_material' : '1, 1',
'virtual/v_weak' : ('D', None), 'state/v_weak' : 1,
'virtual/s_weak' : (1, None), 'state/s_weak' : 'D',
'parameter_v' : 'D', 'parameter_s' : 1},
{'opt_material' : 'D, D'},
{'opt_material' : None}]
modes = ('v_weak', 's_weak', 'eval')
[docs] def get_fargs(self, coef, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)
if coef is None:
coef = nm.ones((1, n_qp, 1, 1), dtype=nm.float64)
if mode == 'weak':
if self.mode == 'v_weak':
qp_var, qp_name = svar, 'grad'
else:
qp_var, qp_name = vvar, 'val'
vvg, _ = self.get_mapping(vvar)
svg, _ = self.get_mapping(svar)
if diff_var is None:
val_qp = self.get(qp_var, qp_name)
fmode = 0
else:
val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
fmode = 1
return coef, val_qp, vvg, svg, fmode
elif mode == 'eval':
vvg, _ = self.get_mapping(vvar)
grad = self.get(svar, 'grad')
val = self.get(vvar, 'val')
return coef, grad, val, vvg
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))
[docs] def get_eval_shape(self, coef, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)
return (n_el, 1, 1, 1), vvar.dtype
[docs] def set_arg_types(self):
self.function = {
'v_weak' : terms.dw_v_dot_grad_s_vw,
's_weak' : terms.dw_v_dot_grad_s_sw,
'eval' : DotProductTerm.d_dot,
}[self.mode]
[docs]class VectorDotScalarTerm(Term):
r"""
Volume dot product of a vector and a scalar.
Can be evaluated.
:Definition:
.. math::
\int_{\Omega} \ul{v} \cdot \ul{c} p \mbox{ , }
\int_{\Omega} \ul{u} \cdot \ul{c} q\\
:Arguments 1:
- material : :math:`\ul{c}`
- virtual/parameter_v: :math:`\ul{v}`
- state/parameter_s: :math:`p`
:Arguments 2:
- material : :math:`\ul{c}`
- state : :math:`\ul{u}`
- virtual : :math:`q`
"""
name = 'dw_vm_dot_s'
arg_types = (('material', 'virtual', 'state'),
('material', 'state', 'virtual'),
('material', 'parameter_v', 'parameter_s'))
arg_shapes = [{'material' : 'D, 1',
'virtual/v_weak' : ('D', None), 'state/v_weak' : 1,
'virtual/s_weak' : (1, None), 'state/s_weak' : 'D',
'parameter_v' : 'D', 'parameter_s' : 1}]
modes = ('v_weak', 's_weak', 'eval')
[docs] @staticmethod
def dw_dot(out, mat, val_qp, bfve, bfsc, geo, fmode):
nel, nqp, dim, nc = mat.shape
nen = bfve.shape[3]
status1 = 0
if fmode in [0, 1, 3]:
aux = nm.zeros((nel, nqp, dim * nen, nc), dtype=nm.float64)
status1 = terms.actBfT(aux, bfve, mat)
if fmode == 0:
status2 = terms.mulAB_integrate(out, aux, val_qp, geo.cmap, 'AB')
if fmode == 1:
status2 = terms.mulAB_integrate(out, aux, bfsc, geo.cmap, 'AB')
if fmode == 2:
aux = (bfsc * dot_sequences(mat, val_qp,
mode='ATB')).transpose((0,1,3,2))
status2 = geo.integrate(out, nm.ascontiguousarray(aux))
if fmode == 3:
status2 = terms.mulAB_integrate(out, bfsc, aux, geo.cmap, 'ATBT')
return status1 and status2
[docs] @staticmethod
def d_dot(out, mat, val1_qp, val2_qp, geo):
v1, v2 = (val1_qp, val2_qp) if val1_qp.shape[2] > 1 \
else (val2_qp, val1_qp)
aux = dot_sequences(v1, mat, mode='ATB')
vec = dot_sequences(aux, v2, mode='AB')
status = geo.integrate(out, vec)
return status
[docs] def get_fargs(self, coef, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)
coef = coef.reshape(coef.shape[:2] + (dim, 1))
if mode == 'weak':
vgv, _ = self.get_mapping(vvar)
vgs, _ = self.get_mapping(svar)
bfve = vgv.bf
bfsc = vgs.bf
if self.mode == 'v_weak':
qp_var, geo, fmode = svar, vgv, 0
else:
qp_var, geo, fmode = vvar, vgs, 2
if diff_var is None:
val_qp = self.get(qp_var, 'val')
else:
val_qp = (nm.array([0], ndmin=4, dtype=nm.float64), 1)
fmode += 1
return coef, val_qp, bfve, bfsc, geo, fmode
elif mode == 'eval':
vvg, _ = self.get_mapping(vvar)
vals = self.get(svar, 'val')
valv = self.get(vvar, 'val')
return coef, vals, valv, vvg
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))
[docs] def get_eval_shape(self, coef, vvar, svar,
mode=None, term_mode=None, diff_var=None, **kwargs):
n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)
return (n_el, 1, 1, 1), vvar.dtype
[docs] def set_arg_types(self):
self.function = {
'v_weak' : self.dw_dot,
's_weak' : self.dw_dot,
'eval' : self.d_dot,
}[self.mode]
[docs]class ScalarDotGradIScalarTerm(Term):
r"""
Dot product of a scalar and the :math:`i`-th component of gradient of a
scalar. The index should be given as a 'special_constant' material
parameter.
:Definition:
.. math::
Z^i = \int_{\Omega} q \nabla_i p
:Arguments:
- material : :math:`i`
- virtual : :math:`q`
- state : :math:`p`
"""
name = 'dw_s_dot_grad_i_s'
arg_types = ('material', 'virtual', 'state')
arg_shapes = {'material' : '.: 1, 1', 'virtual' : (1, 'state'), 'state' : 1}
[docs] @staticmethod
def dw_fun(out, bf, vg, grad, idx, fmode):
cc = nm.ascontiguousarray
bft = cc(nm.tile(bf, (out.shape[0], 1, 1, 1)))
if fmode == 0:
status = terms.mulAB_integrate(out, bft,
cc(grad[..., idx:idx+1, :]),
vg.cmap, mode='ATB')
else:
status = terms.mulAB_integrate(out, bft,
cc(vg.bfg[:,:,idx:(idx + 1),:]),
vg.cmap, mode='ATB')
return status
[docs] def get_fargs(self, material, virtual, state,
mode=None, term_mode=None, diff_var=None, **kwargs):
if mode == 'weak':
if diff_var is None:
grad = self.get(state, 'grad')
fmode = 0
else:
grad = nm.array([0], ndmin=4, dtype=nm.float64)
fmode = 1
vg, _ = self.get_mapping(virtual)
vgs, _ = self.get_mapping(state)
idx = int(material[0, 0])
return vgs.bf, vg, grad, idx, fmode
else:
raise ValueError('unsupported evaluation mode in %s! (%s)'
% (self.name, mode))
[docs] def set_arg_types(self):
self.function = self.dw_fun
[docs]class ScalarDotMGradScalarTerm(Term):
r"""
Volume dot product of a scalar gradient dotted with a material vector with
a scalar.
:Definition:
.. math::
\int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , }
\int_{\Omega} p \ul{y} \cdot \nabla q
:Arguments 1:
- material : :math:`\ul{y}`
- virtual : :math:`q`
- state : :math:`p`
:Arguments 2:
- material : :math:`\ul{y}`
- state : :math:`p`
- virtual : :math:`q`
"""
name = 'dw_s_dot_mgrad_s'
arg_types = (('material', 'virtual', 'state'),
('material', 'state', 'virtual'))
arg_shapes = [{'material' : 'D, 1',
'virtual/grad_state' : (1, None),
'state/grad_state' : 1,
'virtual/grad_virtual' : (1, None),
'state/grad_virtual' : 1}]
modes = ('grad_state', 'grad_virtual')
[docs] @staticmethod
def function(out, out_qp, geo, fmode):
status = geo.integrate(out, out_qp)
return status
[docs] def get_fargs(self, mat, var1, var2,
mode=None, term_mode=None, diff_var=None, **kwargs):
vg1, _ = self.get_mapping(var1)
vg2, _ = self.get_mapping(var2)
if diff_var is None:
if self.mode == 'grad_state':
geo = vg1
bf_t = vg1.bf.transpose((0, 1, 3, 2))
val_qp = self.get(var2, 'grad')
out_qp = bf_t * dot_sequences(mat, val_qp, 'ATB')
else:
geo = vg2
val_qp = self.get(var1, 'val')
out_qp = dot_sequences(vg2.bfg, mat, 'ATB') * val_qp
fmode = 0
else:
if self.mode == 'grad_state':
geo = vg1
bf_t = vg1.bf.transpose((0, 1, 3, 2))
out_qp = bf_t * dot_sequences(mat, vg2.bfg, 'ATB')
else:
geo = vg2
out_qp = dot_sequences(vg2.bfg, mat, 'ATB') * vg1.bf
fmode = 1
return out_qp, geo, fmode