sfepy.terms.terms_dot module¶
-
class
sfepy.terms.terms_dot.
BCNewtonTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Newton boundary condition term.
- Definition
\int_{\Gamma} \alpha q (p - p_{\rm outer})
- Call signature
dw_bc_newton
(material_1, material_2, virtual, state)
- Arguments
material_1 : \alpha
material_2 : p_{\rm outer}
virtual : q
state : p
-
arg_shapes
= {'material_1': '1, 1', 'material_2': '1, 1', 'state': 1, 'virtual': (1, 'state')}¶
-
arg_types
= ('material_1', 'material_2', 'virtual', 'state')¶
-
get_fargs
(alpha, p_outer, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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mode
= 'weak'¶
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name
= 'dw_bc_newton'¶
-
class
sfepy.terms.terms_dot.
DotProductSurfaceTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Surface L^2(\Gamma) dot product for both scalar and vector fields.
- Definition
\int_\Gamma q p \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , } \int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , } \int_\Gamma p r \mbox{ , } \int_\Gamma \ul{u} \cdot \ul{w} \mbox{ , } \int_\Gamma \ul{w} \cdot \ul{n} p \\ \int_\Gamma c q p \mbox{ , } \int_\Gamma c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma c p r \mbox{ , } \int_\Gamma c \ul{u} \cdot \ul{w} \\ \int_\Gamma \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{u} \cdot \ull{M} \cdot \ul{w}
- Call signature
dw_surface_dot
(opt_material, virtual, state)
(opt_material, parameter_1, parameter_2)
- Arguments 1
material : c or \ull{M} (optional)
virtual : q or \ul{v}
state : p or \ul{u}
- Arguments 2
material : c or \ull{M} (optional)
parameter_1 : p or \ul{u}
parameter_2 : r or \ul{w}
-
arg_shapes
= [{'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}]¶
-
arg_types
= (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶
-
integration
= 'surface'¶
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modes
= ('weak', 'eval')¶
-
name
= 'dw_surface_dot'¶
-
class
sfepy.terms.terms_dot.
DotProductVolumeTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Volume L^2(\Omega) weighted dot product for both scalar and vector fields. Can be evaluated. Can use derivatives.
- Definition
\int_\Omega q p \mbox{ , } \int_\Omega \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega p r \mbox{ , } \int_\Omega \ul{u} \cdot \ul{w} \\ \int_\Omega c q p \mbox{ , } \int_\Omega c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega c p r \mbox{ , } \int_\Omega c \ul{u} \cdot \ul{w} \\ \int_\Omega \ul{v} \cdot (\ull{M} \ul{u}) \mbox{ , } \int_\Omega \ul{u} \cdot (\ull{M} \ul{w})
- Call signature
dw_volume_dot
(opt_material, virtual, state)
(opt_material, parameter_1, parameter_2)
- Arguments 1
material : c or \ull{M} (optional)
virtual : q or \ul{v}
state : p or \ul{u}
- Arguments 2
material : c or \ull{M} (optional)
parameter_1 : p or \ul{u}
parameter_2 : r or \ul{w}
-
arg_shapes
= [{'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}]¶
-
arg_types
= (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶
-
modes
= ('weak', 'eval')¶
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name
= 'dw_volume_dot'¶
-
class
sfepy.terms.terms_dot.
DotSProductVolumeOperatorWETHTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Fading memory volume 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
\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q
- Call signature
dw_volume_dot_w_scalar_eth
(ts, material_0, material_1, virtual, state)
- Arguments
ts :
TimeStepper
instancematerial_0 : \Gcal(0)
material_1 : \exp(-\lambda \Delta t) (decay at t_1)
virtual : q
state : p
-
arg_shapes
= {'material_0': '1, 1', 'material_1': '1, 1', 'state': 1, 'virtual': (1, 'state')}¶
-
arg_types
= ('ts', 'material_0', 'material_1', 'virtual', 'state')¶
-
static
function
()¶
-
get_fargs
(ts, mat0, mat1, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
name
= 'dw_volume_dot_w_scalar_eth'¶
-
class
sfepy.terms.terms_dot.
DotSProductVolumeOperatorWTHTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Fading memory volume L^2(\Omega) weighted dot product for scalar fields. Can use derivatives.
- Definition
\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q
- Call signature
dw_volume_dot_w_scalar_th
(ts, material, virtual, state)
- Arguments
ts :
TimeStepper
instancematerial : \Gcal(\tau)
virtual : q
state : p
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arg_shapes
= {'material': '.: N, 1, 1', 'state': 1, 'virtual': (1, 'state')}¶
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arg_types
= ('ts', 'material', 'virtual', 'state')¶
-
static
function
()¶
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name
= 'dw_volume_dot_w_scalar_th'¶
-
class
sfepy.terms.terms_dot.
ScalarDotGradIScalarTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Dot product of a scalar and the i-th component of gradient of a scalar. The index should be given as a ‘special_constant’ material parameter.
- Definition
Z^i = \int_{\Omega} q \nabla_i p
- Call signature
dw_s_dot_grad_i_s
(material, virtual, state)
- Arguments
material : i
virtual : q
state : p
-
arg_shapes
= {'material': '.: 1, 1', 'state': 1, 'virtual': (1, 'state')}¶
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arg_types
= ('material', 'virtual', 'state')¶
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name
= 'dw_s_dot_grad_i_s'¶
-
class
sfepy.terms.terms_dot.
ScalarDotMGradScalarTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Volume dot product of a scalar gradient dotted with a material vector with a scalar.
- Definition
\int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , } \int_{\Omega} p \ul{y} \cdot \nabla q
- Call signature
dw_s_dot_mgrad_s
(material, virtual, state)
(material, state, virtual)
- Arguments 1
material : \ul{y}
virtual : q
state : p
- Arguments 2
material : \ul{y}
state : p
virtual : q
-
arg_shapes
= [{'material': 'D, 1', 'virtual/grad_state': (1, None), 'state/grad_state': 1, 'virtual/grad_virtual': (1, None), 'state/grad_virtual': 1}]¶
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arg_types
= (('material', 'virtual', 'state'), ('material', 'state', 'virtual'))¶
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modes
= ('grad_state', 'grad_virtual')¶
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name
= 'dw_s_dot_mgrad_s'¶
-
class
sfepy.terms.terms_dot.
VectorDotGradScalarTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Volume dot product of a vector and a gradient of scalar. Can be evaluated.
- Definition
\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{M} \nabla p) \mbox{ , } \int_{\Omega} \ul{u} \cdot (\ull{M} \nabla q)
- Call signature
dw_v_dot_grad_s
(opt_material, virtual, state)
(opt_material, state, virtual)
(opt_material, parameter_v, parameter_s)
- Arguments 1
material : c or \ull{M} (optional)
virtual : \ul{v}
state : p
- Arguments 2
material : c or \ull{M} (optional)
state : \ul{u}
virtual : q
- Arguments 3
material : c or \ull{M} (optional)
parameter_v : \ul{u}
parameter_s : p
-
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}]¶
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arg_types
= (('opt_material', 'virtual', 'state'), ('opt_material', 'state', 'virtual'), ('opt_material', 'parameter_v', 'parameter_s'))¶
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modes
= ('v_weak', 's_weak', 'eval')¶
-
name
= 'dw_v_dot_grad_s'¶
-
class
sfepy.terms.terms_dot.
VectorDotScalarTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Volume dot product of a vector and a scalar. Can be evaluated.
- Definition
\int_{\Omega} \ul{v} \cdot \ul{m} p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ul{m} q\\
- Call signature
dw_vm_dot_s
(material, virtual, state)
(material, state, virtual)
(material, parameter_v, parameter_s)
- Arguments 1
material : \ul{m}
virtual : \ul{v}
state : p
- Arguments 2
material : \ul{m}
state : \ul{u}
virtual : q
- Arguments 3
material : \ul{m}
parameter_v : \ul{u}
parameter_s : p
-
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}]¶
-
arg_types
= (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_v', 'parameter_s'))¶
-
modes
= ('v_weak', 's_weak', 'eval')¶
-
name
= 'dw_vm_dot_s'¶