sfepy.terms.terms_dot module¶
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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
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arg_shapes
= {'material_1': '1, 1', 'material_2': '1, 1', 'state': 1, 'virtual': (1, 'state')}¶
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arg_types
= ('material_1', 'material_2', 'virtual', 'state')¶
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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'¶
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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}
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arg_types
= (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶
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integration
= 'surface'¶
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modes
= ('weak', 'eval')¶
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name
= 'dw_surface_dot'¶
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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} \cdot \ul{u} \mbox{ , } \int_\Omega \ul{u} \cdot \ull{M} \cdot \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}
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arg_shapes
= [{'opt_material': '1, 1', 'state': 1, 'parameter_1': 1, 'virtual': (1, 'state'), 'parameter_2': 1}, {'opt_material': None}, {'opt_material': '1, 1', 'state': 'D', 'parameter_1': 'D', 'virtual': ('D', 'state'), 'parameter_2': 'D'}, {'opt_material': 'D, D'}, {'opt_material': None}]¶
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arg_types
= (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶
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modes
= ('weak', 'eval')¶
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name
= 'dw_volume_dot'¶
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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
instance - material_0 : \Gcal(0)
- material_1 : \exp(-\lambda \Delta t) (decay at t_1)
- virtual : q
- state : p
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arg_types
= ('ts', 'material_0', 'material_1', 'virtual', 'state')¶
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static
function
()¶
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get_fargs
(ts, mat0, mat1, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'dw_volume_dot_w_scalar_eth'¶
- ts :
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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
instance - material : \Gcal(\tau)
- virtual : q
- state : p
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arg_types
= ('ts', 'material', 'virtual', 'state')¶
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static
function
()¶
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name
= 'dw_volume_dot_w_scalar_th'¶
- ts :
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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
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arg_shapes
= {'state': 1, 'material': '1, 1', 'virtual': (1, 'state')}¶
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arg_types
= ('material', 'virtual', 'state')¶
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name
= 'dw_s_dot_grad_i_s'¶
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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} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ull{M} \cdot \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
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arg_shapes
= [{'opt_material': '1, 1', 'state/s_weak': 'D', 'parameter_s': 1, 'virtual/v_weak': ('D', None), 'virtual/s_weak': (1, None), 'parameter_v': 'D', 'state/v_weak': 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')¶
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name
= 'dw_v_dot_grad_s'¶