sfepy.terms.terms_adj_navier_stokes module¶
-
class
sfepy.terms.terms_adj_navier_stokes.
AdjConvect1Term
(name, arg_str, integral, region, **kwargs)[source]¶ The first adjoint term to nonlinear convective term dw_convect.
- Definition
\int_{\Omega} ((\ul{v} \cdot \nabla) \ul{u}) \cdot \ul{w}
- Call signature
dw_adj_convect1
(virtual, state, parameter)
- Arguments
virtual : \ul{v}
state : \ul{w}
parameter : \ul{u}
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arg_shapes
= {'parameter': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶
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arg_types
= ('virtual', 'state', 'parameter')¶
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static
function
()¶
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name
= 'dw_adj_convect1'¶
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class
sfepy.terms.terms_adj_navier_stokes.
AdjConvect2Term
(name, arg_str, integral, region, **kwargs)[source]¶ The second adjoint term to nonlinear convective term dw_convect.
- Definition
\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{v}) \cdot \ul{w}
- Call signature
dw_adj_convect2
(virtual, state, parameter)
- Arguments
virtual : \ul{v}
state : \ul{w}
parameter : \ul{u}
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arg_shapes
= {'parameter': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶
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arg_types
= ('virtual', 'state', 'parameter')¶
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static
function
()¶
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name
= 'dw_adj_convect2'¶
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class
sfepy.terms.terms_adj_navier_stokes.
AdjDivGradTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Gateaux differential of \Psi(\ul{u}) = \int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} w.r.t. \ul{u} in the direction \ul{v} or adjoint term to dw_div_grad.
- Definition
w \delta_{u} \Psi(\ul{u}) \circ \ul{v}
- Call signature
dw_adj_div_grad
(material_1, material_2, virtual, parameter)
- Arguments
material_1 : w (weight)
material_2 : \nu (viscosity)
virtual : \ul{v}
state : \ul{u}
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arg_shapes
= {'material_1': '1, 1', 'material_2': '1, 1', 'parameter': 'D', 'virtual': ('D', None)}¶
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arg_types
= ('material_1', 'material_2', 'virtual', 'parameter')¶
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static
function
()¶
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name
= 'dw_adj_div_grad'¶
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class
sfepy.terms.terms_adj_navier_stokes.
NSOFMinGradTerm
(name, arg_str, integral, region, **kwargs)[source]¶ - Call signature
d_of_ns_min_grad
(material_1, material_2, parameter)
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arg_shapes
= {'material_1': '1, 1', 'material_2': '1, 1', 'parameter': 1}¶
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arg_types
= ('material_1', 'material_2', 'parameter')¶
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static
function
()¶
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name
= 'd_of_ns_min_grad'¶
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class
sfepy.terms.terms_adj_navier_stokes.
NSOFSurfMinDPressDiffTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Gateaux differential of \Psi(p) w.r.t. p in the direction q.
- Definition
w \delta_{p} \Psi(p) \circ q
- Call signature
dw_of_ns_surf_min_d_press_diff
(material, virtual)
- Arguments
material : w (weight)
virtual : q
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arg_shapes
= {'material': 1, 'virtual': (1, None)}¶
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arg_types
= ('material', 'virtual')¶
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name
= 'dw_of_ns_surf_min_d_press_diff'¶
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class
sfepy.terms.terms_adj_navier_stokes.
NSOFSurfMinDPressTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity of \Psi(p).
- Definition
\delta \Psi(p) = \delta \left( \int_{\Gamma_{in}}p - \int_{\Gamma_{out}}bpress \right)
- Call signature
d_of_ns_surf_min_d_press
(material_1, material_2, parameter)
- Arguments
material_1 : w (weight)
material_2 : bpress (given pressure)
parameter : p
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arg_shapes
= {'material_1': 1, 'material_2': 1, 'parameter': 1}¶
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arg_types
= ('material_1', 'material_2', 'parameter')¶
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static
function
()¶
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get_eval_shape
(weight, bpress, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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integration
= 'surface'¶
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name
= 'd_of_ns_surf_min_d_press'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SDConvectTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of convective term dw_convect.
Supports the following term modes: 1 (sensitivity) or 0 (original term value).
- Definition
\int_{\Omega} [ u_k \pdiff{u_i}{x_k} w_i (\nabla \cdot \Vcal) - u_k \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} w_i ]
- Call signature
d_sd_convect
(parameter_u, parameter_w, parameter_mesh_velocity)
- Arguments
parameter_u : \ul{u}
parameter_w : \ul{w}
parameter_mesh_velocity : \ul{\Vcal}
-
arg_shapes
= {'parameter_mesh_velocity': 'D', 'parameter_u': 'D', 'parameter_w': 'D'}¶
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arg_types
= ('parameter_u', 'parameter_w', 'parameter_mesh_velocity')¶
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static
function
()¶
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name
= 'd_sd_convect'¶
-
class
sfepy.terms.terms_adj_navier_stokes.
SDDivGradTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of diffusion term dw_div_grad.
Supports the following term modes: 1 (sensitivity) or 0 (original term value).
- Definition
w \nu \int_{\Omega} [ \pdiff{u_i}{x_k} \pdiff{w_i}{x_k} (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} \pdiff{w_i}{x_k} - \pdiff{u_i}{x_k} \pdiff{\Vcal_l}{x_k} \pdiff{w_i}{x_k} ]
- Call signature
d_sd_div_grad
(material_1, material_2, parameter_u, parameter_w, parameter_mesh_velocity)
- Arguments
material_1 : w (weight)
material_2 : \nu (viscosity)
parameter_u : \ul{u}
parameter_w : \ul{w}
parameter_mesh_velocity : \ul{\Vcal}
-
arg_shapes
= {'material_1': '1, 1', 'material_2': '1, 1', 'parameter_mesh_velocity': 'D', 'parameter_u': 'D', 'parameter_w': 'D'}¶
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arg_types
= ('material_1', 'material_2', 'parameter_u', 'parameter_w', 'parameter_mesh_velocity')¶
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static
function
()¶
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get_eval_shape
(mat1, mat2, par_u, par_w, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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get_fargs
(mat1, mat2, par_u, par_w, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'd_sd_div_grad'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SDDivTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of Stokes term dw_stokes in ‘div’ mode.
Supports the following term modes: 1 (sensitivity) or 0 (original term value).
- Definition
\int_{\Omega} p [ (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_k}{x_i} \pdiff{w_i}{x_k} ]
- Call signature
d_sd_div
(parameter_u, parameter_p, parameter_mesh_velocity)
- Arguments
parameter_u : \ul{u}
parameter_p : p
parameter_mesh_velocity : \ul{\Vcal}
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arg_shapes
= {'parameter_mesh_velocity': 'D', 'parameter_p': 1, 'parameter_u': 'D'}¶
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arg_types
= ('parameter_u', 'parameter_p', 'parameter_mesh_velocity')¶
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static
function
()¶
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name
= 'd_sd_div'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SDDotVolumeTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of dot product of scalars or vectors.
- Definition
\int_{\Omega} p q (\nabla \cdot \ul{\Vcal}) \mbox{ , } \int_{\Omega} (\ul{u} \cdot \ul{w}) (\nabla \cdot \ul{\Vcal})
- Call signature
d_sd_volume_dot
(parameter_1, parameter_2, parameter_mesh_velocity)
- Arguments
parameter_1 : p or \ul{u}
parameter_2 : q or \ul{w}
parameter_mesh_velocity : \ul{\Vcal}
-
arg_shapes
= [{'parameter_1': 'D', 'parameter_2': 'D', 'parameter_mesh_velocity': 'D'}, {'parameter_1': 1, 'parameter_2': 1}]¶
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arg_types
= ('parameter_1', 'parameter_2', 'parameter_mesh_velocity')¶
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static
function
()¶
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name
= 'd_sd_volume_dot'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SDGradDivStabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of stabilization term dw_st_grad_div.
- Definition
\gamma \int_{\Omega} [ (\nabla \cdot \ul{u}) (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{u_i}{x_k} \pdiff{\Vcal_k}{x_i} (\nabla \cdot \ul{w}) - (\nabla \cdot \ul{u}) \pdiff{w_i}{x_k} \pdiff{\Vcal_k}{x_i} ]
- Call signature
d_sd_st_grad_div
(material, parameter_u, parameter_w, parameter_mesh_velocity)
- Arguments
material : \gamma
parameter_u : \ul{u}
parameter_w : \ul{w}
parameter_mesh_velocity : \ul{\Vcal}
mode : 1 (sensitivity) or 0 (original term value)
-
arg_shapes
= {'material': '1, 1', 'parameter_mesh_velocity': 'D', 'parameter_u': 'D', 'parameter_w': 'D'}¶
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arg_types
= ('material', 'parameter_u', 'parameter_w', 'parameter_mesh_velocity')¶
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static
function
()¶
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get_eval_shape
(mat, par_u, par_w, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'd_sd_st_grad_div'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SDPSPGCStabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of stabilization terms dw_st_supg_p or dw_st_pspg_c.
- Definition
\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ \pdiff{r}{x_i} (\ul{b} \cdot \nabla u_i) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} \pdiff{\Vcal_k}{x_i} (\ul{b} \cdot \nabla u_i) - \pdiff{r}{x_k} (\ul{b} \cdot \nabla \Vcal_k) \pdiff{u_i}{x_k} ]
- Call signature
d_sd_st_pspg_c
(material, parameter_b, parameter_u, parameter_r, parameter_mesh_velocity)
- Arguments
material : \delta_K
parameter_b : \ul{b}
parameter_u : \ul{u}
parameter_r : r
parameter_mesh_velocity : \ul{\Vcal}
mode : 1 (sensitivity) or 0 (original term value)
-
arg_shapes
= {'material': '1, 1', 'parameter_b': 'D', 'parameter_mesh_velocity': 'D', 'parameter_r': 1, 'parameter_u': 'D'}¶
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arg_types
= ('material', 'parameter_b', 'parameter_u', 'parameter_r', 'parameter_mesh_velocity')¶
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static
function
()¶
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get_eval_shape
(mat, par_b, par_u, par_r, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
get_fargs
(mat, par_b, par_u, par_r, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'd_sd_st_pspg_c'¶
-
class
sfepy.terms.terms_adj_navier_stokes.
SDPSPGPStabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of stabilization term dw_st_pspg_p.
- Definition
\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ [ (\nabla r \cdot \nabla p) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} (\nabla \Vcal_k \cdot \nabla p) - (\nabla r \cdot \nabla \Vcal_k) \pdiff{p}{x_k} ]
- Call signature
d_sd_st_pspg_p
(material, parameter_r, parameter_p, parameter_mesh_velocity)
- Arguments
material : \tau_K
parameter_r : r
parameter_p : p
parameter_mesh_velocity : \ul{\Vcal}
mode : 1 (sensitivity) or 0 (original term value)
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arg_shapes
= {'material': '1, 1', 'parameter_mesh_velocity': 'D', 'parameter_p': 1, 'parameter_r': 1}¶
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arg_types
= ('material', 'parameter_r', 'parameter_p', 'parameter_mesh_velocity')¶
-
static
function
()¶
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get_eval_shape
(mat, par_r, par_p, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'd_sd_st_pspg_p'¶
-
class
sfepy.terms.terms_adj_navier_stokes.
SDSUPGCStabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Sensitivity (shape derivative) of stabilization term dw_st_supg_c.
- Definition
\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ (\ul{b} \cdot \nabla u_k) (\ul{b} \cdot \nabla w_k) (\nabla \cdot \Vcal) - (\ul{b} \cdot \nabla \Vcal_i) \pdiff{u_k}{x_i} (\ul{b} \cdot \nabla w_k) - (\ul{u} \cdot \nabla u_k) (\ul{b} \cdot \nabla \Vcal_i) \pdiff{w_k}{x_i} ]
- Call signature
d_sd_st_supg_c
(material, parameter_b, parameter_u, parameter_w, parameter_mesh_velocity)
- Arguments
material : \delta_K
parameter_b : \ul{b}
parameter_u : \ul{u}
parameter_w : \ul{w}
parameter_mesh_velocity : \ul{\Vcal}
mode : 1 (sensitivity) or 0 (original term value)
-
arg_shapes
= {'material': '1, 1', 'parameter_b': 'D', 'parameter_mesh_velocity': 'D', 'parameter_u': 'D', 'parameter_w': 'D'}¶
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arg_types
= ('material', 'parameter_b', 'parameter_u', 'parameter_w', 'parameter_mesh_velocity')¶
-
static
function
()¶
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get_eval_shape
(mat, par_b, par_u, par_w, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
get_fargs
(mat, par_b, par_u, par_w, par_mv, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'd_sd_st_supg_c'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SUPGCAdjStabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ Adjoint term to SUPG stabilization term dw_st_supg_c.
- Definition
\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ ((\ul{v} \cdot \nabla) \ul{u}) ((\ul{u} \cdot \nabla) \ul{w}) + ((\ul{u} \cdot \nabla) \ul{u}) ((\ul{v} \cdot \nabla) \ul{w}) ]
- Call signature
dw_st_adj_supg_c
(material, virtual, parameter, state)
- Arguments
material : \delta_K
virtual : \ul{v}
state : \ul{w}
parameter : \ul{u}
-
arg_shapes
= {'material': '1, 1', 'parameter': 'D', 'state': 'D', 'virtual': ('D', 'state')}¶
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arg_types
= ('material', 'virtual', 'parameter', 'state')¶
-
static
function
()¶
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get_fargs
(mat, virtual, state, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'dw_st_adj_supg_c'¶
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class
sfepy.terms.terms_adj_navier_stokes.
SUPGPAdj1StabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ The first adjoint term to SUPG stabilization term dw_st_supg_p.
- Definition
\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p (\ul{v} \cdot \nabla \ul{w})
- Call signature
dw_st_adj1_supg_p
(material, virtual, state, parameter)
- Arguments
material : \delta_K
virtual : \ul{v}
state : \ul{w}
parameter : p
-
arg_shapes
= {'material': '1, 1', 'parameter': 1, 'state': 'D', 'virtual': ('D', 'state')}¶
-
arg_types
= ('material', 'virtual', 'state', 'parameter')¶
-
static
function
()¶
-
get_fargs
(mat, virtual, state, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
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name
= 'dw_st_adj1_supg_p'¶
-
class
sfepy.terms.terms_adj_navier_stokes.
SUPGPAdj2StabilizationTerm
(name, arg_str, integral, region, **kwargs)[source]¶ The second adjoint term to SUPG stabilization term dw_st_supg_p as well as adjoint term to PSPG stabilization term dw_st_pspg_c.
- Definition
\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla r (\ul{v} \cdot \nabla \ul{u})
- Call signature
dw_st_adj2_supg_p
(material, virtual, parameter, state)
- Arguments
material : \tau_K
virtual : \ul{v}
parameter : \ul{u}
state : r
-
arg_shapes
= {'material': '1, 1', 'parameter': 'D', 'state': 1, 'virtual': ('D', 'state')}¶
-
arg_types
= ('material', 'virtual', 'parameter', 'state')¶
-
static
function
()¶
-
get_fargs
(mat, virtual, parameter, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶
-
name
= 'dw_st_adj2_supg_p'¶