sfepy.terms.terms_acoustic module
sfepy.terms.terms_basic module
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The first adjoint term to nonlinear convective term dw_convect.
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\int_{\Omega} ((\ul{v} \cdot \nabla) \ul{u}) \cdot \ul{w}
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dw_adj_convect1 | (virtual, state, parameter) |
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The second adjoint term to nonlinear convective term dw_convect.
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\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{v}) \cdot \ul{w}
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dw_adj_convect2 | (virtual, state, parameter) |
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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.
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w \delta_{u} \Psi(\ul{u}) \circ \ul{v}
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dw_adj_div_grad | (material_1, material_2, virtual, parameter) |
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d_of_ns_min_grad | (material_1, material_2, parameter) |
Gateaux differential of \Psi(p) w.r.t. p in the direction q.
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w \delta_{p} \Psi(p) \circ q
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dw_of_ns_surf_min_d_press_diff | (material, virtual) |
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Sensitivity of \Psi(p).
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\delta \Psi(p) = \delta \left( \int_{\Gamma_{in}}p - \int_{\Gamma_{out}}bpress \right)
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d_of_ns_surf_min_d_press | (material_1, material_2, parameter) |
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Sensitivity (shape derivative) of convective term dw_convect.
Supports the following term modes: 1 (sensitivity) or 0 (original term value).
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\int_{\Omega_D} [ 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 ]
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d_sd_convect | (parameter_u, parameter_w, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of diffusion term dw_div_grad.
Supports the following term modes: 1 (sensitivity) or 0 (original term value).
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w \nu \int_{\Omega_D} [ \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} ]
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d_sd_div_grad | (material_1, material_2, parameter_u, parameter_w, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of Stokes term dw_stokes in ‘div’ mode.
Supports the following term modes: 1 (sensitivity) or 0 (original term value).
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\int_{\Omega_D} p [ (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_k}{x_i} \pdiff{w_i}{x_k} ]
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d_sd_div | (parameter_u, parameter_p, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of dot product of scalars or vectors.
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\int_{\Omega_D} p q (\nabla \cdot \ul{\Vcal}) \mbox{ , } \int_{\Omega_D} (\ul{u} \cdot \ul{w}) (\nabla \cdot \ul{\Vcal})
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d_sd_volume_dot | (parameter_1, parameter_2, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of stabilization term dw_st_grad_div.
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\gamma \int_{\Omega_D} [ (\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} ]
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d_sd_st_grad_div | (material, parameter_u, parameter_w, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of stabilization terms dw_st_supg_p or dw_st_pspg_c.
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\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} ]
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d_sd_st_pspg_c | (material, parameter_b, parameter_u, parameter_r, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of stabilization term dw_st_pspg_p.
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\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} ]
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d_sd_st_pspg_p | (material, parameter_r, parameter_p, parameter_mesh_velocity) |
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Sensitivity (shape derivative) of stabilization term dw_st_supg_c.
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\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} ]
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d_sd_st_supg_c | (material, parameter_b, parameter_u, parameter_w, parameter_mesh_velocity) |
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Adjoint term to SUPG stabilization term dw_st_supg_c.
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\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}) ]
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dw_st_adj_supg_c | (material, virtual, parameter, state) |
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The first adjoint term to SUPG stabilization term dw_st_supg_p.
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\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p (\ul{v} \cdot \nabla \ul{w})
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dw_st_adj1_supg_p | (material, virtual, state, parameter) |
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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.
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\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla r (\ul{v} \cdot \nabla \ul{u})
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dw_st_adj2_supg_p | (material, virtual, parameter, state) |
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