Term Overview¶

Term Syntax¶

In general, the syntax of a term call is:

<term name>.<i>.<r>( <arg1>, <arg2>, ... ),

where <i> denotes an integral name (i.e. a name of numerical quadrature to use) and <r> marks a region (domain of the integral).

The following notation is used:

Notation.
symbol	meaning
$\Omega$	volume (sub)domain
$\Gamma$	surface (sub)domain
$d$	dimension of space
$t$	time
$y$	any function
$\ul{y}$	any vector function
$\ul{n}$	unit outward normal
$q$ , $s$	scalar test function
$p$ , $r$	scalar unknown or parameter function
$\bar{p}$	scalar parameter function
$\ul{v}$	vector test function
$\ul{w}$ , $\ul{u}$	vector unknown or parameter function
$\ul{b}$	vector parameter function
$\ull{e}(\ul{u})$	Cauchy strain tensor ( $\frac{1}{2}((\nabla u) + (\nabla u)^T)$ )
$\ull{F}$	deformation gradient $F_{ij} = \pdiff{x_i}{X_j}$
$J$	$\det(F)$
$\ull{C}$	right Cauchy-Green deformation tensor $C = F^T F$
$\ull{E}(\ul{u})$	Green strain tensor $E_{ij} = \frac{1}{2}(\pdiff{u_i}{x_j} + \pdiff{u_j}{x_i} + \pdiff{u_m}{x_i}\pdiff{u_m}{x_j})$
$\ull{S}$	second Piola-Kirchhoff stress tensor
$\ul{f}$	vector volume forces
$f$	scalar volume force (source)
$\rho$	density
$\nu$	kinematic viscosity
$c$	any constant
$\delta_{ij}, \ull{I}$	Kronecker delta, identity matrix
$\tr{\ull{\bullet}}$	trace of a second order tensor ( $\sum_{i=1}^d \bullet_{ii}$ )
$\dev{\ull{\bullet}}$	deviator of a second order tensor ( $\ull{\bullet} - \frac{1}{d}\tr{\ull{\bullet}}$ )
$T_K \in \Tcal_h$	$K$ -th element of triangulation (= mesh) $\Tcal_h$ of domain $\Omega$
$K \from \Ical_h$	$K$ is assigned values from $\{0, 1, \dots, N_h-1\} \equiv \Ical_h$ in ascending order

The suffix “ $_0$ ” denotes a quantity related to a previous time step.

Term names are (usually) prefixed according to the following conventions:

Term name prefixes.
prefix	meaning	evaluation modes	meaning
dw	discrete weak	‘weak’	terms having a virtual (test) argument and zero or more unknown arguments, used for FE assembling
d	discrete	‘eval’	terms having all arguments known, the result is the scalar value of the integral
di	discrete integrated	‘eval’	like ‘d’ but the result is not a scalar (e.g. a vector)
dq	discrete quadrature	‘qp’	terms having all arguments known, the result are the values in quadrature points of elements
ev	evaluate	‘eval’, ‘el_avg’, ‘qp’	terms having all arguments known and supporting all evaluation modes except ‘weak’ (no virtual variables in arguments, no FE assembling)

Term Table¶

Below we list all the terms available in an automatically generated table. The first column lists the name, the second column the argument lists and the third column the mathematical definition of each term.

The notation <virtual> corresponds to a test function, <state> to a unknown function and <parameter> to a known function. By <material> we denote material (constitutive) parameters, or, in general, any given function of space and time that parameterizes a term, for example a given traction force vector.

Table of all terms.
name/class/link	arguments	definition
dw_adj_convect1 `AdjConvect1Term` `termsAdjointNavierStokes`	`<virtual>, <state>, <parameter>`	$\int_{\Omega} ((\ul{v} \cdot \nabla) \ul{u}) \cdot \ul{w}$
dw_adj_convect2 `AdjConvect2Term` `termsAdjointNavierStokes`	`<virtual>, <state>, <parameter>`	$\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{v}) \cdot \ul{w}$
dw_adj_div_grad `AdjDivGradTerm` `termsAdjointNavierStokes`	`<material_1>, <material_2>, <virtual>, <parameter>`	$w \delta_{u} \Psi(\ul{u}) \circ \ul{v}$
dw_bc_newton `BCNewtonTerm` `terms_dot`	`<material_1>, <material_2>, <virtual>, <state>`	$\int_{\Gamma} \alpha q (p - p_{\rm outer})$
dw_biot `BiotTerm` `termsBiot`	`<material>, <virtual>, <state>` `<material>, <state>, <virtual>` `<material>, <parameter_v>, <parameter_s>`	$\int_{\Omega} p\ \alpha_{ij} e_{ij}(\ul{v}) \mbox{ , } \int_{\Omega} q\ \alpha_{ij} e_{ij}(\ul{u})$
dw_biot_eth `BiotETHTerm` `termsBiot`	`<ts>, <material_0>, <material_1>, <virtual>, <state>` `<ts>, <material_0>, <material_1>, <state>, <virtual>`	$\begin{array}{l} \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v}) \mbox{ ,} \\ \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q \end{array}$
ev_biot_stress `BiotStressTerm` `termsBiot`	`<material>, <parameter>`	$- \int_{\Omega} \alpha_{ij} \bar{p}$ $\mbox{vector for } K \from \Ical_h: - \int_{T_K} \alpha_{ij} \bar{p} / \int_{T_K} 1$ $- \alpha_{ij} \bar{p}\|_{qp}$
dw_biot_th `BiotTHTerm` `termsBiot`	`<ts>, <material>, <virtual>, <state>` `<ts>, <material>, <state>, <virtual>`	$\begin{array}{l} \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v}) \mbox{ ,} \\ \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q \end{array}$
ev_cauchy_strain `CauchyStrainTerm` `termsLinElasticity`	`<parameter>`	$\int_{\Omega} \ull{e}(\ul{w})$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \ull{e}(\ul{w}) / \int_{T_K} 1$ $\ull{e}(\ul{w})\|_{qp}$
ev_cauchy_strain_s `CauchyStrainSTerm` `termsLinElasticity`	`<parameter>`	$\int_{\Gamma} \ull{e}(\ul{w})$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \ull{e}(\ul{w}) / \int_{T_K} 1$ $\ull{e}(\ul{w})\|_{qp}$
ev_cauchy_stress `CauchyStressTerm` `termsLinElasticity`	`<material>, <parameter>`	$\int_{\Omega} D_{ijkl} e_{kl}(\ul{w})$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} D_{ijkl} e_{kl}(\ul{w}) / \int_{T_K} 1$ $D_{ijkl} e_{kl}(\ul{w})\|_{qp}$
ev_cauchy_stress_eth `CauchyStressETHTerm` `termsLinElasticity`	`<ts>, <material_0>, <material_1>, <parameter>`	$\int_{\Omega} \int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau} / \int_{T_K} 1$ $\int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau}\|_{qp}$
ev_cauchy_stress_th `CauchyStressTHTerm` `termsLinElasticity`	`<ts>, <material>, <parameter>`	$\int_{\Omega} \int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau} / \int_{T_K} 1$ $\int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{w}(\tau)) \difd{\tau}\|_{qp}$
dw_convect `ConvectTerm` `termsNavierStokes`	`<virtual>, <state>`	$\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v}$
dq_def_grad `DeformationGradientTerm` `terms_hyperelastic_base`	`<state>`	$\ull{F} = \pdiff{\ul{x}}{\ul{X}}\|_{qp} = \ull{I} + \pdiff{\ul{u}}{\ul{X}}\|_{qp} \;, \\ \ul{x} = \ul{X} + \ul{u} \;, J = \det{(\ull{F})}$
dw_diffusion `DiffusionTerm` `termsLaplace`	`<material>, <virtual>, <state>` `<material>, <parameter_1>, <parameter_2>`	$\int_{\Omega} K_{ij} \nabla_i q \nabla_j p \mbox{ , } \int_{\Omega} K_{ij} \nabla_i \bar{p} \nabla_j r$
dw_diffusion_coupling `DiffusionCoupling` `termsLaplace`	`<material>, <virtual>, <state>` `<material>, <state>, <virtual>` `<material>, <parameter_1>, <parameter_2>`	$\int_{\Omega} p K_{j} \nabla_j q$
dw_diffusion_r `DiffusionRTerm` `termsLaplace`	`<material>, <virtual>`	$\int_{\Omega} K_{j} \nabla_j q$
d_diffusion_sa `DiffusionSATerm` `termsAcoustic`	`<material>, <parameter_q>, <parameter_p>, <parameter_v>`	$\int_{\Omega} \left[ (\dvg \ul{\Vcal}) K_{ij} \nabla_i q\, \nabla_j p - K_{ij} (\nabla_j \ul{\Vcal} \nabla q) \nabla_i p - K_{ij} \nabla_j q (\nabla_i \ul{\Vcal} \nabla p)\right]$
ev_diffusion_velocity `DiffusionVelocityTerm` `termsLaplace`	`<material>, <parameter>`	$- \int_{\Omega} K_{ij} \nabla_j \bar{p}$ $\mbox{vector for } K \from \Ical_h: - \int_{T_K} K_{ij} \nabla_j \bar{p} / \int_{T_K} 1$ $- K_{ij} \nabla_j \bar{p}$
ev_div `DivTerm` `termsNavierStokes`	`<parameter>`	$\int_{\Omega} \nabla \cdot \ul{u}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla \cdot \ul{u} / \int_{T_K} 1$ $(\nabla \cdot \ul{u})\|_{qp}$
dw_div `DivOperatorTerm` `termsNavierStokes`	`<opt_material>, <virtual>`	$\int_{\Omega} \nabla \cdot \ul{v} \mbox { or } \int_{\Omega} c \nabla \cdot \ul{v}$
dw_div_grad `DivGradTerm` `termsNavierStokes`	`<opt_material>, <virtual>, <state>` `<opt_material>, <parameter_1>, <parameter_2>`	$\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nu\ \nabla \ul{u} : \nabla \ul{w} \\ \int_{\Omega} \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nabla \ul{u} : \nabla \ul{w}$
dw_electric_source `ElectricSourceTerm` `termsElectric`	`<material>, <virtual>, <parameter>`	$\int_{\Omega} c s (\nabla \phi)^2$
ev_grad `GradTerm` `termsNavierStokes`	`<parameter>`	$\int_{\Omega} \nabla p \mbox{ or } \int_{\Omega} \nabla \ul{w}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla p / \int_{T_K} 1 \mbox{ or } \int_{T_K} \nabla \ul{w} / \int_{T_K} 1$ $(\nabla p)\|_{qp} \mbox{ or } \nabla \ul{w}\|_{qp}$
ev_integrate_mat `IntegrateMatTerm` `termsBasic`	`<material>, <parameter>`	$\int_\Omega m$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} m / \int_{T_K} 1$ $m\|_{qp}$
dw_jump `SurfaceJumpTerm` `termsSurface`	`<opt_material>, <virtual>, <state_1>, <state_2>`	$\int_{\Gamma} c\, q (p_1 - p_2)$
dw_laplace `LaplaceTerm` `sfepy.terms.termsLaplace`	`<opt_material>, <virtual>, <state>` `<opt_material>, <parameter_1>, <parameter_2>`	$\int_{\Omega} c \nabla q \cdot \nabla p \mbox{ , } \int_{\Omega} c \nabla \bar{p} \cdot \nabla r$
dw_lin_convect `LinearConvectTerm` `termsNavierStokes`	`<virtual>, <parameter>, <state>`	$\int_{\Omega} ((\ul{b} \cdot \nabla) \ul{u}) \cdot \ul{v}$ $((\ul{b} \cdot \nabla) \ul{u})\|_{qp}$
dw_lin_elastic `LinearElasticTerm` `termsLinElasticity`	`<material>, <virtual>, <state>` `<material>, <parameter_1>, <parameter_2>`	$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})$
dw_lin_elastic_eth `LinearElasticETHTerm` `termsLinElasticity`	`<ts>, <material_0>, <material_1>, <virtual>, <state>`	$\int_{\Omega} \left [\int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{u}(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v})$
dw_lin_elastic_iso `LinearElasticIsotropicTerm` `termsLinElasticity`	`<material_1>, <material_2>, <virtual>, <state>`	$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) \mbox{ with } D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl}$
dw_lin_elastic_th `LinearElasticTHTerm` `termsLinElasticity`	`<ts>, <material>, <virtual>, <state>`	$\int_{\Omega} \left [\int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{u}(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v})$
dw_lin_prestress `LinearPrestressTerm` `termsLinElasticity`	`<material>, <virtual>` `<material>, <parameter>`	$\int_{\Omega} \sigma_{ij} e_{ij}(\ul{v})$
dw_lin_strain_fib `LinearStrainFiberTerm` `termsLinElasticity`	`<material_1>, <material_2>, <virtual>`	$\int_{\Omega} D_{ijkl} e_{ij}(\ul{v}) \left(d_k d_l\right)$
dw_new_diffusion `NewDiffusionTerm` `terms_new`	`<material>, <virtual>, <state>`
dw_new_lin_elastic `NewLinearElasticTerm` `terms_new`	`<material>, <virtual>, <state>`
dw_new_mass `NewMassTerm` `terms_new`	`<virtual>, <state>`
dw_new_mass_scalar `NewMassScalarTerm` `terms_new`	`<virtual>, <state>`
dw_non_penetration `NonPenetrationTerm` `terms_constraints`	`<opt_material>, <virtual>, <state>` `<opt_material>, <state>, <virtual>`	$\int_{\Gamma} c \lambda \ul{n} \cdot \ul{v} \mbox{ , } \int_{\Gamma} c \hat\lambda \ul{n} \cdot \ul{u} \\ \int_{\Gamma} \lambda \ul{n} \cdot \ul{v} \mbox{ , } \int_{\Gamma} \hat\lambda \ul{n} \cdot \ul{u}$
d_of_ns_surf_min_d_press `NSOFSurfMinDPressTerm` `termsAdjointNavierStokes`	`<material_1>, <material_2>, <parameter>`	$\delta \Psi(p) = \delta \left( \int_{\Gamma_{in}}p - \int_{\Gamma_{out}}bpress \right)$
dw_of_ns_surf_min_d_press_diff `NSOFSurfMinDPressDiffTerm` `termsAdjointNavierStokes`	`<material>, <virtual>`	$w \delta_{p} \Psi(p) \circ q$
dw_permeability_r `PermeabilityRTerm` `termsLaplace`	`<material>, <virtual>, <index>`	$\int_{\Omega} K_{ij} \nabla_j q$
dw_piezo_coupling `PiezoCouplingTerm` `termsPiezo`	`<material>, <virtual>, <state>` `<material>, <state>, <virtual>` `<material>, <parameter_v>, <parameter_s>`	$\int_{\Omega} g_{kij}\ e_{ij}(\ul{v}) \nabla_k p \mbox{ , } \int_{\Omega} g_{kij}\ e_{ij}(\ul{u}) \nabla_k q$
dw_point_load `ConcentratedPointLoadTerm` `termsPoint`	`<material>, <virtual>`	$\ul{f}^i = \ul{\bar f}^i \quad \forall \mbox{ FE node } i \mbox{ in a region }$
dw_point_lspring `LinearPointSpringTerm` `termsPoint`	`<material>, <virtual>, <state>`	$\ul{f}^i = -k \ul{u}^i \quad \forall \mbox{ FE node } i \mbox{ in a region }$
dw_s_dot_grad_i_s `ScalarDotGradIScalarTerm` `terms_dot`	`<material>, <virtual>, <state>`	$Z^i = \int_{\Omega} q \nabla_i p$
d_sd_convect `SDConvectTerm` `termsAdjointNavierStokes`	`<parameter_u>, <parameter_w>, <parameter_mesh_velocity>`	$\int_{\Omega_D} [ u_k \pdiff{u_i}{x_k} w_i (\nabla \cdot \Vcal) - u_k \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} w_i ]$
d_sd_div `SDDivTerm` `termsAdjointNavierStokes`	`<parameter_u>, <parameter_p>, <parameter_mesh_velocity>`	$\int_{\Omega_D} p [ (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_k}{x_i} \pdiff{w_i}{x_k} ]$
d_sd_div_grad `SDDivGradTerm` `termsAdjointNavierStokes`	`<material_1>, <material_2>, <parameter_u>, <parameter_w>, <parameter_mesh_velocity>`	$w \nu \int_{\Omega_D} [ \pdiff{u_i}{x_k} \pdiff{w_i}{x_k} (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} \pdiff{w_i}{x_k} - \pdiff{u_i}{x_k} \pdiff{\Vcal_l}{x_k} \pdiff{w_i}{x_k} ]$
d_sd_lin_elastic `SDLinearElasticTerm` `termsLinElasticity`	`<material>, <parameter_w>, <parameter_u>, <parameter_mesh_velocity>`	$\int_{\Omega} \hat{D}_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})$ $\hat{D}_{ijkl} = D_{ijkl}(\nabla \cdot \ul{\Vcal}) - D_{ijkq}{\partial \Vcal_l \over \partial x_q} - D_{iqkl}{\partial \Vcal_j \over \partial x_q}$
d_sd_st_grad_div `SDGradDivStabilizationTerm` `termsAdjointNavierStokes`	`<material>, <parameter_u>, <parameter_w>, <parameter_mesh_velocity>`	$\gamma \int_{\Omega_D} [ (\nabla \cdot \ul{u}) (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{u_i}{x_k} \pdiff{\Vcal_k}{x_i} (\nabla \cdot \ul{w}) - (\nabla \cdot \ul{u}) \pdiff{w_i}{x_k} \pdiff{\Vcal_k}{x_i} ]$
d_sd_st_pspg_c `SDPSPGCStabilizationTerm` `termsAdjointNavierStokes`	`<material>, <parameter_b>, <parameter_u>, <parameter_r>, <parameter_mesh_velocity>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ \pdiff{r}{x_i} (\ul{b} \cdot \nabla u_i) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} \pdiff{\Vcal_k}{x_i} (\ul{b} \cdot \nabla u_i) - \pdiff{r}{x_k} (\ul{b} \cdot \nabla \Vcal_k) \pdiff{u_i}{x_k} ]$
d_sd_st_pspg_p `SDPSPGPStabilizationTerm` `termsAdjointNavierStokes`	`<material>, <parameter_r>, <parameter_p>, <parameter_mesh_velocity>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ [ (\nabla r \cdot \nabla p) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} (\nabla \Vcal_k \cdot \nabla p) - (\nabla r \cdot \nabla \Vcal_k) \pdiff{p}{x_k} ]$
d_sd_st_supg_c `SDSUPGCStabilizationTerm` `termsAdjointNavierStokes`	`<material>, <parameter_b>, <parameter_u>, <parameter_w>, <parameter_mesh_velocity>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ (\ul{b} \cdot \nabla u_k) (\ul{b} \cdot \nabla w_k) (\nabla \cdot \Vcal) - (\ul{b} \cdot \nabla \Vcal_i) \pdiff{u_k}{x_i} (\ul{b} \cdot \nabla w_k) - (\ul{u} \cdot \nabla u_k) (\ul{b} \cdot \nabla \Vcal_i) \pdiff{w_k}{x_i} ]$
d_sd_surface_ndot `SDSufaceNormalDotTerm` `termsSurface`	`<material>, <parameter>, <parameter_mesh_velocity>`	$\int_{\Gamma} p \ul{c} \cdot \ul{n} \nabla \cdot \ul{\Vcal}$
d_sd_volume_dot `SDDotVolumeTerm` `termsAdjointNavierStokes`	`<parameter_1>, <parameter_2>, <parameter_mesh_velocity>`	$\int_{\Omega_D} p q (\nabla \cdot \ul{\Vcal}) \mbox{ , } \int_{\Omega_D} (\ul{u} \cdot \ul{w}) (\nabla \cdot \ul{\Vcal})$
dw_st_adj1_supg_p `SUPGPAdj1StabilizationTerm` `termsAdjointNavierStokes`	`<material>, <virtual>, <state>, <parameter>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p (\ul{v} \cdot \nabla \ul{w})$
dw_st_adj2_supg_p `SUPGPAdj2StabilizationTerm` `termsAdjointNavierStokes`	`<material>, <virtual>, <parameter>, <state>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla r (\ul{v} \cdot \nabla \ul{u})$
dw_st_adj_supg_c `SUPGCAdjStabilizationTerm` `termsAdjointNavierStokes`	`<material>, <virtual>, <parameter>, <state>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ ((\ul{v} \cdot \nabla) \ul{u}) ((\ul{u} \cdot \nabla) \ul{w}) + ((\ul{u} \cdot \nabla) \ul{u}) ((\ul{v} \cdot \nabla) \ul{w}) ]$
dw_st_grad_div `GradDivStabilizationTerm` `termsNavierStokes`	`<material>, <virtual>, <state>`	$\gamma \int_{\Omega} (\nabla\cdot\ul{u}) \cdot (\nabla\cdot\ul{v})$
dw_st_pspg_c `PSPGCStabilizationTerm` `termsNavierStokes`	`<material>, <virtual>, <parameter>, <state>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ ((\ul{b} \cdot \nabla) \ul{u}) \cdot \nabla q$
dw_st_pspg_p `PSPGPStabilizationTerm` `termsNavierStokes`	`<opt_material>, <virtual>, <state>` `<opt_material>, <parameter_1>, <parameter_2>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla p \cdot \nabla q$
dw_st_supg_c `SUPGCStabilizationTerm` `termsNavierStokes`	`<material>, <virtual>, <parameter>, <state>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ ((\ul{b} \cdot \nabla) \ul{u})\cdot ((\ul{b} \cdot \nabla) \ul{v})$
dw_st_supg_p `SUPGPStabilizationTerm` `termsNavierStokes`	`<material>, <virtual>, <parameter>, <state>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p\cdot ((\ul{b} \cdot \nabla) \ul{v})$
dw_stokes `StokesTerm` `termsNavierStokes`	`<opt_material>, <virtual>, <state>` `<opt_material>, <state>, <virtual>` `<opt_material>, <parameter_v>, <parameter_s>`	$\int_{\Omega} p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} q\ \nabla \cdot \ul{u} \mbox{ or } \int_{\Omega} c\ p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} c\ q\ \nabla \cdot \ul{u}$
d_sum_vals `SumNodalValuesTerm` `termsBasic`	`<parameter>`
d_surface `SurfaceTerm` `termsBasic`	`<parameter>`	$\int_\Gamma 1$
dw_surface_dot `DotProductSurfaceTerm` `terms_dot`	`<opt_material>, <virtual>, <state>` `<opt_material>, <parameter_1>, <parameter_2>`	$\int_\Gamma q p \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , } \int_\Gamma p r \mbox{ , } \int_\Gamma \ul{u} \cdot \ul{w} \mbox{ , } \int_\Gamma \ul{w} \cdot \ul{n} p \\ \int_\Gamma c q p \mbox{ , } \int_\Gamma c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma c p r \mbox{ , } \int_\Gamma c \ul{u} \cdot \ul{w} \\ \int_\Gamma \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{u} \cdot \ull{M} \cdot \ul{w}$
d_surface_flux `SurfaceFluxTerm` `termsLaplace`	`<material>, <parameter>`	$\int_{\Gamma} \ul{n} \cdot K_{ij} \nabla_j \bar{p}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \ul{n} \cdot K_{ij} \nabla_j \bar{p}\ / \int_{T_K} 1$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \ul{n} \cdot K_{ij} \nabla_j \bar{p}$
dw_surface_integrate `IntegrateSurfaceOperatorTerm` `termsBasic`	`<opt_material>, <virtual>`	$\int_{\Gamma} q \mbox{ or } \int_\Gamma c q$
ev_surface_integrate `IntegrateSurfaceTerm` `termsBasic`	`<opt_material>, <parameter>`	$\int_\Gamma y \mbox{ , } \int_\Gamma \ul{y} \mbox{ , } \int_\Gamma \ul{y} \cdot \ul{n} \\ \int_\Gamma c y \mbox{ , } \int_\Gamma c \ul{y} \mbox{ , } \int_\Gamma c \ul{y} \cdot \ul{n} \mbox{ flux }$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (\ul{y} \cdot \ul{n}) / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (c \ul{y} \cdot \ul{n}) / \int_{T_K} 1$ $y\|_{qp} \mbox{ , } \ul{y}\|_{qp} \mbox{ , } (\ul{y} \cdot \ul{n})\|_{qp} \mbox{ flux } \\ c y\|_{qp} \mbox{ , } c \ul{y}\|_{qp} \mbox{ , } (c \ul{y} \cdot \ul{n})\|_{qp} \mbox{ flux }$
dw_surface_laplace `SurfaceLaplaceLayerTerm` `termsAcoustic`	`<material>, <virtual>, <state>` `<material>, <parameter_2>, <parameter_1>`	$\int_{\Gamma} c \partial_\alpha \ul{q}\,\partial_\alpha \ul{p}, \alpha = 1,\dots,N-1$
dw_surface_lcouple `SurfaceCoupleLayerTerm` `termsAcoustic`	`<material>, <virtual>, <state>` `<material>, <state>, <virtual>` `<material>, <parameter_1>, <parameter_2>`	$\int_{\Gamma} c q\,\partial_\alpha p, \int_{\Gamma} c \partial_\alpha p\, q, \int_{\Gamma} c \partial_\alpha r\, s,\alpha = 1,\dots,N-1$
dw_surface_ltr `LinearTractionTerm` `termsSurface`	`<material>, <virtual>`	$\int_{\Gamma} \ul{v} \cdot \ull{\sigma} \cdot \ul{n}$
di_surface_moment `SurfaceMomentTerm` `termsBasic`	`<parameter>, <shift>`	$\int_{\Gamma} \ul{n} (\ul{x} - \ul{x}_0)$
dw_surface_ndot `SufaceNormalDotTerm` `termsSurface`	`<material>, <virtual>` `<material>, <parameter>`	$\int_{\Gamma} q \ul{c} \cdot \ul{n}$
dw_tl_bulk_active `BulkActiveTLTerm` `terms_hyperelastic_tl`	`<material>, <virtual>, <state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_bulk_penalty `BulkPenaltyTLTerm` `terms_hyperelastic_tl`	`<material>, <virtual>, <state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_bulk_pressure `BulkPressureTLTerm` `terms_hyperelastic_tl`	`<virtual>, <state>, <state_p>`	$\int_{\Omega} S_{ij}(p) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_diffusion `DiffusionTLTerm` `terms_hyperelastic_tl`	`<material_1>, <material_2>, <virtual>, <state>, <parameter>`	$\int_{\Omega} \ull{K}(\ul{u}^{(n-1)}) : \pdiff{q}{X} \pdiff{p}{X}$
dw_tl_fib_a `FibresActiveTLTerm` `terms_fibres`	`<material_1>, <material_2>, <material_3>, <material_4>, <material_5>, <virtual>, <state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_he_mooney_rivlin `MooneyRivlinTLTerm` `terms_hyperelastic_tl`	`<material>, <virtual>, <state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_he_neohook `NeoHookeanTLTerm` `terms_hyperelastic_tl`	`<material>, <virtual>, <state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_membrane `TLMembraneTerm` `terms_membrane`	`<material_a1>, <material_a2>, <material_h0>, <virtual>, <state>`
dw_tl_surface_traction `SurfaceTractionTLTerm` `terms_hyperelastic_tl`	`<material>, <virtual>, <state>`	$\int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ull{\sigma} \cdot \ul{v} J$
dw_tl_volume `VolumeTLTerm` `terms_hyperelastic_tl`	`<virtual>, <state>`	$\begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array}$
dw_ul_bulk_penalty `BulkPenaltyULTerm` `terms_hyperelastic_ul`	`<material>, <virtual>, <state>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$
dw_ul_bulk_pressure `BulkPressureULTerm` `terms_hyperelastic_ul`	`<virtual>, <state>, <state_p>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$
dw_ul_compressible `CompressibilityULTerm` `terms_hyperelastic_ul`	`<material>, <virtual>, <state>, <parameter_u>`	$\int_{\Omega} 1\over \gamma p \, q$
dw_ul_he_mooney_rivlin `MooneyRivlinULTerm` `terms_hyperelastic_ul`	`<material>, <virtual>, <state>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$
dw_ul_he_neohook `NeoHookeanULTerm` `terms_hyperelastic_ul`	`<material>, <virtual>, <state>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$
dw_ul_volume `VolumeULTerm` `terms_hyperelastic_ul`	`<virtual>, <state>`	$\begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array}$
dw_v_dot_grad_s `VectorDotGradScalarTerm` `terms_dot`	`<opt_material>, <virtual>, <state>` `<opt_material>, <state>, <virtual>` `<opt_material>, <parameter_v>, <parameter_s>`	$\int_{\Omega} \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \nabla q \\ \int_{\Omega} c \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} c \ul{u} \cdot \nabla q \\ \int_{\Omega} \ul{v} \cdot \ull{M} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ull{M} \cdot \nabla q$
d_volume `VolumeTerm` `termsBasic`	`<parameter>`	$\int_\Omega 1$
dw_volume_dot `DotProductVolumeTerm` `terms_dot`	`<opt_material>, <virtual>, <state>` `<opt_material>, <parameter_1>, <parameter_2>`	$\int_\Omega q p \mbox{ , } \int_\Omega \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega p r \mbox{ , } \int_\Omega \ul{u} \cdot \ul{w} \\ \int_\Omega c q p \mbox{ , } \int_\Omega c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega c p r \mbox{ , } \int_\Omega c \ul{u} \cdot \ul{w} \\ \int_\Omega \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Omega \ul{u} \cdot \ull{M} \cdot \ul{w}$
dw_volume_dot_w_scalar_eth `DotSProductVolumeOperatorWETHTerm` `terms_dot`	`<ts>, <material_0>, <material_1>, <virtual>, <state>`	$\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q$
dw_volume_dot_w_scalar_th `DotSProductVolumeOperatorWTHTerm` `terms_dot`	`<ts>, <material>, <virtual>, <state>`	$\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q$
ev_volume_integrate `IntegrateVolumeTerm` `termsBasic`	`<opt_material>, <parameter>`	$\int_\Omega y \mbox{ , } \int_\Omega \ul{y} \\ \int_\Omega c y \mbox{ , } \int_\Omega c \ul{y}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1$ $y\|_{qp} \mbox{ , } \ul{y}\|_{qp} \\ c y\|_{qp} \mbox{ , } c \ul{y}\|_{qp}$
dw_volume_integrate `IntegrateVolumeOperatorTerm` `termsBasic`	`<opt_material>, <virtual>`	$\int_\Omega q \mbox{ or } \int_\Omega c q$
dw_volume_lvf `LinearVolumeForceTerm` `termsVolume`	`<material>, <virtual>`	$\int_{\Omega} \ul{f} \cdot \ul{v} \mbox{ or } \int_{\Omega} f q$
d_volume_surface `VolumeSurfaceTerm` `termsBasic`	`<parameter>`	$\int_\Gamma \ul{x} \cdot \ul{n}$