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
$\cal{D}$	volume or 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
ev	evaluate	‘eval’, ‘el_eval’, ‘el_avg’, ‘qp’	terms having all arguments known, modes ‘el_avg’, ‘qp’ are not supported by all ev_ terms
de	discrete einsum	any (work in progress)	multi-linear terms defined using an enriched einsum notation

Term Table¶

Below we list all the terms available in automatically generated tables. The first column lists the name, the second column the argument lists and the third column the mathematical definition of each term. The terms are devided into the following tables:

Table of basic terms
Table of large deformation terms (total/updated Lagrangian formulation)
Table of sensitivity terms
Table of special terms
Table of multi-linear terms

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 basic terms¶

Basic terms¶
name/class	arguments	definition	examples
dw_advect_div_free `AdvectDivFreeTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} \nabla \cdot (\ul{y} p) q = \int_{\Omega} (\underbrace{(\nabla \cdot \ul{y})}_{\equiv 0} + \ul{y} \cdot \nabla) p) q$	tim.adv.dif
dw_bc_newton `BCNewtonTerm`	`<material_1>`, `<material_2>`, `<virtual>`, `<state>`	$\int_{\Gamma} \alpha q (p - p_{\rm outer})$
dw_biot `BiotTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>` `<material>`, `<parameter_v>`, `<parameter_s>`	$\int_{\Omega} p\ \alpha_{ij} e_{ij}(\ul{v}) \mbox{ , } \int_{\Omega} q\ \alpha_{ij} e_{ij}(\ul{u})$	bio.npb.lag, bio, the.ela.ess, bio.npb, the.ela, bio.sho.syn
ev_biot_stress `BiotStressTerm`	`<material>`, `<parameter>`	$- \int_{\Omega} \alpha_{ij} \bar{p}$ $\mbox{vector for } K \from \Ical_h: - \int_{T_K} \alpha_{ij} \bar{p} / \int_{T_K} 1$ $- \alpha_{ij} \bar{p}\|_{qp}$
ev_cauchy_strain `CauchyStrainTerm`	`<parameter>`	$\int_{\cal{D}} \ull{e}(\ul{w})$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \ull{e}(\ul{w}) / \int_{T_K} 1$ $\ull{e}(\ul{w})\|_{qp}$
ev_cauchy_stress `CauchyStressTerm`	`<material>`, `<parameter>`	$\int_{\cal{D}} D_{ijkl} e_{kl}(\ul{w})$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} D_{ijkl} e_{kl}(\ul{w}) / \int_{T_K} 1$ $D_{ijkl} e_{kl}(\ul{w})\|_{qp}$
dw_contact `ContactTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Gamma_{c}} \varepsilon_N \langle g_N(\ul{u}) \rangle \ul{n} \ul{v}$	two.bod.con
dw_contact_plane `ContactPlaneTerm`	`<material_f>`, `<material_n>`, `<material_a>`, `<material_b>`, `<virtual>`, `<state>`	$\int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}$	ela.con.pla
dw_contact_sphere `ContactSphereTerm`	`<material_f>`, `<material_c>`, `<material_r>`, `<virtual>`, `<state>`	$\int_{\Gamma} \ul{v} \cdot f(d(\ul{u})) \ul{n}(\ul{u})$	ela.con.sph
dw_convect `ConvectTerm`	`<virtual>`, `<state>`	$\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v}$	nav.sto, nav.sto, nav.sto.iga
dw_convect_v_grad_s `ConvectVGradSTerm`	`<virtual>`, `<state_v>`, `<state_s>`	$\int_{\Omega} q (\ul{u} \cdot \nabla p)$	poi.fun
ev_def_grad `DeformationGradientTerm`	`<parameter>`	$\ull{F} = \pdiff{\ul{x}}{\ul{X}}\|_{qp} = \ull{I} + \pdiff{\ul{u}}{\ul{X}}\|_{qp} \;, \\ \ul{x} = \ul{X} + \ul{u} \;, J = \det{(\ull{F})}$
dw_dg_advect_laxfrie_flux `AdvectionDGFluxTerm`	`<opt_material>`, `<material_advelo>`, `<virtual>`, `<state>`	$\int_{\partial{T_K}} \ul{n} \cdot \ul{f}^{} (p_{in}, p_{out})q$ where $\ul{f}^{}(p_{in}, p_{out}) = \ul{a} \frac{p_{in} + p_{out}}{2} + (1 - \alpha) \ul{n} C \frac{ p_{in} - p_{out}}{2},$	adv.2D, adv.1D, adv.dif.2D
dw_dg_diffusion_flux `DiffusionDGFluxTerm`	`<material>`, `<state>`, `<virtual>` `<material>`, `<virtual>`, `<state>`	$\int_{\partial{T_K}} D \langle \nabla p \rangle [q] \mbox{ , } \int_{\partial{T_K}} D \langle \nabla q \rangle [p]$ where $\langle \nabla \phi \rangle = \frac{\nabla\phi_{in} + \nabla\phi_{out}}{2}$ $[\phi] = \phi_{in} - \phi_{out}$	lap.2D, bur.2D, adv.dif.2D
dw_dg_interior_penalty `DiffusionInteriorPenaltyTerm`	`<material>`, `<material_Cw>`, `<virtual>`, `<state>`	$\int_{\partial{T_K}} \bar{D} C_w \frac{Ord^2}{d(\partial{T_K})}[p][q]$ where $[\phi] = \phi_{in} - \phi_{out}$	lap.2D, bur.2D, adv.dif.2D
dw_dg_nonlinear_laxfrie_flux `NonlinearHyperbolicDGFluxTerm`	`<opt_material>`, `<fun>`, `<fun_d>`, `<virtual>`, `<state>`	$\int_{\partial{T_K}} \ul{n} \cdot f^{} (p_{in}, p_{out})q$ where $\ul{f}^{}(p_{in}, p_{out}) = \frac{\ul{f}(p_{in}) + \ul{f}(p_{out})}{2} + (1 - \alpha) \ul{n} C \frac{ p_{in} - p_{out}}{2},$	bur.2D
dw_diffusion `DiffusionTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} K_{ij} \nabla_i q \nabla_j p \mbox{ , } \int_{\Omega} K_{ij} \nabla_i \bar{p} \nabla_j r$	dar.flo.mul, bio.npb.lag, bio, poi.neu, bio.npb, pie.ela, bio.sho.syn
dw_diffusion_coupling `DiffusionCoupling`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>` `<material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} p K_{j} \nabla_j q \mbox{ , } \int_{\Omega} q K_{j} \nabla_j p$
dw_diffusion_r `DiffusionRTerm`	`<material>`, `<virtual>`	$\int_{\Omega} K_{j} \nabla_j q$
ev_diffusion_velocity `DiffusionVelocityTerm`	`<material>`, `<parameter>`	$- \int_{\cal{D}} K_{ij} \nabla_j \bar{p}$ $\mbox{vector for } K \from \Ical_h: - \int_{T_K} K_{ij} \nabla_j \bar{p} / \int_{T_K} 1$ $- K_{ij} \nabla_j \bar{p}$
dw_div `DivOperatorTerm`	`<opt_material>`, `<virtual>`	$\int_{\Omega} \nabla \cdot \ul{v} \mbox { or } \int_{\Omega} c \nabla \cdot \ul{v}$
ev_div `DivTerm`	`<parameter>`	$\int_{\cal{D}} \nabla \cdot \ul{u}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla \cdot \ul{u} / \int_{T_K} 1$ $(\nabla \cdot \ul{u})\|_{qp}$
dw_div_grad `DivGradTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nu\ \nabla \ul{u} : \nabla \ul{w} \\ \int_{\Omega} \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nabla \ul{u} : \nabla \ul{w}$	nav.sto, sto, nav.sto, sta.nav.sto, sto.sli.bc, nav.sto.iga
dw_dot `DotProductTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\cal{D}} q p \mbox{ , } \int_{\cal{D}} \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , } \int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} p r \mbox{ , } \int_{\cal{D}} \ul{u} \cdot \ul{w} \mbox{ , } \int_\Gamma \ul{w} \cdot \ul{n} p \\ \int_{\cal{D}} c q p \mbox{ , } \int_{\cal{D}} c \ul{v} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} c p r \mbox{ , } \int_{\cal{D}} c \ul{u} \cdot \ul{w} \\ \int_{\cal{D}} \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} \ul{u} \cdot \ull{M} \cdot \ul{w}$	tim.poi.exp, bor, lin.ela.up, pie.ela, poi.fun, lin.ela.dam, the.ele, tim.poi, adv.1D, vib.aco, aco, wel, bal, ela, dar.flo.mul, sto.sli.bc, tim.adv.dif, osc, adv.2D, bur.2D, hyd, aco, poi.per.bou.con
dw_elastic_wave `ElasticWaveTerm`	`<material_1>`, `<material_2>`, `<virtual>`, `<state>`	$\int_{\Omega} D_{ijkl}\ g_{ij}(\ul{v}) g_{kl}(\ul{u})$
dw_elastic_wave_cauchy `ElasticWaveCauchyTerm`	`<material_1>`, `<material_2>`, `<virtual>`, `<state>` `<material_1>`, `<material_2>`, `<state>`, `<virtual>`	$\int_{\Omega} D_{ijkl}\ g_{ij}(\ul{v}) e_{kl}(\ul{u}) \;, \int_{\Omega} D_{ijkl}\ g_{ij}(\ul{u}) e_{kl}(\ul{v})$
dw_electric_source `ElectricSourceTerm`	`<material>`, `<virtual>`, `<parameter>`	$\int_{\Omega} c s (\nabla \phi)^2$	the.ele
ev_grad `GradTerm`	`<parameter>`	$\int_{\cal{D}} \nabla p \mbox{ or } \int_{\cal{D}} \nabla \ul{w}$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} \nabla p / \int_{T_K} 1 \mbox{ or } \int_{T_K} \nabla \ul{w} / \int_{T_K} 1$ $(\nabla p)\|_{qp} \mbox{ or } \nabla \ul{w}\|_{qp}$
dw_integrate `IntegrateOperatorTerm`	`<opt_material>`, `<virtual>`	$\int_{\cal{D}} q \mbox{ or } \int_{\cal{D}} c q$	dar.flo.mul, poi.neu, vib.aco, poi.per.bou.con, aco, aco
ev_integrate `IntegrateTerm`	`<opt_material>`, `<parameter>`	$\int_{\cal{D}} y \mbox{ , } \int_{\cal{D}} \ul{y} \mbox{ , } \int_\Gamma \ul{y} \cdot \ul{n}\\ \int_{\cal{D}} c y \mbox{ , } \int_{\cal{D}} c \ul{y} \mbox{ , } \int_\Gamma c \ul{y} \cdot \ul{n} \mbox{ flux }$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (\ul{y} \cdot \ul{n}) / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (c \ul{y} \cdot \ul{n}) / \int_{T_K} 1$ $y\|_{qp} \mbox{ , } \ul{y}\|_{qp} \mbox{ , } (\ul{y} \cdot \ul{n})\|_{qp} \mbox{ flux } \\ c y\|_{qp} \mbox{ , } c \ul{y}\|_{qp} \mbox{ , } (c \ul{y} \cdot \ul{n})\|_{qp} \mbox{ flux }$
ev_integrate_mat `IntegrateMatTerm`	`<material>`, `<parameter>`	$\int_{\cal{D}} m$ $\mbox{vector for } K \from \Ical_h: \int_{T_K} m / \int_{T_K} 1$ $m\|_{qp}$
dw_jump `SurfaceJumpTerm`	`<opt_material>`, `<virtual>`, `<state_1>`, `<state_2>`	$\int_{\Gamma} c\, q (p_1 - p_2)$	aco
dw_laplace `LaplaceTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} c \nabla q \cdot \nabla p \mbox{ , } \int_{\Omega} c \nabla \bar{p} \cdot \nabla r$	poi.sho.syn, lap.1d, tim.poi.exp, poi.iga, bor, the.ela.ess, poi.fun, the.ele, lap.2D, tim.poi, vib.aco, aco, wel, sin, cub, poi, poi.fie.dep.mat, sto.sli.bc, tim.adv.dif, poi.par.stu, osc, adv.dif.2D, bur.2D, hyd, lap.tim.ebc, aco, lap.cou.lcb, poi.per.bou.con
dw_lin_convect `LinearConvectTerm`	`<virtual>`, `<parameter>`, `<state>`	$\int_{\Omega} ((\ul{b} \cdot \nabla) \ul{u}) \cdot \ul{v}$ $((\ul{b} \cdot \nabla) \ul{u})\|_{qp}$	sta.nav.sto
dw_lin_convect2 `LinearConvect2Term`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} ((\ul{b} \cdot \nabla) \ul{u}) \cdot \ul{v}$ $((\ul{b} \cdot \nabla) \ul{u})\|_{qp}$
dw_lin_elastic `LinearElasticTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})$	its.4, bio, nod.lcb, lin.ela, lin.ela.tra, lin.ela.up, the.ela.ess, lin.ela.iga, bio.npb, pie.ela, its.3, lin.ela.dam, ela.con.pla, its.2, ela, two.bod.con, its.1, bio.npb.lag, ela.con.sph, lin.ela.opt, pre.fib, com.ela.mat, ela.shi.per, lin.vis, the.ela, pie.ela.mac, lin.ela.mM, mat.non, bio.sho.syn
dw_lin_elastic_iso `LinearElasticIsotropicTerm`	`<material_1>`, `<material_2>`, `<virtual>`, `<state>` `<material_1>`, `<material_2>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) \mbox{ with } D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl}$
dw_lin_prestress `LinearPrestressTerm`	`<material>`, `<virtual>` `<material>`, `<parameter>`	$\int_{\Omega} \sigma_{ij} e_{ij}(\ul{v})$	pie.ela.mac, non.hyp.mM, pre.fib
dw_lin_strain_fib `LinearStrainFiberTerm`	`<material_1>`, `<material_2>`, `<virtual>`	$\int_{\Omega} D_{ijkl} e_{ij}(\ul{v}) \left(d_k d_l\right)$	pre.fib
dw_non_penetration `NonPenetrationTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<state>`, `<virtual>`	$\int_{\Gamma} c \lambda \ul{n} \cdot \ul{v} \mbox{ , } \int_{\Gamma} c \hat\lambda \ul{n} \cdot \ul{u} \\ \int_{\Gamma} \lambda \ul{n} \cdot \ul{v} \mbox{ , } \int_{\Gamma} \hat\lambda \ul{n} \cdot \ul{u}$	bio.npb.lag
dw_non_penetration_p `NonPenetrationPenaltyTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Gamma} c (\ul{n} \cdot \ul{v}) (\ul{n} \cdot \ul{u})$	bio.sho.syn
dw_nonsym_elastic `NonsymElasticTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} \ull{D} \nabla\ul{u} : \nabla\ul{v}$	non.hyp.mM
dw_ns_dot_grad_s `NonlinearScalarDotGradTerm`	`<fun>`, `<fun_d>`, `<virtual>`, `<state>` `<fun>`, `<fun_d>`, `<state>`, `<virtual>`	$\int_{\Omega} q \cdot \nabla \cdot \ul{f}(p) = \int_{\Omega} q \cdot \text{div} \ul{f}(p) \mbox{ , } \int_{\Omega} \ul{f}(p) \cdot \nabla q$	bur.2D
dw_piezo_coupling `PiezoCouplingTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>` `<material>`, `<parameter_v>`, `<parameter_s>`	$\int_{\Omega} g_{kij}\ e_{ij}(\ul{v}) \nabla_k p \mbox{ , } \int_{\Omega} g_{kij}\ e_{ij}(\ul{u}) \nabla_k q$	pie.ela
ev_piezo_strain `PiezoStrainTerm`	`<material>`, `<parameter>`	$\int_{\Omega} g_{kij} e_{ij}(\ul{u})$
ev_piezo_stress `PiezoStressTerm`	`<material>`, `<parameter>`	$\int_{\Omega} g_{kij} \nabla_k p$
dw_point_load `ConcentratedPointLoadTerm`	`<material>`, `<virtual>`	$\ul{f}^i = \ul{\bar f}^i \quad \forall \mbox{ FE node } i \mbox{ in a region }$	its.1, its.4, its.2, its.3, she.can
dw_point_lspring `LinearPointSpringTerm`	`<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`	`<material>`, `<virtual>`, `<state>`	$Z^i = \int_{\Omega} q \nabla_i p$
dw_s_dot_mgrad_s `ScalarDotMGradScalarTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>`	$\int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , } \int_{\Omega} p \ul{y} \cdot \nabla q$	adv.2D, adv.1D, adv.dif.2D
dw_shell10x `Shell10XTerm`	`<material_d>`, `<material_drill>`, `<virtual>`, `<state>`	$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})$	she.can
dw_stokes `StokesTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<state>`, `<virtual>` `<opt_material>`, `<parameter_v>`, `<parameter_s>`	$\int_{\Omega} p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} q\ \nabla \cdot \ul{u} \mbox{ or } \int_{\Omega} c\ p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} c\ q\ \nabla \cdot \ul{u}$	nav.sto, sto, nav.sto, lin.ela.up, sta.nav.sto, sto.sli.bc, nav.sto.iga
dw_stokes_wave `StokesWaveTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\ul{\kappa} \cdot \ul{u})$
dw_stokes_wave_div `StokesWaveDivTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>`	$\int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\nabla \cdot \ul{u}) \;, \int_{\Omega} (\ul{\kappa} \cdot \ul{u}) (\nabla \cdot \ul{v})$
ev_sum_vals `SumNodalValuesTerm`	`<parameter>`
ev_surface_flux `SurfaceFluxTerm`	`<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_flux `SurfaceFluxOperatorTerm`	`<opt_material>`, `<virtual>`, `<state>`	$\int_{\Gamma} q \ul{n} \cdot \ull{K} \cdot \nabla p$
dw_surface_ltr `LinearTractionTerm`	`<opt_material>`, `<virtual>` `<opt_material>`, `<parameter>`	$\int_{\Gamma} \ul{v} \cdot \ull{\sigma} \cdot \ul{n}, \int_{\Gamma} \ul{v} \cdot \ul{n},$	nod.lcb, lin.ela.tra, lin.ela.opt, com.ela.mat, ela.shi.per, lin.vis
ev_surface_moment `SurfaceMomentTerm`	`<material>`, `<parameter>`	$\int_{\Gamma} \ul{n} (\ul{x} - \ul{x}_0)$
dw_surface_ndot `SufaceNormalDotTerm`	`<material>`, `<virtual>` `<material>`, `<parameter>`	$\int_{\Gamma} q \ul{c} \cdot \ul{n}$
dw_v_dot_grad_s `VectorDotGradScalarTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<state>`, `<virtual>` `<opt_material>`, `<parameter_v>`, `<parameter_s>`	$\int_{\Omega} \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \nabla q \\ \int_{\Omega} c \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} c \ul{u} \cdot \nabla q \\ \int_{\Omega} \ul{v} \cdot (\ull{M} \nabla p) \mbox{ , } \int_{\Omega} \ul{u} \cdot (\ull{M} \nabla q)$
dw_vm_dot_s `VectorDotScalarTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>` `<material>`, `<parameter_v>`, `<parameter_s>`	$\int_{\Omega} \ul{v} \cdot \ul{m} p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ul{m} q\\$
ev_volume `VolumeTerm`	`<parameter>`	$\int_{\cal{D}} 1$
dw_volume_lvf `LinearVolumeForceTerm`	`<material>`, `<virtual>`	$\int_{\Omega} \ul{f} \cdot \ul{v} \mbox{ or } \int_{\Omega} f q$	poi.iga, poi.par.stu, bur.2D, adv.dif.2D
ev_volume_surface `VolumeSurfaceTerm`	`<parameter>`	$1 / D \int_\Gamma \ul{x} \cdot \ul{n}$
dw_zero `ZeroTerm`	`<virtual>`, `<state>`	$0$	ela

Table of sensitivity terms¶

Sensitivity terms¶
name/class	arguments	definition
dw_adj_convect1 `AdjConvect1Term`	`<virtual>`, `<state>`, `<parameter>`	$\int_{\Omega} ((\ul{v} \cdot \nabla) \ul{u}) \cdot \ul{w}$
dw_adj_convect2 `AdjConvect2Term`	`<virtual>`, `<state>`, `<parameter>`	$\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{v}) \cdot \ul{w}$
dw_adj_div_grad `AdjDivGradTerm`	`<material_1>`, `<material_2>`, `<virtual>`, `<parameter>`	$w \delta_{u} \Psi(\ul{u}) \circ \ul{v}$
ev_sd_convect `SDConvectTerm`	`<parameter_u>`, `<parameter_w>`, `<parameter_mv>`	$\int_{\Omega} [ u_k \pdiff{u_i}{x_k} w_i (\nabla \cdot \Vcal) - u_k \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} w_i ]$
ev_sd_diffusion `SDDiffusionTerm`	`<material>`, `<parameter_q>`, `<parameter_p>`, `<parameter_mesh_velocity>`	$\int_{\Omega} \left[ (\dvg \ul{\Vcal}) K_{ij} \nabla_i q\, \nabla_j p - K_{ij} (\nabla_j \ul{\Vcal} \nabla q) \nabla_i p - K_{ij} \nabla_j q (\nabla_i \ul{\Vcal} \nabla p)\right]$
ev_sd_div `SDDivTerm`	`<parameter_u>`, `<parameter_p>`, `<parameter_mv>`	$\int_{\Omega} p [ (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_k}{x_i} \pdiff{w_i}{x_k} ]$
ev_sd_div_grad `SDDivGradTerm`	`<opt_material>`, `<parameter_u>`, `<parameter_w>`, `<parameter_mv>`	$\nu \int_{\Omega} [ \pdiff{u_i}{x_k} \pdiff{w_i}{x_k} (\nabla \cdot \ul{\Vcal}) - \pdiff{\Vcal_j}{x_k} \pdiff{u_i}{x_j} \pdiff{w_i}{x_k} - \pdiff{u_i}{x_k} \pdiff{\Vcal_l}{x_k} \pdiff{w_i}{x_k} ]$
ev_sd_dot `SDDotTerm`	`<parameter_1>`, `<parameter_2>`, `<parameter_mv>`	$\int_{\Omega} p q (\nabla \cdot \ul{\Vcal}) \mbox{ , } \int_{\Omega} (\ul{u} \cdot \ul{w}) (\nabla \cdot \ul{\Vcal})$
ev_sd_lin_elastic `SDLinearElasticTerm`	`<material>`, `<parameter_w>`, `<parameter_u>`, `<parameter_mesh_velocity>`	$\int_{\Omega} \hat{D}_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})$ $\hat{D}_{ijkl} = D_{ijkl}(\nabla \cdot \ul{\Vcal}) - D_{ijkq}{\partial \Vcal_l \over \partial x_q} - D_{iqkl}{\partial \Vcal_j \over \partial x_q}$
ev_sd_piezo_coupling `SDPiezoCouplingTerm`	`<material>`, `<parameter_u>`, `<parameter_p>`, `<parameter_mv>`	$\int_{\Omega} \hat{g}_{kij}\ e_{ij}(\ul{u}) \nabla_k p$ $\hat{g}_{kij} = g_{kij}(\nabla \cdot \ul{\Vcal}) - g_{kil}{\partial \Vcal_j \over \partial x_l} - g_{lij}{\partial \Vcal_k \over \partial x_l}$
ev_sd_surface_integrate `SDSufaceIntegrateTerm`	`<parameter>`, `<parameter_mesh_velocity>`	$\int_{\Gamma} p \nabla \cdot \ul{\Vcal}$
ev_sd_surface_ltr `SDLinearTractionTerm`	`<opt_material>`, `<parameter>`, `<parameter_mv>`	$\int_{\Gamma} \ul{v} \cdot \ull{\sigma} \cdot \ul{n}, \int_{\Gamma} \ul{v} \cdot \ul{n},$

Table of large deformation terms¶

Large deformation terms¶
name/class	arguments	definition	examples
dw_tl_bulk_active `BulkActiveTLTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_bulk_penalty `BulkPenaltyTLTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$	com.ela.mat, hyp, act.fib
dw_tl_bulk_pressure `BulkPressureTLTerm`	`<virtual>`, `<state>`, `<state_p>`	$\int_{\Omega} S_{ij}(p) \delta E_{ij}(\ul{u};\ul{v})$	per.tl, bal
dw_tl_diffusion `DiffusionTLTerm`	`<material_1>`, `<material_2>`, `<virtual>`, `<state>`, `<parameter>`	$\int_{\Omega} \ull{K}(\ul{u}^{(n-1)}) : \pdiff{q}{\ul{X}} \pdiff{p}{\ul{X}}$	per.tl
dw_tl_fib_a `FibresActiveTLTerm`	`<material_1>`, `<material_2>`, `<material_3>`, `<material_4>`, `<material_5>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$	act.fib
dw_tl_he_genyeoh `GenYeohTLTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_he_mooney_rivlin `MooneyRivlinTLTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$	hyp, bal, com.ela.mat
dw_tl_he_neohook `NeoHookeanTLTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$	hyp, per.tl, com.ela.mat, bal, act.fib
dw_tl_he_ogden `OgdenTLTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} S_{ij}(\ul{u}) \delta E_{ij}(\ul{u};\ul{v})$
dw_tl_membrane `TLMembraneTerm`	`<material_a1>`, `<material_a2>`, `<material_h0>`, `<virtual>`, `<state>`		bal
ev_tl_surface_flux `SurfaceFluxTLTerm`	`<material_1>`, `<material_2>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Gamma} \ul{\nu} \cdot \ull{K}(\ul{u}^{(n-1)}) \pdiff{p}{\ul{X}}$
dw_tl_surface_traction `SurfaceTractionTLTerm`	`<opt_material>`, `<virtual>`, `<state>`	$\int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ull{\sigma} \cdot \ul{v} J$	per.tl
dw_tl_volume `VolumeTLTerm`	`<virtual>`, `<state>`	$\begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array}$	per.tl, bal
ev_tl_volume_surface `VolumeSurfaceTLTerm`	`<parameter>`	$1 / D \int_{\Gamma} \ul{\nu} \cdot \ull{F}^{-1} \cdot \ul{x} J$
dw_ul_bulk_penalty `BulkPenaltyULTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$	hyp.ul
dw_ul_bulk_pressure `BulkPressureULTerm`	`<virtual>`, `<state>`, `<state_p>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$	hyp.ul.up
dw_ul_compressible `CompressibilityULTerm`	`<material>`, `<virtual>`, `<state>`, `<parameter_u>`	$\int_{\Omega} 1\over \gamma p \, q$	hyp.ul.up
dw_ul_he_mooney_rivlin `MooneyRivlinULTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$	hyp.ul, hyp.ul.up
dw_ul_he_neohook `NeoHookeanULTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Omega} \mathcal{L}\tau_{ij}(\ul{u}) e_{ij}(\delta\ul{v})/J$	hyp.ul, hyp.ul.up
dw_ul_volume `VolumeULTerm`	`<virtual>`, `<state>`	$\begin{array}{l} \int_{\Omega} q J(\ul{u}) \\ \mbox{volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) \\ \mbox{rel\_volume mode: vector for } K \from \Ical_h: \int_{T_K} J(\ul{u}) / \int_{T_K} 1 \end{array}$	hyp.ul.up

Table of special terms¶

Special terms¶
name/class	arguments	definition	examples
dw_biot_eth `BiotETHTerm`	`<ts>`, `<material_0>`, `<material_1>`, `<virtual>`, `<state>` `<ts>`, `<material_0>`, `<material_1>`, `<state>`, `<virtual>`	$\begin{array}{l} \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau)\,p(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v}) \mbox{ ,} \\ \int_{\Omega} \left [\int_0^t \alpha_{ij}(t-\tau) e_{kl}(\ul{u}(\tau)) \difd{\tau} \right] q \end{array}$
dw_biot_th `BiotTHTerm`	`<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_stress_eth `CauchyStressETHTerm`	`<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`	`<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_lin_elastic_eth `LinearElasticETHTerm`	`<ts>`, `<material_0>`, `<material_1>`, `<virtual>`, `<state>`	$\int_{\Omega} \left [\int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{u}(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v})$	lin.vis
dw_lin_elastic_th `LinearElasticTHTerm`	`<ts>`, `<material>`, `<virtual>`, `<state>`	$\int_{\Omega} \left [\int_0^t \Hcal_{ijkl}(t-\tau)\,e_{kl}(\ul{u}(\tau)) \difd{\tau} \right]\,e_{ij}(\ul{v})$
ev_of_ns_surf_min_d_press `NSOFSurfMinDPressTerm`	`<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`	`<material>`, `<virtual>`	$w \delta_{p} \Psi(p) \circ q$
ev_sd_st_grad_div `SDGradDivStabilizationTerm`	`<material>`, `<parameter_u>`, `<parameter_w>`, `<parameter_mv>`	$\gamma \int_{\Omega} [ (\nabla \cdot \ul{u}) (\nabla \cdot \ul{w}) (\nabla \cdot \ul{\Vcal}) - \pdiff{u_i}{x_k} \pdiff{\Vcal_k}{x_i} (\nabla \cdot \ul{w}) - (\nabla \cdot \ul{u}) \pdiff{w_i}{x_k} \pdiff{\Vcal_k}{x_i} ]$
ev_sd_st_pspg_c `SDPSPGCStabilizationTerm`	`<material>`, `<parameter_b>`, `<parameter_u>`, `<parameter_r>`, `<parameter_mv>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ \pdiff{r}{x_i} (\ul{b} \cdot \nabla u_i) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} \pdiff{\Vcal_k}{x_i} (\ul{b} \cdot \nabla u_i) - \pdiff{r}{x_k} (\ul{b} \cdot \nabla \Vcal_k) \pdiff{u_i}{x_k} ]$
ev_sd_st_pspg_p `SDPSPGPStabilizationTerm`	`<material>`, `<parameter_r>`, `<parameter_p>`, `<parameter_mv>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ [ (\nabla r \cdot \nabla p) (\nabla \cdot \Vcal) - \pdiff{r}{x_k} (\nabla \Vcal_k \cdot \nabla p) - (\nabla r \cdot \nabla \Vcal_k) \pdiff{p}{x_k} ]$
ev_sd_st_supg_c `SDSUPGCStabilizationTerm`	`<material>`, `<parameter_b>`, `<parameter_u>`, `<parameter_w>`, `<parameter_mv>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ [ (\ul{b} \cdot \nabla u_k) (\ul{b} \cdot \nabla w_k) (\nabla \cdot \Vcal) - (\ul{b} \cdot \nabla \Vcal_i) \pdiff{u_k}{x_i} (\ul{b} \cdot \nabla w_k) - (\ul{u} \cdot \nabla u_k) (\ul{b} \cdot \nabla \Vcal_i) \pdiff{w_k}{x_i} ]$
dw_st_adj1_supg_p `SUPGPAdj1StabilizationTerm`	`<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`	`<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`	`<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`	`<material>`, `<virtual>`, `<state>`	$\gamma \int_{\Omega} (\nabla\cdot\ul{u}) \cdot (\nabla\cdot\ul{v})$	sta.nav.sto
dw_st_pspg_c `PSPGCStabilizationTerm`	`<material>`, `<virtual>`, `<parameter>`, `<state>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ ((\ul{b} \cdot \nabla) \ul{u}) \cdot \nabla q$	sta.nav.sto
dw_st_pspg_p `PSPGPStabilizationTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla p \cdot \nabla q$	sta.nav.sto
dw_st_supg_c `SUPGCStabilizationTerm`	`<material>`, `<virtual>`, `<parameter>`, `<state>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ ((\ul{b} \cdot \nabla) \ul{u})\cdot ((\ul{b} \cdot \nabla) \ul{v})$	sta.nav.sto
dw_st_supg_p `SUPGPStabilizationTerm`	`<material>`, `<virtual>`, `<parameter>`, `<state>`	$\sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p\cdot ((\ul{b} \cdot \nabla) \ul{v})$	sta.nav.sto
dw_volume_dot_w_scalar_eth `DotSProductVolumeOperatorWETHTerm`	`<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`	`<ts>`, `<material>`, `<virtual>`, `<state>`	$\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q$

Table of multi-linear terms¶

Multi-linear terms¶
name/class	arguments	definition
de_cauchy_stress `ECauchyStressTerm`	`<material>`, `<parameter>`	$\int_{\Omega} D_{ijkl} e_{kl}(\ul{w})$
de_convect `EConvectTerm`	`<virtual>`, `<state>` `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v} \mbox{ , } \int_{\Omega} ((\ul{w} \cdot \nabla) \ul{w}) \cdot \bar{\ul{u}}$
de_div `EDivTerm`	`<opt_material>`, `<virtual>` `<opt_material>`, `<parameter>`	$\int_{\Omega} \nabla \cdot \ul{v} \mbox { , } \int_{\Omega} \nabla \cdot \ul{u} \\ \int_{\Omega} c \nabla \cdot \ul{v} \mbox { , } \int_{\Omega} c \nabla \cdot \ul{u}$
de_div_grad `EDivGradTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nu\ \nabla \ul{u} : \nabla \ul{w} \\ \int_{\Omega} \nabla \ul{v} : \nabla \ul{u} \mbox{ , } \int_{\Omega} \nabla \ul{u} : \nabla \ul{w}$
de_dot `EDotTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\cal{D}} q p \mbox{ , } \int_{\cal{D}} \ul{v} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} p r \mbox{ , } \int_{\cal{D}} \ul{u} \cdot \ul{w} \\ \int_{\cal{D}} c q p \mbox{ , } \int_{\cal{D}} c \ul{v} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} c p r \mbox{ , } \int_{\cal{D}} c \ul{u} \cdot \ul{w} \\ \int_{\cal{D}} \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} \ul{u} \cdot \ull{M} \cdot \ul{w}$
de_integrate `EIntegrateOperatorTerm`	`<opt_material>`, `<virtual>`	$\int_\Omega q \mbox{ or } \int_\Omega c q$
de_laplace `ELaplaceTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} c \nabla q \cdot \nabla p \mbox{ , } \int_{\Omega} c \nabla \bar{p} \cdot \nabla r$
de_lin_elastic `ELinearElasticTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<parameter_1>`, `<parameter_2>`	$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u}) \mbox{ , } \int_{\Omega} D_{ijkl}\ e_{ij}(\ul{w}) e_{kl}(\ul{u})$
de_non_penetration_p `ENonPenetrationPenaltyTerm`	`<material>`, `<virtual>`, `<state>`	$\int_{\Gamma} c (\ul{n} \cdot \ul{v}) (\ul{n} \cdot \ul{u})$
de_s_dot_mgrad_s `EScalarDotMGradScalarTerm`	`<material>`, `<virtual>`, `<state>` `<material>`, `<state>`, `<virtual>`	$\int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , } \int_{\Omega} p \ul{y} \cdot \nabla q$
de_stokes `EStokesTerm`	`<opt_material>`, `<virtual>`, `<state>` `<opt_material>`, `<state>`, `<virtual>` `<opt_material>`, `<parameter_v>`, `<parameter_s>`	$\int_{\Omega} p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} q\ \nabla \cdot \ul{u} \mbox{ or } \int_{\Omega} c\ p\ \nabla \cdot \ul{v} \mbox{ , } \int_{\Omega} c\ q\ \nabla \cdot \ul{u} \\ \int_{\Omega} r\ \nabla \cdot \ul{w} \mbox{ , } \int_{\Omega} c r\ \nabla \cdot \ul{w}$