Functions
void	mass (MatrixElemental &localMass, const CurrentFE &massCFE, const Real &coefficient, const UInt &fieldDim)
	Elementary mass for constant mass coefficient. More...

void	stiffness (MatrixElemental &localStiff, const CurrentFE &stiffCFE, const Real &coefficient, const UInt &fieldDim)
	Elementary stiffness for constant coefficient. More...

void	advectionNewton (Real coef, VectorElemental &vel, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock)
	Assemble the term $\int_\Omega \phi_j\cdot\mathbf{u}\phi_i$ . More...

void	grad (MatrixElemental &elmat, const CurrentFE &uCFE, const CurrentFE &pCFE, const UInt &fieldDim)

void	divergence (MatrixElemental &elmat, const CurrentFE &uCFE, const CurrentFE &pCFE, const UInt &fieldDim, const Real &coefficient)

void	stiffStrain (MatrixElemental &localStiff, const CurrentFE &stiffCFE, const Real &coefficient, const UInt &fieldDim)

void	bodyForces (VectorElemental &localForce, const CurrentFE &massRhsCFE, const function_Type &fun, const Real &t, const UInt &fieldDim)

void	stiff_sd (Real coef, const VectorElemental &vec_loc, MatrixElemental &elmat, const CurrentFE &fe, const CurrentFE &fe2, int iblock=0, int jblock=0, int nb=1)
	StreamLine Diffusion. More...

void	grad (const int icoor, const VectorElemental &vec_loc, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, int iblock, int jblock)
	Convective term with a local vector coefficient (useful for Navier-Stokes problem) More...

void	grad_ss (const int icoor, const VectorElemental &vec_loc, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, int iblock=0, int jblock=0)
	Convective term with a local vector coefficient for Navier-Stokes problem in Skew-Symmetric form. More...

void	grad (const int icoor, const VectorElemental &vec_loc, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const CurrentFE &fe3, int iblock=0, int jblock=0)
	Convective term with a local vector coefficient (useful for Navier-Stokes problem+adv-diff) More...

void	grad (const int &icoor, const std::vector< Real > &localVector, MatrixElemental &elmat, const CurrentFE &currentFE1, const CurrentFE &currentFE2, const int &iblock=0, const int &jblock=0)
	Conective term with a local vector given by quadrature node. More...

void	source (Real coef, VectorElemental &f, VectorElemental &elvec, const CurrentFE &fe, int fblock, int eblock)

void	source_fhn (Real coef_f, Real coef_a, VectorElemental &u, VectorElemental &elvec, const CurrentFE &fe, int fblock, int eblock)

void	source_advection (const Real &coefficient, const VectorElemental &beta_loc, const VectorElemental &uk_loc, VectorElemental &elvec, const CurrentFE &fe)
	$(beta\cdot\nabla u^k, v )$ More...

template<typename localVector >
void	weightedMass (MatrixElemental &localMass, const CurrentFE &massCFE, const Real &coefficient, const localVector &localValues, const UInt &fieldDim)
	Elementary weighted mass for constant mass coefficient. More...

template<typename localVector , typename globalVector >
void	interpolate (localVector &localValues, const CurrentFE &interpCFE, const UInt &spaceDim, const DOF &betaDof, const UInt &elementID, const globalVector &beta)
	Interpolation procedure. More...

template<typename localVector , typename globalVector >
void	interpolateGradient (localVector &localGradient, const CurrentFE &interpCFE, const UInt &spaceDim, const DOF &betaDof, const UInt &elementID, const globalVector &beta)
	Interpolation of the gradient. More...

template<typename localVector , typename globalVector >
void	interpolateDivergence (localVector &localDivergence, const CurrentFE &interpCFE, const DOF &betaDof, const UInt &elementID, const globalVector &beta)
	Interpolation of the divergence. More...

template<typename localVector >
void	massDivW (MatrixElemental &localMass, const CurrentFE &massCFE, const Real &coefficient, const localVector &localValues, const UInt &fieldDim)

template<typename localVector >
void	advection (MatrixElemental &localAdv, const CurrentFE &advCFE, const Real &coefficient, const localVector &localValues, const UInt &fieldDim)
	Elementary advection u v. More...

template<typename localTensor >
void	symmetrizedAdvection (MatrixElemental &localAdv, const CurrentFE &advCFE, const Real &coefficient, const localTensor &localGradient, const UInt &fieldDim)
	Elementary advection, term u v. More...

template<typename UsrFct >
void	source (const UsrFct &fct, VectorElemental &elvec, const CurrentFE &fe, int iblock=0)
	source $\int fct \phi_i$ More...

template<typename UsrFct >
void	source (const UsrFct &fct, VectorElemental &elvec, const CurrentFE &fe, Real t, int iblock=0)
	source $\int fct(t) \phi_i$ More...

Public typedefs
typedef std::function< const Real(const Real &, const Real &, const Real &, const Real &, const ID &) >	function_Type
	Use the portable syntax of the boost function. More...

Operators for classical finite elements
void	mass (Real coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock=0, int jblock=0)
	coef(t,x,y,z,u) More...

void	mass (Real coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, UInt nb)

void	mass (const std::vector< Real > &qpt_coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, UInt nb)
	Mass term with coefficients given for each quadrature point. More...

void	stiff_divgrad (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_divgrad_2 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_gradgrad (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_gradgrad_2 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_dergrad_gradbis (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_dergrad_gradbis_Tr (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_dergrad_gradbis_2 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_dergrad_gradbis_Tr_2 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_gradgradTr_gradbis (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_gradgradTr_gradbis_2 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff_gradgradTr_gradbis_3 (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)

void	stiff (Real coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock)

void	stiff (Real coef, Real(*fct)(Real, Real, Real), MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock)

void	stiff (Real coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, int nb)

void	stiff (const std::vector< Real > &qpt_coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, int nb)
	Stiff term with coefficient given for each quadrature node. More...

void	stiff_curl (Real coef, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, int)

void	stiff_div (Real coef, MatrixElemental &elmat, const CurrentFE &fe)
	$coef \cdot ( div u , div v )$ More...

void	stiff_dergradbis (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	$coef \cdot ( [\nabla u^k]^T \nabla u : \nabla v )$ More...

void	stiff_dergrad (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	$coef \cdot ( [\nabla u]^T \nabla u^k + [\nabla u^k]^T \nabla u : \nabla v )$ for Newton on St-Venant More...

void	stiff_derdiv (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe)
	$coef \cdot ( trace { [\nabla u^k]^T \nabla u }, \nabla\cdot v )$ for Newton on St-Venant More...

void	stiff_strain (Real coef, MatrixElemental &elmat, const CurrentFE &fe)
	$coef \cdot ( e(u) , e(v) )$ More...

void	grad (const int icoor, Real coef, MatrixElemental &elmat, const CurrentFE &fe_u, const CurrentFE &fe_p, int iblock, int jblock)

void	div (const int icoor, Real coef, MatrixElemental &elmat, const CurrentFE &fe_u, const CurrentFE &fe_p, int iblock, int jblock)

void	grad_div (Real coef_grad, Real coef_div, MatrixElemental &elmat, const CurrentFE &fe_u, const CurrentFE &fe_p, int block_pres)

void	stab_stokes (Real visc, Real coef_stab, MatrixElemental &elmat, const CurrentFE &fe, int block_pres)

void	advection (Real coef, VectorElemental &vel, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, int nb)

void	source (Real constant, VectorElemental &elvec, const CurrentFE &fe, int iblock)

void	source_mass (const std::vector< Real > &constant, VectorElemental &elvec, const CurrentFE &currentFe, const int &iblock)
	Assembly for the source term $\int c v$ where is a given by the values in the quadrature nodes. More...

void	source_stiff (const std::vector< Real > &constant, VectorElemental &elvec, const CurrentFE &currentFe, const int &iblock)
	Assembly for the source term $\int \nabla c \cdot \nabla v$ where is a given by the values in the quadrature nodes. More...

void	source_divuq (Real alpha, VectorElemental &uLoc, VectorElemental &elvec, const CurrentFE &fe_u, const CurrentFE &fe_p, int iblock)

void	source_gradpv (Real alpha, VectorElemental &pLoc, VectorElemental &elvec, const CurrentFE &fe_p, const CurrentFE &fe_u, int iblock)

template<typename UsrFct >
void	advection (Real coef, const UsrFct &beta, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, int nb, Real t=0.)

void	source (Real constant, VectorElemental &elvec, const CurrentFE &fe, Real t, int iblock)

Elementary operations for the interior penalty stabilization
void	ipstab_grad (const Real coef, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const CurrentFEManifold &bdfe, int iblock=0, int jblock=0)
	$coef < \nabla p1, \nabla q2 >$ More...

void	ipstab_grad (const Real coef, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const CurrentFEManifold &bdfe, int iblock, int jblock, int nb)
	$coef < \nabla u1, \nabla v2 >$ More...

void	ipstab_bgrad (const Real coef, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const VectorElemental &beta, const CurrentFEManifold &bdfe, int iblock, int jblock, int nb)
	$coef < \beta1 . \nabla u1, \beta2 . \nabla v2 >$ More...

void	ipstab_div (const Real coef, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const CurrentFEManifold &bdfe, int iblock=0, int jblock=0)
	$coef < \nabla\cdot u1, \nabla\cdot v2 >$ More...

void	ipstab_bagrad (const Real coef, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const VectorElemental &beta, const CurrentFEManifold &bdfe, int iblock=0, int jblock=0)
	$coef < \|\beta . n\|^2 / \|\beta\| \nabla p1, \nabla q2 >$ More...

void	ipstab_bagrad (const Real coef, MatrixElemental &elmat, const CurrentFE &fe1, const CurrentFE &fe2, const CurrentFE &fe3, const VectorElemental &beta, const CurrentFEManifold &bdfe, int iblock=0, int jblock=0)
	$coef < \|\beta\cdot n\| \nabla p1, \nabla q2 >$ p1 lives in fe1 q2 lives in fe2 beta lives in fe3 More...

Shape derivative terms for Newton FSI
void	source_mass1 (Real coef, const VectorElemental &uk_loc, const VectorElemental &wk_loc, const VectorElemental &convect_loc, const VectorElemental &d_loc, VectorElemental &elvec, const CurrentFE &fe)
	$coef \cdot ( \nabla (-w^k):[I\nabla\cdot d - (\nabla d)^T] u^k + convect^T[I\nabla\cdot d - (\nabla d)^T] (\nabla u^k)^T , v )$ for Newton FSI More...

void	source_mass2 (Real coef, const VectorElemental &uk_loc, const VectorElemental &dw_loc, VectorElemental &elvec, const CurrentFE &fe)
	$coef \cdot ( \nabla u^k dw, v )$ for Newton FSI More...

void	source_mass3 (Real coef, const VectorElemental &un_loc, const VectorElemental &uk_loc, const VectorElemental &d_loc, VectorElemental &elvec, const CurrentFE &fe)

void	source_stress (Real coef, Real mu, const VectorElemental &uk_loc, const VectorElemental &pk_loc, const VectorElemental &d_loc, VectorElemental &elvec, const CurrentFE &fe_u, const CurrentFE &fe_p)
	$coef \cdot ( [-p^k I + 2\mu e(u^k)] [I\nabla\cdot d - (\nabla d)^T] , \nabla v )$ for Newton FSI More...

void	source_stress2 (Real coef, const VectorElemental &uk_loc, const VectorElemental &d_loc, VectorElemental &elvec, const CurrentFE &fe_u)
	$+ \mu ( \nabla u^k \nabla d + [\nabla d]^T[\nabla u^k]^T : \nabla v )$ More...

void	source_press (Real coef, const VectorElemental &uk_loc, const VectorElemental &d_loc, VectorElemental &elvec, const CurrentFE &fe_u, const CurrentFE &fe_p, int iblock=0)
	$coef * ( (\nabla u^k):[I\nabla\cdot d - (\nabla d)^T] , q )$ for Newton FSI More...

void	source_press2 (Real coef, const VectorElemental &p_loc, const VectorElemental &d_loc, VectorElemental &elvec, const CurrentFE &fe, int iblock)

void	source_press (Real coef, const VectorElemental &uk_loc, MatrixElemental &elmat, const CurrentFE &fe_u, const CurrentFE &fe_p, ID mmDim, int iblock=0)
	$coef * ( (\nabla u^k):[I\nabla\cdot d - (\nabla d)^T] , q )$ for Newton FSI More...

void	shape_terms ( Real coef, Real mu, const VectorElemental &un_loc, const VectorElemental &uk_loc, const VectorElemental &wk_loc, const VectorElemental &convect_loc, const VectorElemental &pk_loc, MatrixElemental &elmat, const CurrentFE &fe, const CurrentFE &fe_p, ID mmDim, MatrixElemental &, int iblock=0, bool wImplicit=false, Real alpha=0., std::shared_ptr< MatrixElemental > elmat_convect=std::shared_ptr< MatrixElemental >())
	Shape terms for the CE system in FSI Newton. More...

Mass matrix
void	mass_divw (Real coef, const VectorElemental &w_loc, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, UInt nb)

void	mass_divw (const std::vector< Real > &coef, const VectorElemental &w_loc, MatrixElemental &elmat, const CurrentFE &fe, int iblock, int jblock, UInt nb)
	Idem `mass_divw` , but with coefficient given by quadrature node. More...

void	mass_gradu (Real coef, const VectorElemental &u0_loc, MatrixElemental &elmat, const CurrentFE &fe)

Cholesky
void	choldc (KNM< Real > &a, KN< Real > &p)

void	cholsl (KNM< Real > &a, KN< Real > &p, KN< Real > &b, KN< Real > &x)

Operators for H(div) finite elements
void	grad_Hdiv (Real coef, MatrixElemental &elmat, const CurrentFE &dualFE, const CurrentFE &primalFE, int iblock, int jblock)

void	div_Hdiv (Real coef, MatrixElemental &elmat, const CurrentFE &dualFE, const CurrentFE &primalFE, int iblock, int jblock)

void	TP_VdotN_Hdiv (Real coef, MatrixElemental &elmat, const ReferenceFEHybrid &hybridFE, const ReferenceFEHybrid &dualDotNFE, int iblock, int jblock)

void	TP_TP_Hdiv (Real coef, MatrixElemental &elmat, const ReferenceFEHybrid &hybridFE, int iblock, int jblock)

void	mass_Hdiv (Real coef, MatrixElemental &elmat, const CurrentFE &dualFE, int iblock, int jblock)

void	mass_Hdiv (Matrix const &Invperm, MatrixElemental &elmat, const CurrentFE &dualFE, int iblock, int jblock)

void	mass_Hdiv (Real(*InvpermFun)(const Real &, const Real &, const Real &), MatrixElemental &elmat, const CurrentFE &dualFE, int iblock, int jblock)

void	source_Hdiv (const Vector &source, VectorElemental &elvec, const CurrentFE &dualFE, int iblock)

Detailed Description

/namespace AssemblyElemental

This namespace is specially designed to contain the elementary operations (corresponding to differential operators) that build the local contributions to be used in the assembly procedures.

Typedef Documentation

◆ function_Type

typedef std::function< const Real (const Real&, const Real&, const Real&, const Real&, const ID&) > function_Type

Use the portable syntax of the boost function.

Definition at line 84 of file AssemblyElemental.hpp.

Function Documentation

◆ mass() [1/4]

void mass	(	MatrixElemental &	localMass,
		const CurrentFE &	massCFE,
		const Real &	coefficient,
		const UInt &	fieldDim
	)

Elementary mass for constant mass coefficient.

This function assembles the local mass matrix when the mass coefficient is constant.

Parameters

localMass	The local matrix to be filled (not cleaned by this function)
massCFE	The currentFE structure already updated for the assembly. It requires phi and wDetJacobian to be accessible.
coefficient	The mass coefficient
fieldDim	The dimension of the FE space (scalar/vectorial)

Definition at line 46 of file AssemblyElemental.cpp.

◆ stiffness()

void stiffness	(	MatrixElemental &	localStiff,
		const CurrentFE &	stiffCFE,
		const Real &	coefficient,
		const UInt &	fieldDim
	)

Elementary stiffness for constant coefficient.

This function assembles the local stiffness matrix when the coefficient is constant.

Parameters

localStiff	The local matrix to be filled (not cleaned by this function)
stiffCFE	The currentFE structure already updated for the assembly. It requires dphi and wDetJacobian to be accessible.
coefficient	The coefficient
fieldDim	The dimension of the FE space (scalar/vectorial)

Definition at line 106 of file AssemblyElemental.cpp.

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◆ advectionNewton()

void advectionNewton	(	Real	coef,
		VectorElemental &	vel,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock
	)

Assemble the term $\int_\Omega \phi_j\cdot\mathbf{u}\phi_i$ .

Definition at line 173 of file AssemblyElemental.cpp.

◆ grad() [1/5]

void grad	(	MatrixElemental &	elmat,
		const CurrentFE &	uCFE,
		const CurrentFE &	pCFE,
		const UInt &	fieldDim
	)

Definition at line 204 of file AssemblyElemental.cpp.

◆ divergence()

void divergence	(	MatrixElemental &	elmat,
		const CurrentFE &	uCFE,
		const CurrentFE &	pCFE,
		const UInt &	fieldDim,
		const Real &	coefficient
	)

Definition at line 235 of file AssemblyElemental.cpp.

◆ stiffStrain()

void stiffStrain	(	MatrixElemental &	localStiff,
		const CurrentFE &	stiffCFE,
		const Real &	coefficient,
		const UInt &	fieldDim
	)

Definition at line 267 of file AssemblyElemental.cpp.

◆ bodyForces()

void bodyForces	(	VectorElemental &	localForce,
		const CurrentFE &	massRhsCFE,
		const function_Type &	fun,
		const Real &	t,
		const UInt &	fieldDim
	)

Definition at line 303 of file AssemblyElemental.cpp.

◆ mass() [2/4]

void mass	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock
	)

coef(t,x,y,z,u)

Definition at line 362 of file AssemblyElemental.cpp.

◆ mass() [3/4]

void mass	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		UInt	nb
	)

Definition at line 405 of file AssemblyElemental.cpp.

◆ mass() [4/4]

void mass	(	const std::vector< Real > &	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		UInt	nb
	)

Mass term with coefficients given for each quadrature point.

Definition at line 467 of file AssemblyElemental.cpp.

◆ stiff_divgrad()

void stiff_divgrad	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 530 of file AssemblyElemental.cpp.

◆ stiff_divgrad_2()

void stiff_divgrad_2	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 582 of file AssemblyElemental.cpp.

◆ stiff_gradgrad()

void stiff_gradgrad	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 635 of file AssemblyElemental.cpp.

◆ stiff_gradgrad_2()

void stiff_gradgrad_2	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 687 of file AssemblyElemental.cpp.

◆ stiff_dergrad_gradbis()

void stiff_dergrad_gradbis	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 742 of file AssemblyElemental.cpp.

◆ stiff_dergrad_gradbis_Tr()

void stiff_dergrad_gradbis_Tr	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 800 of file AssemblyElemental.cpp.

◆ stiff_dergrad_gradbis_2()

void stiff_dergrad_gradbis_2	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 858 of file AssemblyElemental.cpp.

◆ stiff_dergrad_gradbis_Tr_2()

void stiff_dergrad_gradbis_Tr_2	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 917 of file AssemblyElemental.cpp.

◆ stiff_gradgradTr_gradbis()

void stiff_gradgradTr_gradbis	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 976 of file AssemblyElemental.cpp.

◆ stiff_gradgradTr_gradbis_2()

void stiff_gradgradTr_gradbis_2	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 1038 of file AssemblyElemental.cpp.

◆ stiff_gradgradTr_gradbis_3()

void stiff_gradgradTr_gradbis_3	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 1099 of file AssemblyElemental.cpp.

◆ ipstab_grad() [1/2]

void ipstab_grad	(	const Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const CurrentFEManifold &	bdfe,
		int	iblock,
		int	jblock
	)

$coef < \nabla p1, \nabla q2 >$

Definition at line 1171 of file AssemblyElemental.cpp.

◆ ipstab_grad() [2/2]

void ipstab_grad	(	const Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const CurrentFEManifold &	bdfe,
		int	iblock,
		int	jblock,
		int	nb
	)

$coef < \nabla u1, \nabla v2 >$

Definition at line 1272 of file AssemblyElemental.cpp.

◆ ipstab_bgrad()

void ipstab_bgrad	(	const Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const VectorElemental &	beta,
		const CurrentFEManifold &	bdfe,
		int	iblock,
		int	jblock,
		int	nb
	)

$coef < \beta1 . \nabla u1, \beta2 . \nabla v2 >$

Definition at line 1379 of file AssemblyElemental.cpp.

◆ ipstab_div()

void ipstab_div	(	const Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const CurrentFEManifold &	bdfe,
		int	iblock,
		int	jblock
	)

$coef < \nabla\cdot u1, \nabla\cdot v2 >$

Definition at line 1513 of file AssemblyElemental.cpp.

◆ ipstab_bagrad() [1/2]

void ipstab_bagrad	(	const Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const VectorElemental &	beta,
		const CurrentFEManifold &	bdfe,
		int	iblock,
		int	jblock
	)

$coef < |\beta . n|^2 / |\beta| \nabla p1, \nabla q2 >$

Definition at line 1604 of file AssemblyElemental.cpp.

◆ ipstab_bagrad() [2/2]

void ipstab_bagrad	(	const Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const CurrentFE &	fe3,
		const VectorElemental &	beta,
		const CurrentFEManifold &	bdfe,
		int	iblock,
		int	jblock
	)

$coef < |\beta\cdot n| \nabla p1, \nabla q2 >$ p1 lives in fe1 q2 lives in fe2 beta lives in fe3

Definition at line 1727 of file AssemblyElemental.cpp.

◆ stiff() [1/4]

void stiff	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock
	)

Definition at line 1848 of file AssemblyElemental.cpp.

◆ stiff() [2/4]

void stiff	(	Real	coef,
		Real(*)(Real, Real, Real)	fct,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock
	)

Definition at line 1894 of file AssemblyElemental.cpp.

◆ stiff() [3/4]

void stiff	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		int	nb
	)

Definition at line 1942 of file AssemblyElemental.cpp.

◆ stiff() [4/4]

void stiff	(	const std::vector< Real > &	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		int	nb
	)

Stiff term with coefficient given for each quadrature node.

Definition at line 2009 of file AssemblyElemental.cpp.

◆ stiff_curl()

void stiff_curl	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		int
	)

Definition at line 2077 of file AssemblyElemental.cpp.

◆ stiff_div()

void stiff_div	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

$coef \cdot ( div u , div v )$

Definition at line 2503 of file AssemblyElemental.cpp.

◆ stiff_dergradbis()

void stiff_dergradbis	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

$coef \cdot ( [\nabla u^k]^T \nabla u : \nabla v )$

Definition at line 2539 of file AssemblyElemental.cpp.

◆ stiff_dergrad()

void stiff_dergrad	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

$coef \cdot ( [\nabla u]^T \nabla u^k + [\nabla u^k]^T \nabla u : \nabla v )$ for Newton on St-Venant

Definition at line 2600 of file AssemblyElemental.cpp.

◆ stiff_derdiv()

void stiff_derdiv	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

$coef \cdot ( trace { [\nabla u^k]^T \nabla u }, \nabla\cdot v )$ for Newton on St-Venant

Definition at line 2665 of file AssemblyElemental.cpp.

◆ stiff_strain()

void stiff_strain	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

$coef \cdot ( e(u) , e(v) )$

Definition at line 2722 of file AssemblyElemental.cpp.

◆ mass_divw() [1/2]

void mass_divw	(	Real	coef,
		const VectorElemental &	w_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		UInt	nb
	)

Weighted Mass matrix with a permeability tensor which is a constant scalar matrix (i.e. $K^{-1} = coef \cdot Id$ , coef being the inverse of the permeability).

Definition at line 2772 of file AssemblyElemental.cpp.

◆ mass_divw() [2/2]

void mass_divw	(	const std::vector< Real > &	coef,
		const VectorElemental &	w_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		UInt	nb
	)

Idem mass_divw , but with coefficient given by quadrature node.

Definition at line 2846 of file AssemblyElemental.cpp.

◆ mass_gradu()

void mass_gradu	(	Real	coef,
		const VectorElemental &	u0_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe
	)

Definition at line 2921 of file AssemblyElemental.cpp.

◆ stiff_sd()

void stiff_sd	(	Real	coef,
		const VectorElemental &	vec_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		const CurrentFE &	fe2,
		int	iblock,
		int	jblock,
		int	nb
	)

StreamLine Diffusion.

Definition at line 2980 of file AssemblyElemental.cpp.

◆ grad() [2/5]

void grad	(	const int	icoor,
		Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p,
		int	iblock,
		int	jblock
	)

Definition at line 3085 of file AssemblyElemental.cpp.

◆ div()

void div	(	const int	icoor,
		Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p,
		int	iblock,
		int	jblock
	)

Definition at line 3114 of file AssemblyElemental.cpp.

◆ grad_div()

void grad_div	(	Real	coef_grad,
		Real	coef_div,
		MatrixElemental &	elmat,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p,
		int	block_pres
	)

Definition at line 3139 of file AssemblyElemental.cpp.

◆ stab_stokes()

void stab_stokes	(	Real	visc,
		Real	coef_stab,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	block_pres
	)

Definition at line 3168 of file AssemblyElemental.cpp.

◆ advection() [1/3]

void advection	(	Real	coef,
		VectorElemental &	vel,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		int	nb
	)

Definition at line 3194 of file AssemblyElemental.cpp.

◆ grad() [3/5]

void grad	(	const int	icoor,
		const VectorElemental &	vec_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		int	iblock,
		int	jblock
	)

Convective term with a local vector coefficient (useful for Navier-Stokes problem)

Definition at line 3250 of file AssemblyElemental.cpp.

◆ grad_ss()

void grad_ss	(	const int	icoor,
		const VectorElemental &	vec_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		int	iblock,
		int	jblock
	)

Convective term with a local vector coefficient for Navier-Stokes problem in Skew-Symmetric form.

Definition at line 3293 of file AssemblyElemental.cpp.

◆ grad() [4/5]

void grad	(	const int	icoor,
		const VectorElemental &	vec_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe1,
		const CurrentFE &	fe2,
		const CurrentFE &	fe3,
		int	iblock,
		int	jblock
	)

Convective term with a local vector coefficient (useful for Navier-Stokes problem+adv-diff)

Definition at line 3340 of file AssemblyElemental.cpp.

◆ grad() [5/5]

void grad	(	const int &	icoor,
		const std::vector< Real > &	localVector,
		MatrixElemental &	elmat,
		const CurrentFE &	currentFE1,
		const CurrentFE &	currentFE2,
		const int &	iblock = `0`,
		const int &	jblock = `0`
	)

Conective term with a local vector given by quadrature node.

To use this function, we must ensure that the velocity is stored in a good way in the std::vector: If there are nQ quadrature nodes, the i-th component (starting from 0) of the velocity in the iq-th quadrature node (also starting from 0) has to be stored in the ( i*nQ + iq)-th element of the std::vector.

Definition at line 3388 of file AssemblyElemental.cpp.

◆ source() [1/5]

void source	(	Real	constant,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		int	iblock
	)

Definition at line 3483 of file AssemblyElemental.cpp.

◆ source() [2/5]

void source	(	Real	coef,
		VectorElemental &	f,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		int	fblock,
		int	eblock
	)

Definition at line 3499 of file AssemblyElemental.cpp.

◆ source_mass()

void source_mass	(	const std::vector< Real > &	constant,
		VectorElemental &	elvec,
		const CurrentFE &	currentFe,
		const int &	iblock
	)

Assembly for the source term $\int c v$ where $c$ is a given by the values in the quadrature nodes.

This function add in the elementary vector the term $\int c v$ . The function $c$ is given by its values in the quadrature nodes.

Parameters

constant	Values of the function in the quadrature nodes
elvec	The local vector where to add the values
currentFe	The currentFE associated to the cell where to assemble
iblock	The component of v that is concerned

Definition at line 3528 of file AssemblyElemental.cpp.

◆ source_stiff()

void source_stiff	(	const std::vector< Real > &	constant,
		VectorElemental &	elvec,
		const CurrentFE &	currentFe,
		const int &	iblock
	)

Assembly for the source term $\int \nabla c \cdot \nabla v$ where $c$ is a given by the values in the quadrature nodes.

The function $\nabla c$ is given by its values in the quadrature nodes, coordinate after coordinate (first, the values for the first componant of the gradient in all the quadrature nodes, then second component,...).

Parameters

constant	Values of the gradient in the quadrature nodes
elvec	The local vector where to add the values
currentFe	The currentFE associated to the cell where to assemble
iblock	The component of v that is concerned

Definition at line 3542 of file AssemblyElemental.cpp.

◆ source_divuq()

void source_divuq	(	Real	alpha,
		VectorElemental &	uLoc,
		VectorElemental &	elvec,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p,
		int	iblock
	)

Definition at line 3562 of file AssemblyElemental.cpp.

◆ source_gradpv()

void source_gradpv	(	Real	alpha,
		VectorElemental &	pLoc,
		VectorElemental &	elvec,
		const CurrentFE &	fe_p,
		const CurrentFE &	fe_u,
		int	iblock
	)

Definition at line 3583 of file AssemblyElemental.cpp.

◆ source_fhn()

void source_fhn	(	Real	coef_f,
		Real	coef_a,
		VectorElemental &	u,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		int	fblock,
		int	eblock
	)

Definition at line 3604 of file AssemblyElemental.cpp.

◆ source_advection()

void source_advection	(	const Real &	coefficient,
		const VectorElemental &	beta_loc,
		const VectorElemental &	uk_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

$(beta\cdot\nabla u^k, v )$

$( beta\cdot\nabla u^k, v )$

Definition at line 3635 of file AssemblyElemental.cpp.

◆ source_mass1()

void source_mass1	(	Real	coef,
		const VectorElemental &	uk_loc,
		const VectorElemental &	wk_loc,
		const VectorElemental &	convect_loc,
		const VectorElemental &	d_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

$coef \cdot ( \nabla (-w^k):[I\nabla\cdot d - (\nabla d)^T] u^k + convect^T[I\nabla\cdot d - (\nabla d)^T] (\nabla u^k)^T , v )$ for Newton FSI

Remark: convect = $u^n-w^k$

Definition at line 3722 of file AssemblyElemental.cpp.

◆ source_mass2()

void source_mass2	(	Real	coef,
		const VectorElemental &	uk_loc,
		const VectorElemental &	dw_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

$coef \cdot ( \nabla u^k dw, v )$ for Newton FSI

Definition at line 3871 of file AssemblyElemental.cpp.

◆ source_mass3()

void source_mass3	(	Real	coef,
		const VectorElemental &	un_loc,
		const VectorElemental &	uk_loc,
		const VectorElemental &	d_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe
	)

Definition at line 3956 of file AssemblyElemental.cpp.

◆ source_stress()

void source_stress	(	Real	coef,
		Real	mu,
		const VectorElemental &	uk_loc,
		const VectorElemental &	pk_loc,
		const VectorElemental &	d_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p
	)

$coef \cdot ( [-p^k I + 2\mu e(u^k)] [I\nabla\cdot d - (\nabla d)^T] , \nabla v )$ for Newton FSI

Definition at line 4063 of file AssemblyElemental.cpp.

◆ source_stress2()

void source_stress2	(	Real	coef,
		const VectorElemental &	uk_loc,
		const VectorElemental &	d_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe_u
	)

$+ \mu ( \nabla u^k \nabla d + [\nabla d]^T[\nabla u^k]^T : \nabla v )$

Definition at line 4194 of file AssemblyElemental.cpp.

◆ source_press() [1/2]

void source_press	(	Real	coef,
		const VectorElemental &	uk_loc,
		const VectorElemental &	d_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p,
		int	iblock
	)

$coef * ( (\nabla u^k):[I\nabla\cdot d - (\nabla d)^T] , q )$ for Newton FSI

Definition at line 4290 of file AssemblyElemental.cpp.

◆ source_press2()

void source_press2	(	Real	coef,
		const VectorElemental &	p_loc,
		const VectorElemental &	d_loc,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		int	iblock
	)

Definition at line 4371 of file AssemblyElemental.cpp.

◆ choldc()

void choldc	(	KNM< Real > &	a,
		KN< Real > &	p
	)

Cholesky decomposition and solution for a KNM matrix.

Definition at line 4470 of file AssemblyElemental.cpp.

◆ cholsl()

void cholsl	(	KNM< Real > &	a,
		KN< Real > &	p,
		KN< Real > &	b,
		KN< Real > &	x
	)

Definition at line 4497 of file AssemblyElemental.cpp.

◆ source_press() [2/2]

void source_press	(	Real	coef,
		const VectorElemental &	uk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe_u,
		const CurrentFE &	fe_p,
		ID	mmDim,
		int	iblock
	)

$coef * ( (\nabla u^k):[I\nabla\cdot d - (\nabla d)^T] , q )$ for Newton FSI

fe_u.phi( i, ig )

d_loc.vec() [ i + jcoor * fe_u.nbFEDof() ];

Definition at line 4524 of file AssemblyElemental.cpp.

◆ shape_terms()

void shape_terms	(	Real	coef,
		Real	mu,
		const VectorElemental &	un_loc,
		const VectorElemental &	uk_loc,
		const VectorElemental &	wk_loc,
		const VectorElemental &	convect_loc,
		const VectorElemental &	pk_loc,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		const CurrentFE &	fe_p,
		ID	mmDim,
		MatrixElemental &	,
		int	iblock = `0`,
		bool	wImplicit = `false`,
		Real	alpha = `0.`,
		std::shared_ptr< MatrixElemental >	elmat_convect = `std::shared_ptr< MatrixElemental >()`
	)

Shape terms for the CE system in FSI Newton.

It is the sum of the terms source_mass1, source_stressand source_stress2. the difference between this method and the previous ones is that here the shape terms are assembled in a matrix, instead of a vector. This implies some extra loop and the explicit construction of the tensor $[I\nabla\cdot d - (\nabla d)^T]$ instead of it's multiplication times a vector. However the computation of these terms need to be done once per Newton iterations, instead of once per Jacobian-vector multiplication.

Note that the term source_mass2is not considered if the fluid domain velocity w is trated explicitly. This method is currently tested only for the P1-P1 stabilized space discretization.

d_loc.vec() [ i + jcoor * fe.nbFEDof() ]

a part of source_stress

building the tensor $\eta = [I\nabla\cdot d - (\nabla d)^T]$

source_mass1

source_stress

source_stress2

alpha

building the tensor $\eta = [I\nabla\cdot d - (\nabla d)^T]$

-2*{jcoor, kcoor} {icoor} + {jcoor, icoor}{kcoor}

Definition at line 4714 of file AssemblyElemental.cpp.

◆ grad_Hdiv()

void grad_Hdiv	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	dualFE,
		const CurrentFE &	primalFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the gradient of an element in $ H(div, K ) $ space, i.e. the opposite of the transpose divergence matrix, with $ K $ the current element. In formula

$\mathrm{coef} < \nabla q, w > \equiv - \mathrm{coef} < q, \nabla \cdot w > \,,$

for $q \in L^2(K)$ , $w \in H(div, K)$ and $\mathrm{coef}$ a real scalar.

Parameters

coef	Constant real coefficient.
elmat	Mixed element matrix.
dualFE	Current dual finite element in .
primalFE	Current primal finite element in .
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Definition at line 5079 of file AssemblyElemental.cpp.

◆ div_Hdiv()

void div_Hdiv	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	dualFE,
		const CurrentFE &	primalFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the divergence of an element in $ H(div,K ) $ , with $ K $ the current element. In formula

$\mathrm{coef} < q, \nabla \cdot w > \,,$

for $q \in L^2(K)$ , $w \in H(div, K)$ and $\mathrm{coef}$ a real scalar.

Parameters

coef	Constant real coefficient.
elmat	Mixed element matrix.
dualFE	Current dual finite element in .
primalFE	Current primal finite element in .
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Definition at line 5105 of file AssemblyElemental.cpp.

◆ TP_VdotN_Hdiv()

void TP_VdotN_Hdiv	(	Real	coef,
		MatrixElemental &	elmat,
		const ReferenceFEHybrid &	hybridFE,
		const ReferenceFEHybrid &	dualDotNFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the product between an hybrid variable and a dual variable dot product outward unit normal, in the current element $ K $ . In formula

$\mathrm{coef} < \lambda, v \cdot n >\,,$

for $\lambda \in H^{1/2}(\partial K)$ , $v \in H(div, K)$ , $ coef $ a real scalar and $ n $ the normal unit vector oriented outward of the current element $ K $ .
The $\lambda$ are the Lagrange multiplier basis functions that enforce continuity of the normal component of the vectorial functions across two neighbouring elements. They can be interprated as trace of primal variable.
See Hybridization for Mixed Hybrid Finite Element Method.
Thanks to the Piola transform, the computation is performed on the boundary of the reference element. But in general, the boundary of a 3D reference element is not a 2D reference element.
Example: REFERENCE TETRA -> 3 REFERENCE TRIA + 1 EQUILATERAL TRIANGLE... REFERENCE PRISM -> 2 TRIA + 3 QUAD...? REFERENCE HEXA -> 6 REFERENCE QUAD.

Parameters

coef	Constant real coefficient.
elmat	Mixed element matrix.
hybridFE	Reference hybrid finite element.
dualDotNFE	Reference dual dot product outward unit normal finite element.
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Note: The previous way of construction, worked only for RTO hexa, calls
TP_TP_Hdiv(coef, elmat, hybridFE, iblock, jblock);

Definition at line 5131 of file AssemblyElemental.cpp.

◆ TP_TP_Hdiv()

void TP_TP_Hdiv	(	Real	coef,
		MatrixElemental &	elmat,
		const ReferenceFEHybrid &	hybridFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the mass matrix for the hybrid variable, in the current element $ K $ . In formula

$\mathrm{coef} < \lambda, \mu > \,,$

for $\lambda, \mu \in H^{1/2}(\partial K)$ and $ coef $ a real scalar.
The $\lambda$ and $\mu$ are the Lagrange multiplier basis functions that enforce continuity of the normal component of the vectorial functions across two neighbouring elements. They can be interprated as trace of primal variable.
See Hybridization for Mixed Hybrid Finite Element Method.
Thanks to the Piola transform, the computation is performed on the boundary of the reference element. But in general, the boundary of a 3D Reference element is not a 2D reference element.
Example: REFERENCE TETRA -> 3 REFERENCE TRIA + 1 EQUILATERAL TRIANGLE... REFERENCE PRISM -> 2 TRIA + 3 QUAD...? REFERENCE HEXA -> 6 REFERENCE QUAD.

Parameters

coef	Constant real coefficient.
elmat	Mixed element matrix.
hybridFE	Reference hybrid finite element.
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Note: This is an obsolete function, call TP_VdotN_Hdiv instead.

Definition at line 5171 of file AssemblyElemental.cpp.

◆ mass_Hdiv() [1/3]

void mass_Hdiv	(	Real	coef,
		MatrixElemental &	elmat,
		const CurrentFE &	dualFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the mass matrix in $ H(div, K ) $ with constant real permeability, with $ K $ the current element. In formula

$\mathrm{coef} < u, w > \,,$

for $u, w \in H(div, K)$ and $ coef $ a real scalar.
Weighted Mass matrix with a permeability tensor which is a constant scalar matrix, i.e. $K^{-1} = \mathrm{coef} \, I$ , $\mathrm{coef}$ being the inverse of the permeability.

Attention: It is $\mathrm{coef}$ that is used, and not its inverse.

Parameters

coef	Constant real coefficient.
elmat	Mixed element matrix.
dualFE	Current dual finite element in .
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Note: $\mathrm{coeff}$ is the inverse of the permeability coefficient.

Definition at line 5208 of file AssemblyElemental.cpp.

◆ mass_Hdiv() [2/3]

void mass_Hdiv	(	Matrix const &	Invperm,
		MatrixElemental &	elmat,
		const CurrentFE &	dualFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the mass matrix in $ H(div, K ) $ with constant matrix permeability, with $ K $ the current element. In formula

$< \mathrm{Invperm}\, u, w > \,,$

for $u, w \in H(div, K)$ and $\mathrm{Invperm}$ a real constant matrix.
Weighted mass matrix in $ H(div, K) $ with permeability matrix which is a constant per element symmetric positive definite matrix, non diagonal a priori, and already inverted, with Lapack LU or Choleski for instance.

Parameters

Invperm	Constant coefficient tensor, constant means constant over the current element.
elmat	Mixed element matrix.
dualFE	Current dual finite element in .
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Note: $\mathrm{Invperm}$ is the inverse of the permeability matrix.

Definition at line 5237 of file AssemblyElemental.cpp.

◆ mass_Hdiv() [3/3]

void mass_Hdiv	(	Real(*)(const Real &, const Real &, const Real &)	InvpermFun,
		MatrixElemental &	elmat,
		const CurrentFE &	dualFE,
		int	iblock = `0`,
		int	jblock = `0`
	)

Compute the mass matrix in $ H(div, K ) $ with real function permeability, with $ K $ the current element. In formula

$< \mathrm{InvpermFun}\, u, w > \,,$

for $u, w \in H(div, K)$ and $\mathrm{InvpermFun}$ a real function.
Weighted mass matrix with a permeability that is a scalar function. The inverse function of the permeability should be provided. We note again that it is the inverse of the permeability that is provided directly $\mathrm{InvpermFun} = K^{-1}$ .

Parameters

InvpermFun	Scalar function inverse of the permeability.
elmat	Mixed element matrix.
dualFE	Current dual finite element in .
iblock	Subarray index where to store the integral just computed.
jblock	Subarray index where to store the integral just computed.

Note: $\mathrm{InvpermFun}$ is the inverse of the permeability function.

Definition at line 5277 of file AssemblyElemental.cpp.

◆ source_Hdiv()

void source_Hdiv	(	const Vector &	source,
		VectorElemental &	elvec,
		const CurrentFE &	dualFE,
		int	iblock = `0`
	)

Compute the source vector in $ H(div, K ) $ with constant vector permeability, with $ K $ the current element. In formula

$< g, w > \,,$

for $w \in H(div, K)$ and $ g $ a constant vector.

Parameters

source	constant vector as the source.
elvect	element vector.
dualFE	Current dual finite element in .
iblock	Subarray index where to store the integral just computed.

Definition at line 5315 of file AssemblyElemental.cpp.

◆ weightedMass()

void LifeV::AssemblyElemental::weightedMass	(	MatrixElemental &	localMass,
		const CurrentFE &	massCFE,
		const Real &	coefficient,
		const localVector &	localValues,
		const UInt &	fieldDim
	)

Elementary weighted mass for constant mass coefficient.

This function assembles the local mass matrix when the mass coefficient is constant.

Parameters

localMass	The local matrix to be filled (not cleaned by this function)
massCFE	The currentFE structure already updated for the assembly. It requires phi and wDetJacobian to be accessible.
coefficient	The mass coefficient
fieldDim	The dimension of the FE space (scalar/vectorial)

Definition at line 113 of file AssemblyElemental.hpp.

◆ interpolate()

void LifeV::AssemblyElemental::interpolate	(	localVector &	localValues,
		const CurrentFE &	interpCFE,
		const UInt &	spaceDim,
		const DOF &	betaDof,
		const UInt &	elementID,
		const globalVector &	beta
	)

Interpolation procedure.

Definition at line 185 of file AssemblyElemental.hpp.

◆ interpolateGradient()

void LifeV::AssemblyElemental::interpolateGradient	(	localVector &	localGradient,
		const CurrentFE &	interpCFE,
		const UInt &	spaceDim,
		const DOF &	betaDof,
		const UInt &	elementID,
		const globalVector &	beta
	)

Interpolation of the gradient.

Definition at line 216 of file AssemblyElemental.hpp.

◆ interpolateDivergence()

void LifeV::AssemblyElemental::interpolateDivergence	(	localVector &	localDivergence,
		const CurrentFE &	interpCFE,
		const DOF &	betaDof,
		const UInt &	elementID,
		const globalVector &	beta
	)

Interpolation of the divergence.

Definition at line 249 of file AssemblyElemental.hpp.

◆ massDivW()

void LifeV::AssemblyElemental::massDivW	(	MatrixElemental &	localMass,
		const CurrentFE &	massCFE,
		const Real &	coefficient,
		const localVector &	localValues,
		const UInt &	fieldDim
	)

Definition at line 277 of file AssemblyElemental.hpp.

◆ advection() [2/3]

void LifeV::AssemblyElemental::advection	(	MatrixElemental &	localAdv,
		const CurrentFE &	advCFE,
		const Real &	coefficient,
		const localVector &	localValues,
		const UInt &	fieldDim
	)

Elementary advection u v.

Definition at line 327 of file AssemblyElemental.hpp.

◆ symmetrizedAdvection()

void LifeV::AssemblyElemental::symmetrizedAdvection	(	MatrixElemental &	localAdv,
		const CurrentFE &	advCFE,
		const Real &	coefficient,
		const localTensor &	localGradient,
		const UInt &	fieldDim
	)

Elementary advection, term u v.

Definition at line 385 of file AssemblyElemental.hpp.

◆ advection() [3/3]

void LifeV::AssemblyElemental::advection	(	Real	coef,
		const UsrFct &	beta,
		MatrixElemental &	elmat,
		const CurrentFE &	fe,
		int	iblock,
		int	jblock,
		int	nb,
		Real	t = `0.`
	)

Definition at line 555 of file AssemblyElemental.hpp.

◆ source() [3/5]

void LifeV::AssemblyElemental::source	(	Real	constant,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		Real	t,
		int	iblock
	)

◆ source() [4/5]

void LifeV::AssemblyElemental::source	(	const UsrFct &	fct,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		int	iblock = `0`
	)

source $\int fct \phi_i$

Definition at line 727 of file AssemblyElemental.hpp.

◆ source() [5/5]

void LifeV::AssemblyElemental::source	(	const UsrFct &	fct,
		VectorElemental &	elvec,
		const CurrentFE &	fe,
		Real	t,
		int	iblock = `0`
	)

source $\int fct(t) \phi_i$

Definition at line 749 of file AssemblyElemental.hpp.

Functions

Public typedefs

Operators for classical finite elements

Elementary operations for the interior penalty stabilization

Shape derivative terms for Newton FSI

Mass matrix

Cholesky

Operators for H(div) finite elements

Detailed Description

Typedef Documentation

◆ function_Type

Function Documentation

◆ mass() [1/4]

◆ stiffness()

◆ advectionNewton()

◆ grad() [1/5]

◆ divergence()

◆ stiffStrain()

◆ bodyForces()

◆ mass() [2/4]

◆ mass() [3/4]

◆ mass() [4/4]

◆ stiff_divgrad()

◆ stiff_divgrad_2()

◆ stiff_gradgrad()

◆ stiff_gradgrad_2()

◆ stiff_dergrad_gradbis()

◆ stiff_dergrad_gradbis_Tr()

◆ stiff_dergrad_gradbis_2()

◆ stiff_dergrad_gradbis_Tr_2()

◆ stiff_gradgradTr_gradbis()

◆ stiff_gradgradTr_gradbis_2()

◆ stiff_gradgradTr_gradbis_3()

◆ ipstab_grad() [1/2]

◆ ipstab_grad() [2/2]

◆ ipstab_bgrad()

◆ ipstab_div()

◆ ipstab_bagrad() [1/2]

◆ ipstab_bagrad() [2/2]

◆ stiff() [1/4]

◆ stiff() [2/4]

◆ stiff() [3/4]

◆ stiff() [4/4]

◆ stiff_curl()

◆ stiff_div()

◆ stiff_dergradbis()

◆ stiff_dergrad()

◆ stiff_derdiv()

◆ stiff_strain()

◆ mass_divw() [1/2]

◆ mass_divw() [2/2]

◆ mass_gradu()

◆ stiff_sd()

◆ grad() [2/5]

◆ div()

◆ grad_div()

◆ stab_stokes()

◆ advection() [1/3]

◆ grad() [3/5]

◆ grad_ss()

◆ grad() [4/5]

◆ grad() [5/5]

◆ source() [1/5]

◆ source() [2/5]

◆ source_mass()

◆ source_stiff()

◆ source_divuq()

◆ source_gradpv()

◆ source_fhn()

◆ source_advection()

◆ source_mass1()

◆ source_mass2()

◆ source_mass3()

◆ source_stress()

◆ source_stress2()

◆ source_press() [1/2]

◆ source_press2()

◆ choldc()

◆ cholsl()

◆ source_press() [2/2]