File containing the procedures for the local assembly of the differential operators. More...

#include <boost/numeric/ublas/matrix.hpp>
#include <lifev/core/LifeV.hpp>
#include <lifev/core/array/MatrixElemental.hpp>
#include <lifev/core/array/VectorElemental.hpp>
#include <lifev/core/fem/CurrentFEManifold.hpp>
#include <lifev/core/fem/ReferenceFEHybrid.hpp>
#include <lifev/core/fem/CurrentFE.hpp>
#include <lifev/core/fem/DOF.hpp>

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Namespaces
	LifeV
	Default Physical Solver.

	LifeV::AssemblyElemental

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

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

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...

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...

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	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 (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	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	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...

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...

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...

Public typedefs
typedef boost::numeric::ublas::matrix< Real >	Matrix

typedef boost::numeric::ublas::zero_matrix< Real >	ZeroMatrix

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

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_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_2 (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_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	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)

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

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)

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...

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_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_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_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	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...

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	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)

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

File containing the procedures for the local assembly of the differential operators.

Contributor:: Samuel Quinodoz samue.nosp@m.l.qu.nosp@m.inodo.nosp@m.z@ep.nosp@m.fl.ch Samuel Quinodoz samue.nosp@m.l.qu.nosp@m.inodo.nosp@m.z@ep.nosp@m.fl.ch

To delete: L. 195 : stiff_curl L. 271 : grad_div L. 326 : stab_stokes L. 434 : grad_ss L. 493 : source_fhn L. 617 : choldc L. 618 : cholsl

Definition in file AssemblyElemental.hpp.

Namespaces

Functions

Public typedefs

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