PiolaOperators::Weak Class Reference

Common weak operators using Piola mapped discretizations. More...

#include <PiolaOperators.h>

Static Public Member Functions
static void	Advection (Matrices &EM, const FiniteElement &fe, const Vec3 &AC, const std::array< std::array< int, 3 >, 3 > &idx, double scale=1.0, WeakOperators::ConvectionForm cnvForm=WeakOperators::CONVECTIVE)
	Compute an advection term. More...
static void	Convection (Matrices &EM, const FiniteElement &fe, const Vec3 &U, const Tensor &dUdX, const std::array< std::array< int, 3 >, 3 > &idx, double scale, WeakOperators::ConvectionForm form=WeakOperators::CONVECTIVE)
	Compute a (nonlinear) convection term. More...
static void	Gradient (Matrices &EM, const FiniteElement &fe, std::array< int, 3 > &idx, double scale=1.0)
	Compute a gradient term. More...
static void	ItgConstraint (std::vector< Matrix > &EM, const FiniteElement &fe, const std::array< int, 3 > &idx)
	Compute an integration constraint. More...
static void	Laplacian (Matrices &EM, const FiniteElement &fe, const std::array< std::array< int, 3 >, 3 > &idx, double scale, bool stress)
	Compute a laplacian. More...
static void	Mass (Matrices &EM, const FiniteElement &fe, const std::array< std::array< int, 3 >, 3 > &idx, double scale)
	Compute a mass term. More...
static void	Source (Vectors &EV, const FiniteElement &fe, const Vec3 &f, const std::array< int, 3 > &idx, double scale)
	Compute a vector-source term. More...

Detailed Description

Common weak operators using Piola mapped discretizations.

Member Function Documentation

Advection()

void PiolaOperators::Weak::Advection ( Matrices &  EM, const FiniteElement &  fe, const Vec3 &  AC, const std::array< std::array< int, 3 >, 3 > &  idx, double  scale = 1.0, WeakOperators::ConvectionForm  cnvForm = WeakOperators::CONVECTIVE  )

static

Compute an advection term.

Parameters

[out]	EM	The element matrices to add contribution to
[in]	fe	The finite element to evaluate for
[in]	AC	Advecting field
[in]	idx	Matrix block indices
[in]	scale	Scaling factor for contribution
[in]	cnvForm	Form of advection operator

References PiolaOperators::Copy().

Convection()

void PiolaOperators::Weak::Convection ( Matrices &  EM, const FiniteElement &  fe, const Vec3 &  U, const Tensor &  dUdX, const std::array< std::array< int, 3 >, 3 > &  idx, double  scale, WeakOperators::ConvectionForm  form = WeakOperators::CONVECTIVE  )

static

Compute a (nonlinear) convection term.

Parameters

[out]	EM	The element matrix to add contribution to
[in]	fe	The finite element to evaluate for
[in]	U	Advecting field
[in]	dUdX	Field gradient
[in]	idx	Matrix block indices
[in]	scale	Scaling factor for contribution
[in]	form	Which form of the convective form to use

References PiolaOperators::Copy(), FiniteElement::detJxW, Tensor::dim(), utl::matrix< T >::multiply(), and FiniteElement::P.

Gradient()

void PiolaOperators::Weak::Gradient ( Matrices &  EM, const FiniteElement &  fe, std::array< int, 3 > &  idx, double  scale = 1.0  )

static

Compute a gradient term.

Parameters

[out]	EM	The element matrix to add contribution to
[in]	fe	The finite element to evaluate for
[in]	idx	Matrix block indices
[in]	scale	Scaling factor for contribution

References FiniteElement::basis(), utl::matrix< T >::cols(), FiniteElement::detJxW, FiniteElement::dNdX, FiniteElement::dPdX, utl::matrix< T >::outer_product(), and utl::vector< T >::size().

ItgConstraint()

void PiolaOperators::Weak::ItgConstraint ( std::vector< Matrix > &  EM, const FiniteElement &  fe, const std::array< int, 3 > &  idx  )

static

Compute an integration constraint.

Parameters

[out]	EM	The element matrix to add contribution to
[in]	idx	Matrix block indices
[in]	fe	The finite element to evaluate for

Laplacian()

void PiolaOperators::Weak::Laplacian ( Matrices &  EM, const FiniteElement &  fe, const std::array< std::array< int, 3 >, 3 > &  idx, double  scale, bool  stress  )

static

Compute a laplacian.

Parameters

[out]	EM	The element matrix to add contribution to
[in]	fe	The finite element to evaluate for
[in]	idx	Matrix block indices
[in]	scale	Scaling factor for contribution
[in]	stress	Whether to add extra stress formulation terms

Only the upper blocks are added with the stress formulation

References PiolaOperators::Copy(), FiniteElement::detJxW, FiniteElement::dPdX, and utl::matrix< T >::multiply().

Mass()

void PiolaOperators::Weak::Mass ( Matrices &  EM, const FiniteElement &  fe, const std::array< std::array< int, 3 >, 3 > &  idx, double  scale  )

static

Compute a mass term.

Parameters

[out]	EM	The element matrices to add contribution to
[in]	fe	The finite element to evaluate for
[in]	idx	Matrix block indices
[in]	scale	Scaling factor for contribution

References PiolaOperators::Copy(), FiniteElement::detJxW, M, SystemMatrix::multiply(), and FiniteElement::P.

Source()

void PiolaOperators::Weak::Source ( Vectors &  EV, const FiniteElement &  fe, const Vec3 &  f, const std::array< int, 3 > &  idx, double  scale  )

static

Compute a vector-source term.

Parameters

[out]	EV	The element vectors to add contribution to
[in]	fe	The finite element to evaluate for
[in]	f	Vector with contributions
	idx	Vector block indices
[in]	scale	Scaling factor for contribution

References utl::matrix< T >::cols(), PiolaOperators::Copy(), FiniteElement::detJxW, FiniteElement::dNdX, utl::matrix< T >::multiply(), FiniteElement::P, and Vec3::ptr().

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The documentation for this class was generated from the following files:

• Apps/Common/PiolaOperators.h
• Apps/Common/PiolaOperators.C